PHYSICS -- 2009/10
Physics is about the nature of basic things such as motion,forces, energy,matter,
heat,sound,light & the composition of atoms.
Language of Science: Mathematics
When scientific findings in nature are expressed mathematically, they are easier to verify or to disprove by experiment.
** Science was transformed in the 1600’s when it was learned that nature can be analyzed,
modeled, and described mathematically.
** The equations of science provide compact expressions of relationships between concepts.
Scientific Method: it includes some, if not all, of the following:
1) Recognize a problem.
2) Make an educated guess – a hypothesis – about the answer.
3) Predict the consequences of the hypothesis.
4) Perform experiments to test predictions.
5) Formulate the simplest general rule that organizes the main ingredients: hypothesis, prediction, and experimental outcome.
** Galileo and Bacon are usually credited as the principal founders of the scientific method
** Scientific method is extremely effective in gaining, organizing, and applying new knowledge
Scientific Attitude: If a scientist finds evidence that contradicts a hypothesis, law, or principle, then the hypothesis, law, or principle must be changed or abandoned.
1) FACT – is a close agreement by competent observers who make a series of observations of the same phenomenon.
2) Hypothesis – is an educated guess that is not fully accepted until demonstrated by experiment.
PHYSICS CONCEPT #1: An object in mechanical equilibrium is stable, without changes in motion.
Force:
A force is needed to change an object’s state of motion.
Force is a – push or pull on an object
Net force -- the combination of all forces acting on an object.
Unit of force is the Newton.
______________ is the force of gravity acting downward on an object.
A __________ is an arrow that represents the magnitude and direction of a quantity.
A ___________ ______________ is a quantity that can be described by both magnitude and direction. Force is an example.
A __________ _______________ is a quantity that can be described by magnitude only and has no direction. Time, area, and volume are examples.
Mechanical Equilibrium:
You can express the equilibrium rule mathematically as ΣF = 0
Mechanical equilibrium is a state wherein no physical changes occur; it is a state of steadiness.
Whenever the net force on an object is zero (ΣF = 0), the object is said to be in mechanical equilibrium – this is known as the ________________ rule.
The symbol Σ stands for “the sum of” and F stands for “forces.”
For a suspended object at rest, the forces acting upward on the object must be balanced by other forces acting downward to make the vector sum equal zero.
Support Force:
For an object at rest on a horizontal surface, the support force must equal the object’s weight.
A _____________ ___________ is the upward force that balances the weight of an object on a surface. A support force is often called the _______________ _____________.
An upward support force is ________________ and a downward weight is ________________.
The weight of a book sitting on a table is a negative force that squeezes downward on the atoms of the table. The atoms squeeze upward on the book. The compressed atoms produce the positive support force.
Equilibrium for Moving Objects:
Objects at __________ are said to be in ___________ equilibrium; objects moving at constant speed in a straight-line path are said to be in dynamic equilibrium.
Equilibrium is a state of no ______________. An object under the influence of only one force cannot be in __________________. Only when there is no force at all, or when two or more forces combine to zero, can an object be in _______________________.
Both ___________ and ____________ equilibrium are examples of ______________ equilibrium.
Vectors:
The ______________________ Rule: To find the resultant of two nonparallel vectors, construct a parallelogram wherein the two vectors are adjacent sides. The diagonal of the parallelogram shows the resultant.
The sum of two or more vectors is called their __________________.
Combining vectors is simple when they are parallel. If they are in the same direction, they ______.
If they are in opposite directions, they ____________. To find the resultant of nonparallel vectors, use the ___________________ rule.
When an object is suspended at rest from two non-vertical ropes, there are three forces acting on it: a tension in the left rope, a tension in the right rope, and the object’s weight. The resultant of rope tensions must have the same magnitude as the object’s weight.
PHYSICS CONCEPT #2 -- FORCES CAUSE CHANGES IN MOTION
Galileo on Motion – he argued that only when friction is present—as it usually is – is a force needed to keep an object moving.
** one of Galileo’s greatest contributions to physics was demolishing the notion that a force is necessary to keep an object moving. A force is any push or pull.
** friction is the force that acts between materials that touch as they move past each other.
** Galileo found that a ball rolling on a smooth horizontal plane has almost constant velocity, and if friction were entirely absent, the ball would move forever. Galileo also stated that the tendency of a moving body to keep moving is natural and that every object resists change to its state of motion.
** the property of a body to resist changes to its state of motion is called ________________.
NEWTON’S LAW OF INERTIA-- Newton’s first law – states that every object continues in a state of rest or of uniform speed in a straight line, unless acted on by a nonzero net force.
** forces are needed to overcome any friction that may be present. Forces are also needed to set objects in motion initially.
** once an object is moving in a force-free environment, it will move in a straight line indefinitely.
Measure of Inertia -- the more mass an object has, the greater its inertia and the more force it takes to change its state of motion.
** Mass is the quantity of matter in an object. Mass is a measure of the inertia of an object. Mass is measured in kilograms.
** Weight is the force of gravity on an object. Weight depends on an object’s location. The mass of an object is the same whether the object is located on Earth, on the moon, or in outer space.
** Mass and weight are proportional to each other in a given place. Objects with great mass have great weight; objects with little mass have little weight.
** In most parts of the world, the measure of matter is commonly expressed in units of mass. The SI unit of mass is the kilogram and its symbol is kg.
** The SI unit of force is the Newton. The SI symbol for the Newton is N and is written with a capital letter because it is named after a person.
** Objects within moving vehicles move with the vehicles.
PHYSICS CONCEPT #3 -- You can describe the motion of an object by its position, speed, direction, and acceleration.
Motion is Relative:
** An object is moving if its position relative to a fixed point is changing.
** When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object.
** Unless stated otherwise, when we discuss the speeds of things in our environment, we mean speed with respect to the surface of Earth.
Speed – You can calculate the speed of an object by dividing the distance covered by time.
** Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes.
** Speed is how fast an object is moving.
** Any combination of units for distance and time that are useful and convenient are legitimate for describing speed.
** Some units that describe speed are miles per hour (mi/h) and kilometers per hour (km/h). The slash symbol (/) is read as “per”.
** The speed of an object at any instant is called the instantaneous speed.
** The average speed of an object is the total distance covered divided by the time.
** Average speed does not indicate variations in the speed that may take place during the trip.
** A simple rearrangement of the definition of average speed gives the total distance covered:
Total distance covered = average speed x travel time
Velocity – Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves.
** Velocity is speed in a given direction.
** A quantity such as velocity, which specifies direction as well as magnitude, is called a vector quantity.
** Quantities that require only magnitude for a description are ______________ quantities.
** Constant speed means steady speed.
** Constant velocity means both constant speed and constant direction, which is a straight line.
** If either an object’s speed or its direction (or both) is changing, then the object’s velocity is changing.
Acceleration—you can calculate the acceleration of an object by dividing the change in its velocity by time.
** Acceleration – is the rate at which the velocity is changing
** In Physics, the term acceleration applies to decreases as well as increases in speed.
** Acceleration also applies to change in direction.
** Acceleration is defined as the rate of change in velocity rather than speed.
** Acceleration, like velocity, is a vector quantity because it is directional.
** If an object’s speed, direction, or both, changes, the object changes velocity and accelerates.
** When the direction is not changing, acceleration may be expressed as the rate at which speed changes.
** Since acceleration is the change in velocity or speed per time interval, its units are those of speed per time. m/sec/sec -- which is m/sec2
Free Fall – How Fast? The acceleration of an object in free fall is about 9.8 m/sec2
** Gravity causes objects to accelerate downward once they begin to fall.
** In real life, air resistance affects the acceleration of a falling object.
** An object moving under the influence of the gravitational force only is said to be in _________
__________. Freely falling objects are affected only by gravity.
** The elapsed time is the time that has elapsed, or passed, since the beginning of any motion.
** For free fall, it is customary to use the letter (g) to represent the acceleration because the acceleration is due to gravity.
** Although g varies slightly in different parts of the world, its average value is nearly 9.8 m/s2
** The instantaneous speed of an object falling from rest is equal to the acceleration multiplied by the amount of time it falls(the elapsed time).
** The instantaneous speed (v) of an object falling from rest after an elapsed time (t) can be expressed in equation form as v = gt. Note that the letter (v) symbolizes both speed and velocity.
** At the highest point of a rising object, when the object is changing its direction of motion from upward to downward, its instantaneous speed is zero.
** As an object rises, its speed decreases at the same rate it increases when moving downward—at 9.8 m/sec2
** The instantaneous speed at points of equal elevation in a moving object’s path is the same whether the object is moving upward or downward.
Free Fall – How Far? For each second of free fall, an object falls a greater distance than it did in the previous second.
** The initial speed of the fall is zero and takes a full second to get to 9.8 m/s
** Whenever an object’s initial speed is zero and the acceleration (a) is constant, that is, steady and “non-jerky”, the equations for the velocity and distance traveled are:
v = at d= ½ at2
Graphs of Motion – On a speed-versus-time graph the slope represents speed per time, or acceleration.
** On a speed-versus-time graph, if the line forms a straight line, time and speed are directly proportional to each other.
** The slope of the line is the vertical change divided by the horizontal change for any part of the line.
** On a distance-versus-time graph for a falling object, the relationship is quadratic and the curve is parabolic.
Air Resistance and Falling Objects – Air resistance noticeably slows the motion of things with large surface areas like falling feathers or pieces of paper. But air resistance less noticeably affects the motion of more compact objects like stones and baseballs.
** Air resistance can affect the acceleration of objects outside a vacuum.
** In many cases, however, the effect of air resistance is small enough to be neglected.
** With negligible air resistance, falling objects can be considered to be falling freely.
How Fast, How Far, How Quickly, How Fast Changes – Acceleration is the rate at which velocity itself changes
** When we wish to specify how fast something freely falls from rest after a certain elapsed time, we are talking about speed or velocity. The appropriate equation in these cases is v = gt
** When we wish to specify how far an object has fallen, we are talking about distance. The appropriate equation is these cases is d =1/2 gt2
PHYSICS CONCEPT #4: Projectile motion can be described by the horizontal and vertical components of motion.
Vector and Scalar Quantities: A vector quantity includes both magnitude and direction, but a scalar quantity includes only magnitude.
** Sketches in physics often include arrows, where each arrow represents the magnitude and the direction of a certain quantity.
** Velocity is a vector quantity, as is acceleration.
** Scalars can be added, subtracted, multiplied, and divided like ordinary numbers.
Velocity Vectors: The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.
** An airplane’s velocity is a combination of the velocity of the airplane relative to the air and the velocity of the air relative to the ground ( the wind velocity).
** For two velocity vectors that are perpendicular, the result of adding the two vectors, called the resultant, is the diagonal of the rectangle described by the two vectors.
** To add equal-magnitude vectors, a square is constructed, and the resultant is the diagonal of the square. For any square, the length of the diagonal is √2, or 1.414 times either of its sides.
Components of Vectors – The perpendicular components of a vector are independent of each other.
** two vectors at right angles that add up to a given vector are known as the components of the vector they replace.
** the process of determining the components of a vector is called resolution.
** any vector drawn on a piece of paper can be resolved into vertical and horizontal components that are perpendicular.
Projectile Motion—the horizontal component of motion for a projectile is just like the horizontal motion of a ball rolling freely along a level surface without friction. The vertical component of a projectile’s velocity is like the motion for a freely falling object.
** A cannonball shot from a cannon, a stone thrown into the air, a ball rolling off the edge of a table, a spacecraft circling Earth – all of these are examples of projectiles.
** A projectile is any object that moves through the air or space, acted on only by gravity (and air resistance, if any).
** When no horizontal force acts on a projectile, the horizontal velocity remains constant.
** The horizontal component of motion for a projectile is completely independent of the vertical component of motion.
Projectiles Launched Horizontally – the downward motion of a horizontally launch projectile is the same as that of free fall.
** When projectiles are launched horizontal, gravity acts only downward, so the only acceleration is downward.
** The vertical distance fallen has nothing to do with the horizontal component of motion.
** The path traced by a projectile accelerating only in the vertical direction while moving at constant horizontal velocity is a parabola.
Projectiles Launched at an Angle – the vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 4.9 t2 meters
** the maximum horizontal range for projectiles is attained at a projection angle of 45o
** when the effect of air resistance on a projectile’s motion is significant, the range is diminished and the path is not a true parabola.
** if air resistance is negligible, a projectile hits the ground with the same speed it had originally when it was projected upward from the ground.
PHYSICS CONCEPT #5—An object accelerates when a net force acts on it
Force causes acceleration – unbalanced forces acting on an object cause the object to accelerate.
** the combination of forces acting on an object is the net force; acceleration depends on net force.
** doubling the force on an object doubles its acceleration.
** an object’s acceleration is directly proportional to the net force acting on it.
Mass Resists Acceleration – for a constant force, an increase in the mass will result in a decrease in the acceleration.
** the same force applied to twice as much mass results in only half the acceleration.
** for a given force, the acceleration produced in inversely proportional to the mass. Inversely means that the two values change in opposite directions.
Newton’s Second Law – states that the acceleration produced by a net force on a object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
** Newton’s second law – describes the relationship among an object’s mass, an object’s acceleration, and the net force on an object.
** In equation form, Newton’s second law is written as follows:
Acceleration = net force/ mass or a = F/m
** acceleration is equal to the net force divided by the mass
Friction – the force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.
** friction acts on materials that are in contact with each other, and it always acts in a direction to oppose relative motion.
** liquids and gases are called fluids because they flow. Fluid friction occurs when an object moves through a fluid.
** Air resistance is the friction acting on something moving through air.
** A diagram showing all of the forces acting on an object is called a free-body diagram.
Applying Force – Pressure -- for a constant force, an increase in the area of contact will result in a decrease in the pressure.
** Pressure is the amount of force per unit of area.
** In equation form, pressure is defined as follows:
Pressure = force/area of application or P = F/A
** Pressure is measured in newtons per square meter, or pascals (Pa). One newton per square meter is equal to one pascal.
** The smaller the area supporting a given force, the greater the pressure on that surface.
Free Fall Explained -- all freely falling objects fall with the same acceleration because the net force on an object is only its weight, and the ratio of weight to mass is the same for all objects.
** A 10-kg cannonball and a 1-kg stone dropped from an elevated position at the same time will fall together and strike the ground at practically the same time.
** Since mass and weight are proportional, a 10-kg cannonball experiences 10 times as much gravitational force as a 1-kg stone.
Falling and Air Resistance – the air resistance force an object experiences depends on the object’s speed and area.
** the force due to air resistance diminishes the net force acting on falling objects
** Terminal speed – is the speed at which the acceleration of a falling object is zero because friction balances the weight.
** Terminal velocity – is terminal speed together with the direction of motion
PHYSICS CONCEPT #6: For every force, there is an equal and opposite force.
Forces and Interactions – a force is always part of a mutual action that involves another force.
** A mutual action is an interaction between one thing and another.
** An example of interaction occurs when a hammer exerts a force on a nail, and the nail exerts a force on the hammer.
Newton’s Third Law – states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
** Newton’s third law – describes the relationship between two forces in an interaction. Newton’s third law is often stated: “ To every action there is always an equal and opposing reaction.”
** In an interaction, one force is called the action force. The other force is called the reaction force. The action and reaction forces are equal in strength and opposite in direction.
** When you walk on a floor, you push against the floor, and the floor simultaneously pushes against you.
Identifying Action and Reaction – to identify a pair of action-reaction forces, first identify the interacting objects A and B, and if the action is A on B, the reaction is B on A.
** When a boulder falls to Earth, the action is Earth exerting a force on the boulder, and the reaction is the boulder simultaneously exerting a force on Earth.
** A rocket accelerates because the rocket pushes exhaust gas and the exhaust gas pushes on the rocket.
Action and Reaction on Different Masses – a given force exerted on a small mass produces a greater acceleration than the same force exerted on a large mass.
** recall that Newton’s second law states that acceleration is proportional to the net force and inversely proportional to the mass.
** when a boulder falls toward Earth, Earth also moves toward the boulder. Because Earth has a huge mass, its acceleration toward the boulder is infinitesimally small. A rocker accelerates because it continually recoils from the exhaust gases ejected from its engine.
PHYSICS CONCEPT #7 – momentum is conserved for all collisions as long as external forces don’t interfere.
Momentum – a moving object can have a large momentum if it has a large mass, a high speed, or both.
** Momentum is the mass of the object multiplied by its velocity.
** A moving truck has more momentum than a car moving at the same speed because the truck has more mass.
** A fast car can have more momentum than a slow truck.
** A truck at rest has no momentum at all.
Impulse Changes Momentum – the change in momentum depends on the force that acts and the length of time it acts.
** The quantity force x time interval is called impulse. In short-hand notation, impulse = F ∆t
** The greater the impulse exerted on something, the greater will be the change in momentum. The exact relationship is impulse = change in momentum or Ft = ∆(mv)
** To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swings.
** In the case of decreasing momentum, a longer contact time reduces the force and decreases the resulting deceleration. A padded dashboard in a car is safer than a rigid, metal one because the padded dashboard increases the time of contact.
Bouncing – the impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop.
** it take a greater impulse to catch a flower pot and throw it back up than merely to catch it.
** A karate expert strikes the bricks in such a way that her hand is made to bounce back, yielding as much as twice the impulse to the bricks.
Conservation of Momentum – law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged.
** the law of conservation of momentum describes the momentum of a system
** if the system undergoes changes wherein all forces are internal – for example, in atomic nuclei undergoing radioactive decay, cars colliding, or stars exploding—the net momentum of the system before and after the event is the same.
** the momentum before firing a cannon is zero. After firing, the momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.
Collisions – whenever objects collide in the absence of external forces, the net momentum of both objects before the collision equals the net momentum of both objects after the collision.
** when objects collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision.
** Colliding objects bounce perfectly in perfect elastic collisions.
** A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision.
** Whenever colliding objects become tangled or couple together, a totally inelastic collision occurs.
** Perfectly elastic collisions are not common in the everyday world. At the microscopic level, however, perfectly elastic collisions are commonplace. For example, electrically charged particles bounce off one another without generating heat.
Momentum Vectors – the vector sum of momenta is the same before and after a collision.
** momentum is conserved even when the interacting objects don’t move along the same straight line.
** The momentum of a car wreck is equal to the vector sum of the momenta of each of the cars before the collision.
** when a firecracker bursts, the vector sum of the momenta of its fragments adds up to the firecracker’s momentum just before bursting.
PHYSICS CONCEPT #8 – Energy can change from one form to another without a net loss or gain
Work – work is done when a force acts on an object and the object moves in the direction of the force.
** Work is the product of the force on an object and the distance through which the object is moved.
** in the simplest case, when the force is constant, the motion takes place in a straight line in the direction of the force: work = force x distance In equation form, W = Fd
** Work generally falls into two categories: work done against another force and work done to change the speed of an object. In both categories, work involves a transfer of energy between something and its surroundings.
The unit of work is the Newton-meter (N-m), also called the joule. One joule (J) of work is done when a force of 1N is exerted over a distance of 1 m.
Power -- power equals the amount of work done divided by the time interval during which the work is done.
** Power is the rate at which work is done: power = work done/ time interval
** a high-power engine does work rapidly. If an engine has twice the power of another engine, this means that it can do twice the work in the same amount of time or the same amount of work in half the time.
** The unit of power is the joule per second, which is also known as the watt. One watt (W) of power is expended when one joule of work is done in one second.
** In the US, we customarily rate engines in units of horsepower and electricity in kilowatts, but either may be used. One horsepower (hp) is the same as 0.75 kW.
Mechanical Energy – the two forms of mechanical energy are kinetic energy and potential energy.
** The property of an object or system that enables it to do work is energy.
** Like work, energy is measured in joules.
** Mechanical energy is the energy due to the position of something or the movement of something.
Potential Energy – three examples of potential energy are elastic potential energy, chemical energy, and gravitational potential energy.
** Energy that is stored and held in readiness is called potential energy. (PE) because in the stored state it has the potential for doing work.
** A stretched or compressed spring, a bow that is drawn back, and a stretched rubber band have elastic potential energy.
** The chemical energy in fuels is potential energy at the submicroscopic level. This energy is available when a chemical change in the fuels takes place.
** The potential energy due to the elevated position of an object is gravitational potential energy.
** The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it. Gravitational potential energy = weight x height. In equation form, PE = mgh The height in this equation is the distance above some chosen reference level.
Kinetic Energy – the kinetic energy of a moving object is equal to the work required to bring it to its speed from rest, or the work the object can do while being brought to rest.
** The energy of motion is kinetic energy (KE)
** The kinetic energy of an object is equal to half the object’s mass multiplied by the square of its speed. In equation form, this is KE = ½ mv2
** The net force on an object multiplied by the distance along which the force acts equals the object’s kinetic energy. In equation form, this is Fd = ½ mv2
Work-Energy Theorem – states that whenever work is done, energy changes
** The work-energy theorem describes the relationship between work and energy.
** Work equals change in kinetic energy. In equation form, Work = ∆KE, where the delta symbol,∆, means “change in”. The work in this equation is the net work.
** if you push a box across a floor at a constant speed, you are pushing just hard enough to overcome friction. In this example, the net force and net work are zero, and KE = 0.
** Kinetic energy often appears hidden in different forms of energy. Random molecular motion is sensed as heat. Sound consists of molecules vibrating in rhythmic patterns. Light energy originates in the motion of electrons in atoms. Electrons in motion make electric currents.
Conservation of Energy – the law of conservation of energy states that energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.
** The study of the various forms of energy and the transformations from one form into another is the law of conservation of energy.
** Everywhere along, the path of a pendulum bob, the sum of potential energy and kinetic energy is the same. At the highest points, the energy is only potential energy. At the lowest point, the energy is only kinetic energy.
** The sun shines because some of its nuclear energy is transformed into radiant energy. In nuclear reactors, nuclear energy is transformed into heat.
** Some electric-generating plants transform the energy of falling water into electrical energy. Electrical energy then travels through wires to homes.
Machines – transfer energy from one place to another or transforms it from one form to another.
** A machine is a device used to multiply forces or to change the direction of forces. A machine cannot put out more energy than is put into it.
** A lever is a simple machine made of a bar that turns about a fixed point.
** If heat from friction is negligible, the work put into a machine equals the work put out by the machine: work input = work output (force x distance)input = (force x distance) output
** The pivot point of a lever is the fulcrum.
** The ratio of output force to input force for a machine is called the mechanical advantage.
** A type 1 lever has the fulcrum between the input force and the load. If the fulcrum is closer to the load, a small input force exerted through a large distance produces a larger output force over a shorter distance. The directions of input and output are opposite.
** For a type 2 lever, the load is between the fulcrum and the input force. Force is increased at the expense of distance. Input and output forces have the same direction.
** In a type 3 lever, the fulcrum is at one end and the load is at the other. The input force is applied between them. The input and output forces have the same direction.
** A pulley is a kind of lever that can be used to change the direction of a force.
** A single pulley with a fixed axis behaves like a type 1 lever. A single pulley with an axis that moves behaves like a type 2 lever.
** A system of pulleys multiplies the force and it may change the direction of the force. The mechanical advantage for a simple pulley system is the same as the number of strands of rope that actually support the load.
Efficiency – in any machine, some energy is transformed into atomic or molecular kinetic energy- making the machine warmer.
** The efficiency of a machine is the ratio of useful energy output to total energy input, or the percentage of the work input that is converted to work output. No real machine can be 100% efficient. The wasted energy is dissipated as heat.
** An inclined plane is a machine. Its theoretical mechanical advantage, assuming negligible friction, is the length of the incline divided by the height of the inclined plane.
** Efficiency can also be expressed as the ration of actual mechanical advantage to the theoretical mechanical advantage.
** To convert efficiency to percent, express it as a decimal and multiply by 100%.
Energy for Life – there is more energy stored in the molecules in food than there is in the reaction products after the food is metabolized. This energy difference sustains life.
** most living organisms on this planet feed on various hydrocarbon compounds that release energy when they react with oxygen. In metabolism of food in the body, carbon combines with oxygen to form carbon dioxide.
** Only green plants and certain one-celled organisms can make carbon dioxide combine with water to produce hydrocarbon compounds such as sugar. This process is called photosynthesis and requires an energy input, which normally comes from sunlight.
Sources of Energy—The sun is the source of practically all our energy on Earth.
** Sunlight is directly transformed into electricity by photovoltaic cells or in the flexible solar shingles on the roofs of buildings. We use the energy in sunlight to generate electricity indirectly as well.
** Wind, caused by unequal warming of Earth’s surface, is another form of solar power. Wind can be used to turn generator turbines within specially equipped windmills.
** Hydrogen is the least polluting of all fuels. Because it takes energy to make hydrogen (to extract it from water and carbon compounds), it is not a source of energy. In a fuel cell, hydrogen and oxygen gas are compressed at electrodes to produce water and electric current.
** The most concentrated form of usable energy is stored in nuclear fuels.
** Earth’s interior is kept hot by producing a form of nuclear power, radioactivity.
** Geothermal energy is held in underground reservoirs of hot water.
PHYSICS CONCEPT #9 —Centripetal force keeps an object in circular motion
Rotation and Revolution – two types of circular motion are rotation and revolution
** An axis is the straight line around which rotation takes place.
** When an object turns about an internal axis – that is, an axis located within the body of the object – the motion is called rotation, or spin. A Ferris wheel rotates about an axis.
** When an object turns about an external axis, the motion is called revolution. Riders revolve about the axis of a Ferris wheel.
** Earth undergoes both types of circular motion. It revolves around the sun once every 365 ¼ days, and it rotates around an axis passing through its geographical poles once every 24 hours.
Rotational Speed – tangential speed depends on rotational speed and the distance from the axis of rotation.
** Linear speed is the distance traveled per unit time. The linear speed is greater on the outer edge of a rotating object, such as a merry-go-round, than it is closer to the axis.
** Tangential speed is the speed of something moving along a circular path. For circular motion, the terms linear speed and tangential speed are interchangeable.
** Rotational speed, which is sometimes called angular speed, is the number of rotations per unit of time. All parts of a merry-go-round have the same rotational speed.
** Tangential speed and rotational speed are related.
Tangential speed ~ radial distance x rotational speed
v ~ rw
** As you move away from the axis of a rotating platform, your tangential speed increases while your rotational speed stays the same.
** Wheels of a train stay on the track because their rims are slightly tapered. So when a train rounds a curve, wheels on the outer track ride on the wider part of the tapered rims (and cover a greater distance in the same time) while opposite wheels ride on their narrow parts (covering a smaller distance in the same time)
Centripetal Force – the centripetal force on an object depends on the object’s tangential speed, its mass, and the radius of its circular path.
** Any object moving in a circle undergoes an acceleration that is directed to the center of the circle. This is centripetal acceleration. Centripetal means “toward the center”.
** The force directed toward a fixed center that causes an object to follow a circular path is called centripetal force.
** Centripetal forces can be exerted in a variety of ways. Anything that moves in a circular path is acted on by a centripetal force.
** Centripetal force can be calculated using the following equation:
Centripetal force = mass x speed 2 / radius of curvature
Fc = mv2/r
** Centripetal force Fc is measured in newtons when mass m is expressed in kilograms, speed v in m/s, and radius of curvature r in meters.
** The centripetal force acting on a circularly moving object is the net force that acts exactly along the radial direction – toward the center of the circular path.
Centripetal and Centrifugal Forces -- The “centrifugal-force effect” is attributed not to any real force but to inertia – the tendency of the moving body to follow a straight-line path.
** The apparent outward force on a rotating or revolving body is called centrifugal force. Centrifugal means “center-fleeing,” or “away from the center.”
** If you are in a car that rounds a sharp corner to the left, you tend to pitch outward against the right door. This happens not because of some outward or centrifugal force, but because there is no centripetal force holding you in a circular motion.
** Likewise, the only force exerted on a whirling can at the end of a string is centripetal force. No outward force acts on the can.
Centrifugal Force in a Rotating Reference Frame—Centrifugal force is an effect of rotation. It is not part of an interaction and therefore it cannot be a true force.
** Because centrifugal force is merely an effect of rotation, it is not a true force like gravitational, electromagnetic, and nuclear forces.
** Physicists refer to centrifugal force as a “fictitious force.”
** To observers in a rotating system, however, centrifugal force is very real.
PHYSICS CONCEPT #10: An object will remain upright if its center of mass is above the area of support.
Torque – to make an object turn or rotate, apply a torque.
** Torque is produced by a turning force and tends to produce rotational acceleration.
** Force and torque are different; forces tend to make things accelerate whereas torques produce rotation.
** A torque is produced when a force is applied with “leverage.” You use leverage when you use a screwdriver to open the lid of a paint can.
** The lever arm is the distance from the turning axis to the point of contact.
** Torque can be calculated using the following equation: torque = force 1 x lever arm
Balanced Torques -- when balanced torques act on an object, there is no change in rotation.
** Children of unequal weight can balance on a seesaw by sitting at different distances from the pivot point.
** Scales balances with sliding weights are based on balanced torques.
Center of Mass – the center of mass of an object is the point located at the object’s average position of mass.
** The point where all of the mass of an object can be considered concentrated is called the center of mass.
** For a symmetrical object, the center of mass is at the geometric center of the object. For irregularly shaped objects, the location of the center of mass varies.
** Spin can be applied to an object by applying a force that does not pass through the object’s center of mass. Kicking a football in the middle, for example, will make it travel without rotating.
Kicking the football above or below its center will make it rotate.
Center of Gravity – for everyday objects, the center of gravity is the same as the center of mass
** The center of gravity, or CG, is the average position of all of the particles of weight that make up an object. For most objects on and near Earth, the terms center of mass and center of gravity are interchangeable.
** If you throw a wrench so that it rotates as it moves through the air, you’ll see it wobble about its CG. The center of gravity itself would follow a parabolic path.
** An object’s CG is its balance point; supporting the CG supports the entire object. A meter stick can be balanced by applying a force at its geometric midpoint – the location of its CG.
** Any object suspended at a single point will hang with its CG directly below the point of suspension.
Torque and Center of Gravity – if the center of gravity of an object is above the area of support, the object will remain upright.
** If the CG extends outside the area of support, an unbalanced torque exists, and the object will topple.
** The Leaning Tower of Pisa does not topple because its CG does not extend beyond its base.
** It is difficult to balance a broom upright in the palm of your hand because the support base is small and far beneath the CG.
Center of Gravity of People – the center of gravity of a person is not located in a fixed place, but depends on body orientation.
** When you stand erect with your arms at your sides, your CG is within your body.
** The CG us slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.
** Raising your arms vertically over your head raises your CG by several centimeters.
** When you stand, your CG is somewhere above your support base, which is the area bounded by your feet.
Stability – when an object is toppled, the center of gravity of that object is raised, lowered, or unchanged.
** An object balanced so that any displacement lowers its center of mass is in unstable equilibrium.
** An object balanced so that any displacement raises its center of mass is in stable equilibrium. Raising the CG of an object in stable equilibrium requires increasing the object’s potential energy, which requires work.
** An object balanced so that any small movement neither raises nor lowers its center of gravity is in neutral equilibrium.
** An object with a low CG is usually more stable than an object with a relatively high CG.
PHYSICS CONCEPT #11 – Rotating objects tend to keep rotating while nonrotating objects tend to remain nonrotating.
Rotational Inertia – the greater the rotational inertia, the more difficult it is to change the rotational speed of an object.
** The resistance of an object to change in its rotational motion is called rotational inertia, or moment of inertia.
** A torque is required to change the rotational state of motion of an object.
** Rotational inertia depends on mass and how the mass is distributed. The greater the distance between an object’s mass concentration and the axis of rotation, the greater the rotational inertia.
** A short pendulum has less rotational inertia and therefore swings back and forth more frequently than a long pendulum. Likewise, bent legs swing back and forth more easily than outstretched legs.
** Formulas to calculate rotational inertia for different objects vary and depend on the shape of an object and the location of the rotational axis.
Rotational Inertia and Gymnastics – The three principal axes of rotation in the human body are the longitudinal axis, the transverse axis, and the medial axes.
** The three axes of rotation in the human body are at right angles to one another. All three axes pass through the center of gravity of the body.
** The vertical axis that passes from the head to toe is the longitudinal axis. Rotational inertia about this axis is increased by extending a leg or the arms.
** You rotate about your transverse axis when you perform a somersault or a flip. Tucking in your arms and legs reduces your rotational inertia about the transverse axis; straightening your arms and legs increases your rotational inertia about this axis.
** The third axis of rotation for the human body is the front-to-back axis, or medial axis. You rotate about the medial axis when executing a cartwheel.
Rotational Inertia and Rolling – Objects of the same shape but different sizes accelerate equally when rolled down an incline.
** An object with a greater rotational inertia takes more time to get rolling than an object with a smaller rotational inertia. A hollow cylinder, for example, rolls down an incline much slower than a solid cylinder.
** All objects of the same shape roll down an incline with the same acceleration, even if their masses are different.
Angular Momentum – Newton’s first law of inertia for rotating systems states that an object or system of objects will maintain its angular momentum unless acted upon by an unbalanced external torque.
** All moving objects have momentum.
** Linear momentum is the product of the mass and velocity of an object.
** Rotating objects have angular momentum. Angular momentum is the product of rotational inertia, I , and rotational velocity, w.
angular momentum = rotational inertia x rotational velocity
angular momentum = I x w
** When a direction is assigned to rotational speed, it is called rotational velocity.
** When an object is small compared with the radial distance to its axis of rotation, its angular momentum is equal to the magnitude of its linear momentum, mv , multiplied by the radial distance, r.
angular momentum = mvr
** A moving bicycle is easier to balance than a bicycle at rest because of the angular momentum provided by the spinning wheels.
Conservation of Angular Momentum – it is conserved when no external torque acts on an object.
** The law of conservation of angular momentum states that if no unbalanced external torque acts on a rotating system, the angular momentum of the system is constant.
** A person who spins with arms extended obtains greater rotational speed when the arms are drawn in. In other words, whenever a rotating body contracts, its rotational speed increases.
** Zero-angular-momentum twists and turns are performed by turning one part of the body against the other.
Simulated Gravity – from within a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.
** Occupants in today’s space vehicles feel weightless because they lack a support force. Future space habitats will probably spin, effectively supplying a support force that simulates gravity.
** We experience 1 g on Earth’s surface due to gravity. Small-diameter space structures would have to rotate at high speeds to provide a simulated gravitational acceleration of 1 g.
PHYSICS CONCEPT #12 – Everything pulls on everything else.
The Falling Apple -- Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree – they are both pulled by Earth’s gravity.
** Newton understood the concept of inertia, that without an outside force, moving objects continue to move at constant speed in a straight line. He knew that if an object undergoes a change in speed or direction, then a force is responsible.
The Falling Moon – the moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.
** Newton reasoned that the moon must be falling around Earth. The moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it. He hypothesized that the moon was a projectile circling Earth under the attraction of gravity.
** Newton compared the motion of the moon to a cannonball fired from the top of a high mountain. If the cannonball were fired with enough speed, its path would become a circle and the cannonball would circle indefinitely.
** both the orbiting cannonball and the moon have a component of velocity parallel to Earth’s surface. This sideways or tangential velocity is sufficient to ensure nearly circular motion around Earth rather than into it.
** Newton reasoned that the mass of the moon should not affect how it falls, just as mass has no effect on the acceleration of freely falling objects on Earth. How far the moon falls should relate only to its distance from Earth’s center.
The Falling Earth – Newton’s theory of gravity confirmed the Copernican theory of the solar system.
** The planets don’t crash into the sun because they have tangential velocities. If the tangential velocities of the planets were reduced to zero, their motion would be straight toward the sun and they would indeed crash into it. Any objects in the solar system with insufficient tangential velocities have long ago crashed into the sun.
Newton’s Law of Universal Gravitation – gravity in universal, everything pulls on everything else in a way that involves only mass and distance.
** Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.
** The law of universal gravitation can be expressed in equation form:
F = G (m1m2/d2), where m1 and m2 are the objects’ masses, and d is the distance between their centers of mass.
** The universal gravitational constant, G, in the equation describes the strength of gravity. In scientific notation, G = 6.67 x 10-11 N-m2/kg2 . The value of G tells us that the force of gravity is a very weak force. It is the weakest of the presently known four fundamental forces.
Gravity and Distance: The Inverse-Square Law – gravity decreases according to the inverse square law. The force of gravity weakens as the square of distance.
** When a quantity varies as the inverse square of its distance from its source, it follows and inverse-square law. For example, the inverse square of 3 is (1/3)2 or 1/9
** This law applies to all cases where the effect from a localized source spreads evenly throughout the surrounding space, such as the weakening of gravity with distance. Other examples are light, radiation, and sound.
Gravitational Field – Earth can be thought of as being surrounded by a gravitational field that interacts with objects and causes them to experience gravitational forces.
** A gravitational field occupies the space surrounding a massive body. A gravitational field is an example of a force field, for any mass in the field space experiences a force.
** Iron filings sprinkled over a sheet of paper on top of a magnet reveal the shape of the magnet’s
magnetic field. The pattern of filings shows the strength and direction of the magnetic field at different locations around the magnet. Earth is a giant magnet and, like all magnets, is surrounded by a magnetic field.
** The strength of Earth’s gravitational field, like the strength of its force on objects, follows the inverse-square law. Earth’s gravitational field is strongest near Earth’s surface and weaker at greater distances from Earth.
Gravitational Field Inside a Planet – the gravitational field of Earth at its center is zero.
** The gravitational field of Earth exists inside Earth as well as outside.
** If you traveled through an imaginary hole drilled completely through Earth, you’d gain speed as you fell from the North Pole toward the center of Earth, and lose speed moving away from the center toward the South Pole.
Weight and Weightlessness – pressure against Earth is the sensation we interpret as weight.
** The force of gravity, like any force, causes acceleration. Because we are almost always in contact with Earth, we think of gravity primarily as something that presses us against Earth rather than something that accelerates us.
** If you stand on a scale, gravity pulls you against the supporting floor and scale, and the floor and scale push upward on you. This pair of forces compresses a spring-like gauge inside the scale. The weight reading on the scale is linked to the amount of compression.
** Weightlessness is not the absence of gravity; rather, it is the absence of a support force. Astronauts in orbit are without a support force and experience weightlessness.
Ocean Tides – Newton showed that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of Earth.
** The moon’s gravitational attraction is stronger on Earth’s oceans closer to the moon, and weaker on the oceans farther from the moon. This difference causes the oceans to bulge out on opposite sides of Earth. Because Earth spins, a fixed point on Earth passes beneath both bulges each day, producing two high tides and two low tides.
** A spring tide is a high or low tide that occurs when the sun, Earth, and moon are all lined up.
The tides due to the sun and the moon coincide, making high tides higher than average and low tides lower than average. Spring tides occur during a new or full moon.
** A neap tide occurs when the moon is halfway between a new moon and a full moon. The pulls of the moon and sun are perpendicular to each other. As a result, the solar and lunar tides do not overlap, so the high tides are not as high and low tides are not as low.
Black Holes – when a massive star collapses into a black hole, there is no change in the gravitational field at any point beyond the original radius of the star.
** Two main processes occur continuously in stars like our sun: gravitation, which tends to pull solar material inward, and thermonuclear fusion, which blows material outward.
** If the fusion rate increases, the sun will get hotter and bigger; if the fusion rate decreases, the sun will get cooler and smaller.
** When the sun runs out of fusion fuel (hydrogen), gravitation will dominate and the sun will start to collapse. The collapse will cause helium to fuse into carbon, and the sun will expand into a red giant. When the helium is used up, the sun will collapse into a black dwarf.
** For stars more massive than the sun, once thermonuclear fusion ends, gravitational collapse will take over, eventually forming a black hole. The density of a black hole is so great that its enormous gravitational field prevents even light from escaping. The gravitational field beyond the original radius of the star is no different after the collapse than before.
Universal Gravitation – The formulation of the law of universal gravitation is one of the major reasons for the success in science that followed, for it provided hope that other phenomena of the world might also be described by equally simple and universal laws.
** Earth is round because of gravitation. Earth attracted itself together before it became solid. Any “corners” of Earth have been pulled in so that Earth is a giant sphere.
** The solar system began when a slightly rotating ball of interstellar gas contracted due to mutual gravitation. To conserve angular momentum, the rotational speed of the ball of gas increased, causing the particles to sweep out into a disk shape.
** The deviation of an orbiting object from its path around a center of force caused by the action of an additional center of force is called a perturbation.
** The planet Neptune was discovered when a perturbation in the orbit of Uranus led scientists to conclude that a disturbing body beyond the orbit of Uranus was the culprit.
** According to current scientific understanding, the universe originated and grew from the explosion of a primordial fireball some 13.7 billon years ago. This is the “Big Bang” theory of the origin of the universe. All the matter of the universe was hurled outward from this event and continues in an outward expansion.
** More recent evidence suggests the universe is not only expanding, but accelerating outward. It is pushed by an antigravity dark energy that makes up an estimated 73 percent of the universe. Twenty-three percent of the universe is composed of the yet-to-be discovered particles of exotic dark matter. Ordinary matter makes up only 4 percent.
Physics Concept #13 -- The path of an Earth satellite follows the curvature of Earth.
Earth Satellites -- A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time of 1 second it takes to fall 4.9 m, will orbit the earth.
** An Earth satellite is a projectile moving fast enough to fall continually around Earth rather than into it.
** A geometric fact about the curvature of Earth is that its surface drops a vertical distance of nearly 5 meters for every 8000 meters tangent to its surface.
** The orbital speed for close orbit about Earth is 8 km/s (29,000 km/h or 18,000 mi/h)
** A satellite must stay about 150 kilometers or more above Earth’s surface to keep from burning due to the friction of the atmosphere.
Circular Orbits -- A satellite in circular orbit around Earth is always moving perpendicularly to gravity and parallel to Earth’s surface at constant speed.
** In circular orbit the speed of a circling satellite is not changed by gravity.
**
PHYSICS -- 2009/10
Physics is about the nature of basic things such as __________ , ____________, ____________,
_____________, ___________, _____________, _____________& _________________________.
Language of Science: Mathematics
When scientific findings in nature are expressed mathematically, they are easier to verify or to disprove by experiment.
** Science was transformed in the 1600’s when it was learned that nature can be analyzed,
modeled, and described mathematically.
** The equations of science provide compact expressions of relationships between concepts.
Scientific Method: it includes some, if not all, of the following:
1) Recognize a problem.
2) Make an educated guess – a hypothesis – about the answer.
3) Predict the consequences of the hypothesis.
4) Perform experiments to test predictions.
5) Formulate the simplest general rule that organizes the main ingredients: hypothesis, prediction, and experimental outcome.
** Galileo and Bacon are usually credited as the principal founders of the scientific method
** Scientific method is extremely effective in gaining, organizing, and applying new
knowledge
Scientific Attitude: If a scientist finds evidence that contradicts a hypothesis, law, or principle,
then the hypothesis, law, or principle must be changed or abandoned.
1) FACT – is a close agreement by competent observers who make a series of observations of
the same phenomenon.
2) Hypothesis – is an educated guess that is not fully accepted until demonstrated by
experiment.
PHYSICS CONCEPT #1: An object in mechanical equilibrium is stable, without changes in motion.
Force:
A force is needed to change an object’s state of motion.
Force is a –
Net force --
Unit of force is the _____________.
______________ is the force of gravity acting downward on an object.
A __________ is an arrow that represents the magnitude and direction of a quantity.
A ___________ ______________ is a quantity that can be described by both magnitude and direction. Force is an example.
A __________ _______________ is a quantity that can be described by magnitude only and has no direction. Time, area, and volume are examples.
Mechanical Equilibrium:
You can express the equilibrium rule mathematically as ΣF = 0
Mechanical equilibrium is a state wherein no physical changes occur; it is a state of steadiness.
Whenever the net force on an object is zero (ΣF = 0), the object is said to be in mechanical equilibrium – this is known as the ________________ rule.
The symbol Σ stands for “the sum of” and F stands for “forces.”
For a suspended object at rest, the forces acting upward on the object must be balanced by other forces acting downward to make the vector sum equal zero.
Support Force:
For an object at rest on a horizontal surface, the support force must equal the object’s weight.
A _____________ ___________ is the upward force that balances the weight of an object on a surface. A support force is often called the _______________ _____________.
An upward support force is ________________ and a downward weight is ________________.
The weight of a book sitting on a table is a negative force that squeezes downward on the atoms of the table. The atoms squeeze upward on the book. The compressed atoms produce the positive support force.
Equilibrium for Moving Objects:
Objects at __________ are said to be in ___________ equilibrium; objects moving at constant speed in a straight-line path are said to be in dynamic equilibrium.
Equilibrium is a state of no ______________. An object under the influence of only one force cannot be in __________________. Only when there is no force at all, or when two or more forces combine to zero, can an object be in _______________________.
Both ___________ and ____________ equilibrium are examples of ______________ equilibrium.
Vectors:
The ______________________ Rule: To find the resultant of two nonparallel vectors, construct a parallelogram wherein the two vectors are adjacent sides. The diagonal of the parallelogram shows the resultant.
The sum of two or more vectors is called their __________________.
Combining vectors is simple when they are parallel. If they are in the same direction, they ______.
If they are in opposite directions, they ____________. To find the resultant of nonparallel vectors, use the ___________________ rule.
When an object is suspended at rest from two non-vertical ropes, there are three forces acting on it: a tension in the left rope, a tension in the right rope, and the object’s weight. The resultant of rope tensions must have the same magnitude as the object’s weight.
PHYSICS CONCEPT #2 -- FORCES CAUSE CHANGES IN MOTION
Galileo on Motion – he argued that only when friction is present—as it usually is – is a force needed to keep an object moving.
** one of Galileo’s greatest contributions to physics was demolishing the notion that a force is necessary to keep an object moving. A force is any push or pull.
** friction is the force that acts between materials that touch as they move past each other.
** Galileo found that a ball rolling on a smooth horizontal plane has almost constant velocity, and if friction were entirely absent, the ball would move forever. Galileo also stated that the tendency of a moving body to keep moving is natural and that every object resists change to its state of motion.
** the property of a body to resist changes to its state of motion is called ________________.
NEWTON’S LAW OF INERTIA-- Newton’s first law – states that every object continues in a state of rest or of uniform speed in a straight line, unless acted on by a nonzero net force.
** forces are needed to overcome any friction that may be present. Forces are also needed to set objects in motion initially.
** once an object is moving in a force-free environment, it will move in a straight line indefinitely.
Measure of Inertia -- the more mass an object has, the greater its inertia and the more force it takes to change its state of motion.
** Mass is the quantity of matter in an object. Mass is a measure of the inertia of an object. Mass is measured in kilograms.
** Weight is the force of gravity on an object. Weight depends on an object’s location. The mass of an object is the same whether the object is located on Earth, on the moon, or in outer space.
** Mass and weight are proportional to each other in a given place. Objects with great mass have great weight; objects with little mass have little weight.
** In most parts of the world, the measure of matter is commonly expressed in units of mass. The SI unit of mass is the kilogram and its symbol is kg.
** The SI unit of force is the Newton. The SI symbol for the Newton is N and is written with a capital letter because it is named after a person.
** Objects within moving vehicles move with the vehicles.
PHYSICS CONCEPT #3 -- You can describe the motion of an object by its position, speed, direction, and acceleration.
Motion is Relative:
** An object is moving if its position relative to a fixed point is changing.
** When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object.
** Unless stated otherwise, when we discuss the speeds of things in our environment, we mean speed with respect to the surface of Earth.
Speed – You can calculate the speed of an object by dividing the distance covered by time.
** Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes.
** Speed is how fast an object is moving.
** Any combination of units for distance and time that are useful and convenient are legitimate for describing speed.
** Some units that describe speed are miles per hour (mi/h) and kilometers per hour (km/h). The slash symbol (/) is read as “per”.
** The speed of an object at any instant is called the instantaneous speed.
** The average speed of an object is the total distance covered divided by the time.
** Average speed does not indicate variations in the speed that may take place during the trip.
** A simple rearrangement of the definition of average speed gives the total distance covered:
Total distance covered = average speed x travel time
Velocity – Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves.
** Velocity is speed in a given direction.
** A quantity such as velocity, which specifies direction as well as magnitude, is called a vector quantity.
** Quantities that require only magnitude for a description are ______________ quantities.
** Constant speed means steady speed.
** Constant velocity means both constant speed and constant direction, which is a straight line.
** If either an object’s speed or its direction (or both) is changing, then the object’s velocity is changing.
Acceleration—you can calculate the acceleration of an object by dividing the change in its velocity by time.
** Acceleration – is the rate at which the velocity is changing
** In Physics, the term acceleration applies to decreases as well as increases in speed.
** Acceleration also applies to change in direction.
** Acceleration is defined as the rate of change in velocity rather than speed.
** Acceleration, like velocity, is a vector quantity because it is directional.
** If an object’s speed, direction, or both, changes, the object changes velocity and accelerates.
** When the direction is not changing, acceleration may be expressed as the rate at which speed changes.
** Since acceleration is the change in velocity or speed per time interval, its units are those of speed per time. m/sec/sec -- which is m/sec2
Free Fall – How Fast? The acceleration of an object in free fall is about 9.8 m/sec2
** Gravity causes objects to accelerate downward once they begin to fall.
** In real life, air resistance affects the acceleration of a falling object.
** An object moving under the influence of the gravitational force only is said to be in _________
__________. Freely falling objects are affected only by gravity.
** The elapsed time is the time that has elapsed, or passed, since the beginning of any motion.
** For free fall, it is customary to use the letter (g) to represent the acceleration because the acceleration is due to gravity.
** Although g varies slightly in different parts of the world, its average value is nearly 9.8 m/s2
** The instantaneous speed of an object falling from rest is equal to the acceleration multiplied by the amount of time it falls(the elapsed time).
** The instantaneous speed (v) of an object falling from rest after an elapsed time (t) can be expressed in equation form as v = gt. Note that the letter (v) symbolizes both speed and velocity.
** At the highest point of a rising object, when the object is changing its direction of motion from upward to downward, its instantaneous speed is zero.
** As an object rises, its speed decreases at the same rate it increases when moving downward—at 9.8 m/sec2
** The instantaneous speed at points of equal elevation in a moving object’s path is the same whether the object is moving upward or downward.
Free Fall – How Far? For each second of free fall, an object falls a greater distance than it did in the previous second.
** The initial speed of the fall is zero and takes a full second to get to 9.8 m/s
** Whenever an object’s initial speed is zero and the acceleration (a) is constant, that is, steady and “non-jerky”, the equations for the velocity and distance traveled are:
v = at d= ½ at2
Graphs of Motion – On a speed-versus-time graph the slope represents speed per time, or acceleration.
** On a speed-versus-time graph, if the line forms a straight line, time and speed are directly proportional to each other.
** The slope of the line is the vertical change divided by the horizontal change for any part of the line.
** On a distance-versus-time graph for a falling object, the relationship is quadratic and the curve is parabolic.
Air Resistance and Falling Objects – Air resistance noticeably slows the motion of things with large surface areas like falling feathers or pieces of paper. But air resistance less noticeably affects the motion of more compact objects like stones and baseballs.
** Air resistance can affect the acceleration of objects outside a vacuum.
** In many cases, however, the effect of air resistance is small enough to be neglected.
** With negligible air resistance, falling objects can be considered to be falling freely.
How Fast, How Far, How Quickly, How Fast Changes – Acceleration is the rate at which velocity itself changes
** When we wish to specify how fast something freely falls from rest after a certain elapsed time, we are talking about speed or velocity. The appropriate equation in these cases is v = gt
** When we wish to specify how far an object has fallen, we are talking about distance. The appropriate equation is these cases is d =1/2 gt2
PHYSICS CONCEPT #4: Projectile motion can be described by the horizontal and vertical components of motion.
Vector and Scalar Quantities: A vector quantity includes both magnitude and direction, but a scalar quantity includes only magnitude.
** Sketches in physics often include arrows, where each arrow represents the magnitude and the direction of a certain quantity.
** Velocity is a vector quantity, as is acceleration.
** Scalars can be added, subtracted, multiplied, and divided like ordinary numbers.
Velocity Vectors: The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.
** An airplane’s velocity is a combination of the velocity of the airplane relative to the air and the velocity of the air relative to the ground ( the wind velocity).
** For two velocity vectors that are perpendicular, the result of adding the two vectors, called the resultant, is the diagonal of the rectangle described by the two vectors.
** To add equal-magnitude vectors, a square is constructed, and the resultant is the diagonal of the square. For any square, the length of the diagonal is √2, or 1.414 times either of its sides.
Components of Vectors – The perpendicular components of a vector are independent of each other.
** two vectors at right angles that add up to a given vector are known as the components of the vector they replace.
** the process of determining the components of a vector is called resolution.
** any vector drawn on a piece of paper can be resolved into vertical and horizontal components that are perpendicular.
Projectile Motion—the horizontal component of motion for a projectile is just like the horizontal motion of a ball rolling freely along a level surface without friction. The vertical component of a projectile’s velocity is like the motion for a freely falling object.
** A cannonball shot from a cannon, a stone thrown into the air, a ball rolling off the edge of a table, a spacecraft circling Earth – all of these are examples of projectiles.
** A projectile is any object that moves through the air or space, acted on only by gravity (and air resistance, if any).
** When no horizontal force acts on a projectile, the horizontal velocity remains constant.
** The horizontal component of motion for a projectile is completely independent of the vertical component of motion.
Projectiles Launched Horizontally – the downward motion of a horizontally launch projectile is the same as that of free fall.
** When projectiles are launched horizontal, gravity acts only downward, so the only acceleration is downward.
** The vertical distance fallen has nothing to do with the horizontal component of motion.
** The path traced by a projectile accelerating only in the vertical direction while moving at constant horizontal velocity is a parabola.
Projectiles Launched at an Angle – the vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 4.9 t2 meters
** the maximum horizontal range for projectiles is attained at a projection angle of 45o
** when the effect of air resistance on a projectile’s motion is significant, the range is diminished and the path is not a true parabola.
** if air resistance is negligible, a projectile hits the ground with the same speed it had originally when it was projected upward from the ground.
PHYSICS CONCEPT #5—An object accelerates when a net force acts on it
Force causes acceleration – unbalanced forces acting on an object cause the object to accelerate.
** the combination of forces acting on an object is the net force; acceleration depends on net force.
** doubling the force on an object doubles its acceleration.
** an object’s acceleration is directly proportional to the net force acting on it.
Mass Resists Acceleration – for a constant force, an increase in the mass will result in a decrease in the acceleration.
** the same force applied to twice as much mass results in only half the acceleration.
** for a given force, the acceleration produced in inversely proportional to the mass. Inversely means that the two values change in opposite directions.
Newton’s Second Law – states that the acceleration produced by a net force on a object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
** Newton’s second law – describes the relationship among an object’s mass, an object’s acceleration, and the net force on an object.
** In equation form, Newton’s second law is written as follows:
Acceleration = net force/ mass or a = F/m
** acceleration is equal to the net force divided by the mass
Friction – the force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.
** friction acts on materials that are in contact with each other, and it always acts in a direction to oppose relative motion.
** liquids and gases are called fluids because they flow. Fluid friction occurs when an object moves through a fluid.
** Air resistance is the friction acting on something moving through air.
** A diagram showing all of the forces acting on an object is called a free-body diagram.
Applying Force – Pressure -- for a constant force, an increase in the area of contact will result in a decrease in the pressure.
** Pressure is the amount of force per unit of area.
** In equation form, pressure is defined as follows:
Pressure = force/area of application or P = F/A
** Pressure is measured in newtons per square meter, or pascals (Pa). One newton per square meter is equal to one pascal.
** The smaller the area supporting a given force, the greater the pressure on that surface.
Free Fall Explained -- all freely falling objects fall with the same acceleration because the net force on an object is only its weight, and the ratio of weight to mass is the same for all objects.
** A 10-kg cannonball and a 1-kg stone dropped from an elevated position at the same time will fall together and strike the ground at practically the same time.
** Since mass and weight are proportional, a 10-kg cannonball experiences 10 times as much gravitational force as a 1-kg stone.
Falling and Air Resistance – the air resistance force an object experiences depends on the object’s speed and area.
** the force due to air resistance diminishes the net force acting on falling objects
** Terminal speed – is the speed at which the acceleration of a falling object is zero because friction balances the weight.
** Terminal velocity – is terminal speed together with the direction of motion
PHYSICS CONCEPT #6: For every force, there is an equal and opposite force.
Forces and Interactions – a force is always part of a mutual action that involves another force.
** A mutual action is an interaction between one thing and another.
** An example of interaction occurs when a hammer exerts a force on a nail, and the nail exerts a force on the hammer.
Newton’s Third Law – states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
** Newton’s third law – describes the relationship between two forces in an interaction. Newton’s third law is often stated: “ To every action there is always an equal and opposing reaction.”
** In an interaction, one force is called the action force. The other force is called the reaction force. The action and reaction forces are equal in strength and opposite in direction.
** When you walk on a floor, you push against the floor, and the floor simultaneously pushes against you.
Identifying Action and Reaction – to identify a pair of action-reaction forces, first identify the interacting objects A and B, and if the action is A on B, the reaction is B on A.
** When a boulder falls to Earth, the action is Earth exerting a force on the boulder, and the reaction is the boulder simultaneously exerting a force on Earth.
** A rocket accelerates because the rocket pushes exhaust gas and the exhaust gas pushes on the rocket.
Action and Reaction on Different Masses – a given force exerted on a small mass produces a greater acceleration than the same force exerted on a large mass.
** recall that Newton’s second law states that acceleration is proportional to the net force and inversely proportional to the mass.
** when a boulder falls toward Earth, Earth also moves toward the boulder. Because Earth has a huge mass, its acceleration toward the boulder is infinitesimally small. A rocker accelerates because it continually recoils from the exhaust gases ejected from its engine.
PHYSICS CONCEPT #7 – momentum is conserved for all collisions as long as external forces don’t interfere.
Momentum – a moving object can have a large momentum if it has a large mass, a high speed, or both.
** Momentum is the mass of the object multiplied by its velocity.
** A moving truck has more momentum than a car moving at the same speed because the truck has more mass.
** A fast car can have more momentum than a slow truck.
** A truck at rest has no momentum at all.
Impulse Changes Momentum – the change in momentum depends on the force that acts and the length of time it acts.
** The quantity force x time interval is called impulse. In short-hand notation, impulse = F ∆t
** The greater the impulse exerted on something, the greater will be the change in momentum. The exact relationship is impulse = change in momentum or Ft = ∆(mv)
** To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swings.
** In the case of decreasing momentum, a longer contact time reduces the force and decreases the resulting deceleration. A padded dashboard in a car is safer than a rigid, metal one because the padded dashboard increases the time of contact.
Bouncing – the impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop.
** it take a greater impulse to catch a flower pot and throw it back up than merely to catch it.
** A karate expert strikes the bricks in such a way that her hand is made to bounce back, yielding as much as twice the impulse to the bricks.
Conservation of Momentum – law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged.
** the law of conservation of momentum describes the momentum of a system
** if the system undergoes changes wherein all forces are internal – for example, in atomic nuclei undergoing radioactive decay, cars colliding, or stars exploding—the net momentum of the system before and after the event is the same.
** the momentum before firing a cannon is zero. After firing, the momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.
Collisions – whenever objects collide in the absence of external forces, the net momentum of both objects before the collision equals the net momentum of both objects after the collision.
** when objects collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision.
** Colliding objects bounce perfectly in perfect elastic collisions.
** A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision.
** Whenever colliding objects become tangled or couple together, a totally inelastic collision occurs.
** Perfectly elastic collisions are not common in the everyday world. At the microscopic level, however, perfectly elastic collisions are commonplace. For example, electrically charged particles bounce off one another without generating heat.
Momentum Vectors – the vector sum of momenta is the same before and after a collision.
** momentum is conserved even when the interacting objects don’t move along the same straight line.
** The momentum of a car wreck is equal to the vector sum of the momenta of each of the cars before the collision.
** when a firecracker bursts, the vector sum of the momenta of its fragments adds up to the firecracker’s momentum just before bursting.
PHYSICS CONCEPT #8 – Energy can change from one form to another without a net loss or gain
Work – work is done when a force acts on an object and the object moves in the direction of the force.
** Work is the product of the force on an object and the distance through which the object is moved.
** in the simplest case, when the force is constant, the motion takes place in a straight line in the direction of the force: work = force x distance In equation form, W = Fd
** Work generally falls into two categories: work done against another force and work done to change the speed of an object. In both categories, work involves a transfer of energy between something and its surroundings.
The unit of work is the Newton-meter (N-m), also called the joule. One joule (J) of work is done when a force of 1N is exerted over a distance of 1 m.
Power -- power equals the amount of work done divided by the time interval during which the work is done.
** Power is the rate at which work is done: power = work done/ time interval
** a high-power engine does work rapidly. If an engine has twice the power of another engine, this means that it can do twice the work in the same amount of time or the same amount of work in half the time.
** The unit of power is the joule per second, which is also known as the watt. One watt (W) of power is expended when one joule of work is done in one second.
** In the US, we customarily rate engines in units of horsepower and electricity in kilowatts, but either may be used. One horsepower (hp) is the same as 0.75 kW.
Mechanical Energy – the two forms of mechanical energy are kinetic energy and potential energy.
** The property of an object or system that enables it to do work is energy.
** Like work, energy is measured in joules.
** Mechanical energy is the energy due to the position of something or the movement of something.
Potential Energy – three examples of potential energy are elastic potential energy, chemical energy, and gravitational potential energy.
** Energy that is stored and held in readiness is called potential energy. (PE) because in the stored state it has the potential for doing work.
** A stretched or compressed spring, a bow that is drawn back, and a stretched rubber band have elastic potential energy.
** The chemical energy in fuels is potential energy at the submicroscopic level. This energy is available when a chemical change in the fuels takes place.
** The potential energy due to the elevated position of an object is gravitational potential energy.
** The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it. Gravitational potential energy = weight x height. In equation form, PE = mgh The height in this equation is the distance above some chosen reference level.
Kinetic Energy – the kinetic energy of a moving object is equal to the work required to bring it to its speed from rest, or the work the object can do while being brought to rest.
** The energy of motion is kinetic energy (KE)
** The kinetic energy of an object is equal to half the object’s mass multiplied by the square of its speed. In equation form, this is KE = ½ mv2
** The net force on an object multiplied by the distance along which the force acts equals the object’s kinetic energy. In equation form, this is Fd = ½ mv2
Work-Energy Theorem – states that whenever work is done, energy changes
** The work-energy theorem describes the relationship between work and energy.
** Work equals change in kinetic energy. In equation form, Work = ∆KE, where the delta symbol,∆, means “change in”. The work in this equation is the net work.
** if you push a box across a floor at a constant speed, you are pushing just hard enough to overcome friction. In this example, the net force and net work are zero, and KE = 0.
** Kinetic energy often appears hidden in different forms of energy. Random molecular motion is sensed as heat. Sound consists of molecules vibrating in rhythmic patterns. Light energy originates in the motion of electrons in atoms. Electrons in motion make electric currents.
Conservation of Energy – the law of conservation of energy states that energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.
** The study of the various forms of energy and the transformations from one form into another is the law of conservation of energy.
** Everywhere along, the path of a pendulum bob, the sum of potential energy and kinetic energy is the same. At the highest points, the energy is only potential energy. At the lowest point, the energy is only kinetic energy.
** The sun shines because some of its nuclear energy is transformed into radiant energy. In nuclear reactors, nuclear energy is transformed into heat.
** Some electric-generating plants transform the energy of falling water into electrical energy. Electrical energy then travels through wires to homes.
Machines – transfer energy from one place to another or transforms it from one form to another.
** A machine is a device used to multiply forces or to change the direction of forces. A machine cannot put out more energy than is put into it.
** A lever is a simple machine made of a bar that turns about a fixed point.
** If heat from friction is negligible, the work put into a machine equals the work put out by the machine: work input = work output (force x distance)input = (force x distance) output
** The pivot point of a lever is the fulcrum.
** The ratio of output force to input force for a machine is called the mechanical advantage.
** A type 1 lever has the fulcrum between the input force and the load. If the fulcrum is closer to the load, a small input force exerted through a large distance produces a larger output force over a shorter distance. The directions of input and output are opposite.
** For a type 2 lever, the load is between the fulcrum and the input force. Force is increased at the expense of distance. Input and output forces have the same direction.
** In a type 3 lever, the fulcrum is at one end and the load is at the other. The input force is applied between them. The input and output forces have the same direction.
** A pulley is a kind of lever that can be used to change the direction of a force.
** A single pulley with a fixed axis behaves like a type 1 lever. A single pulley with an axis that moves behaves like a type 2 lever.
** A system of pulleys multiplies the force and it may change the direction of the force. The mechanical advantage for a simple pulley system is the same as the number of strands of rope that actually support the load.
Efficiency – in any machine, some energy is transformed into atomic or molecular kinetic energy- making the machine warmer.
** The efficiency of a machine is the ratio of useful energy output to total energy input, or the percentage of the work input that is converted to work output. No real machine can be 100% efficient. The wasted energy is dissipated as heat.
** An inclined plane is a machine. Its theoretical mechanical advantage, assuming negligible friction, is the length of the incline divided by the height of the inclined plane.
** Efficiency can also be expressed as the ration of actual mechanical advantage to the theoretical mechanical advantage.
** To convert efficiency to percent, express it as a decimal and multiply by 100%.
Energy for Life – there is more energy stored in the molecules in food than there is in the reaction products after the food is metabolized. This energy difference sustains life.
** most living organisms on this planet feed on various hydrocarbon compounds that release energy when they react with oxygen. In metabolism of food in the body, carbon combines with oxygen to form carbon dioxide.
** Only green plants and certain one-celled organisms can make carbon dioxide combine with water to produce hydrocarbon compounds such as sugar. This process is called photosynthesis and requires an energy input, which normally comes from sunlight.
Sources of Energy—The sun is the source of practically all our energy on Earth.
** Sunlight is directly transformed into electricity by photovoltaic cells or in the flexible solar shingles on the roofs of buildings. We use the energy in sunlight to generate electricity indirectly as well.
** Wind, caused by unequal warming of Earth’s surface, is another form of solar power. Wind can be used to turn generator turbines within specially equipped windmills.
** Hydrogen is the least polluting of all fuels. Because it takes energy to make hydrogen (to extract it from water and carbon compounds), it is not a source of energy. In a fuel cell, hydrogen and oxygen gas are compressed at electrodes to produce water and electric current.
** The most concentrated form of usable energy is stored in nuclear fuels.
** Earth’s interior is kept hot by producing a form of nuclear power, radioactivity.
** Geothermal energy is held in underground reservoirs of hot water.
PHYSICS CONCEPT #9 —Centripetal force keeps an object in circular motion
Rotation and Revolution – two types of circular motion are rotation and revolution
** An axis is the straight line around which rotation takes place.
** When an object turns about an internal axis – that is, an axis located within the body of the object – the motion is called rotation, or spin. A Ferris wheel rotates about an axis.
** When an object turns about an external axis, the motion is called revolution. Riders revolve about the axis of a Ferris wheel.
** Earth undergoes both types of circular motion. It revolves around the sun once every 365 ¼ days, and it rotates around an axis passing through its geographical poles once every 24 hours.
Rotational Speed – tangential speed depends on rotational speed and the distance from the axis of rotation.
** Linear speed is the distance traveled per unit time. The linear speed is greater on the outer edge of a rotating object, such as a merry-go-round, than it is closer to the axis.
** Tangential speed is the speed of something moving along a circular path. For circular motion, the terms linear speed and tangential speed are interchangeable.
** Rotational speed, which is sometimes called angular speed, is the number of rotations per unit of time. All parts of a merry-go-round have the same rotational speed.
** Tangential speed and rotational speed are related.
Tangential speed ~ radial distance x rotational speed
v ~ rw
** As you move away from the axis of a rotating platform, your tangential speed increases while your rotational speed stays the same.
** Wheels of a train stay on the track because their rims are slightly tapered. So when a train rounds a curve, wheels on the outer track ride on the wider part of the tapered rims (and cover a greater distance in the same time) while opposite wheels ride on their narrow parts (covering a smaller distance in the same time)
Centripetal Force – the centripetal force on an object depends on the object’s tangential speed, its mass, and the radius of its circular path.
** Any object moving in a circle undergoes an acceleration that is directed to the center of the circle. This is centripetal acceleration. Centripetal means “toward the center”.
** The force directed toward a fixed center that causes an object to follow a circular path is called centripetal force.
** Centripetal forces can be exerted in a variety of ways. Anything that moves in a circular path is acted on by a centripetal force.
** Centripetal force can be calculated using the following equation:
Centripetal force = mass x speed 2 / radius of curvature
Fc = mv2/r
** Centripetal force Fc is measured in newtons when mass m is expressed in kilograms, speed v in m/s, and radius of curvature r in meters.
** The centripetal force acting on a circularly moving object is the net force that acts exactly along the radial direction – toward the center of the circular path.
Centripetal and Centrifugal Forces -- The “centrifugal-force effect” is attributed not to any real force but to inertia – the tendency of the moving body to follow a straight-line path.
** The apparent outward force on a rotating or revolving body is called centrifugal force. Centrifugal means “center-fleeing,” or “away from the center.”
** If you are in a car that rounds a sharp corner to the left, you tend to pitch outward against the right door. This happens not because of some outward or centrifugal force, but because there is no centripetal force holding you in a circular motion.
** Likewise, the only force exerted on a whirling can at the end of a string is centripetal force. No outward force acts on the can.
Centrifugal Force in a Rotating Reference Frame—Centrifugal force is an effect of rotation. It is not part of an interaction and therefore it cannot be a true force.
** Because centrifugal force is merely an effect of rotation, it is not a true force like gravitational, electromagnetic, and nuclear forces.
** Physicists refer to centrifugal force as a “fictitious force.”
** To observers in a rotating system, however, centrifugal force is very real.
PHYSICS CONCEPT #10: An object will remain upright if its center of mass is above the area of support.
Torque – to make an object turn or rotate, apply a torque.
** Torque is produced by a turning force and tends to produce rotational acceleration.
** Force and torque are different; forces tend to make things accelerate whereas torques produce rotation.
** A torque is produced when a force is applied with “leverage.” You use leverage when you use a screwdriver to open the lid of a paint can.
** The lever arm is the distance from the turning axis to the point of contact.
** Torque can be calculated using the following equation: torque = force 1 x lever arm
Balanced Torques -- when balanced torques act on an object, there is no change in rotation.
** Children of unequal weight can balance on a seesaw by sitting at different distances from the pivot point.
** Scales balances with sliding weights are based on balanced torques.
Center of Mass – the center of mass of an object is the point located at the object’s average position of mass.
** The point where all of the mass of an object can be considered concentrated is called the center of mass.
** For a symmetrical object, the center of mass is at the geometric center of the object. For irregularly shaped objects, the location of the center of mass varies.
** Spin can be applied to an object by applying a force that does not pass through the object’s center of mass. Kicking a football in the middle, for example, will make it travel without rotating.
Kicking the football above or below its center will make it rotate.
Center of Gravity – for everyday objects, the center of gravity is the same as the center of mass
** The center of gravity, or CG, is the average position of all of the particles of weight that make up an object. For most objects on and near Earth, the terms center of mass and center of gravity are interchangeable.
** If you throw a wrench so that it rotates as it moves through the air, you’ll see it wobble about its CG. The center of gravity itself would follow a parabolic path.
** An object’s CG is its balance point; supporting the CG supports the entire object. A meter stick can be balanced by applying a force at its geometric midpoint – the location of its CG.
** Any object suspended at a single point will hang with its CG directly below the point of suspension.
Torque and Center of Gravity – if the center of gravity of an object is above the area of support, the object will remain upright.
** If the CG extends outside the area of support, an unbalanced torque exists, and the object will topple.
** The Leaning Tower of Pisa does not topple because its CG does not extend beyond its base.
** It is difficult to balance a broom upright in the palm of your hand because the support base is small and far beneath the CG.
Center of Gravity of People – the center of gravity of a person is not located in a fixed place, but depends on body orientation.
** When you stand erect with your arms at your sides, your CG is within your body.
** The CG us slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.
** Raising your arms vertically over your head raises your CG by several centimeters.
** When you stand, your CG is somewhere above your support base, which is the area bounded by your feet.
Stability – when an object is toppled, the center of gravity of that object is raised, lowered, or unchanged.
** An object balanced so that any displacement lowers its center of mass is in unstable equilibrium.
** An object balanced so that any displacement raises its center of mass is in stable equilibrium. Raising the CG of an object in stable equilibrium requires increasing the object’s potential energy, which requires work.
** An object balanced so that any small movement neither raises nor lowers its center of gravity is in neutral equilibrium.
** An object with a low CG is usually more stable than an object with a relatively high CG.
PHYSICS CONCEPT #11 – Rotating objects tend to keep rotating while nonrotating objects tend to remain nonrotating.
Rotational Inertia – the greater the rotational inertia, the more difficult it is to change the rotational speed of an object.
** The resistance of an object to change in its rotational motion is called rotational inertia, or moment of inertia.
** A torque is required to change the rotational state of motion of an object.
** Rotational inertia depends on mass and how the mass is distributed. The greater the distance between an object’s mass concentration and the axis of rotation, the greater the rotational inertia.
** A short pendulum has less rotational inertia and therefore swings back and forth more frequently than a long pendulum. Likewise, bent legs swing back and forth more easily than outstretched legs.
** Formulas to calculate rotational inertia for different objects vary and depend on the shape of an object and the location of the rotational axis.
Rotational Inertia and Gymnastics – The three principal axes of rotation in the human body are the longitudinal axis, the transverse axis, and the medial axes.
** The three axes of rotation in the human body are at right angles to one another. All three axes pass through the center of gravity of the body.
** The vertical axis that passes from the head to toe is the longitudinal axis. Rotational inertia about this axis is increased by extending a leg or the arms.
** You rotate about your transverse axis when you perform a somersault or a flip. Tucking in your arms and legs reduces your rotational inertia about the transverse axis; straightening your arms and legs increases your rotational inertia about this axis.
** The third axis of rotation for the human body is the front-to-back axis, or medial axis. You rotate about the medial axis when executing a cartwheel.
Rotational Inertia and Rolling – Objects of the same shape but different sizes accelerate equally when rolled down an incline.
** An object with a greater rotational inertia takes more time to get rolling than an object with a smaller rotational inertia. A hollow cylinder, for example, rolls down an incline much slower than a solid cylinder.
** All objects of the same shape roll down an incline with the same acceleration, even if their masses are different.
Angular Momentum – Newton’s first law of inertia for rotating systems states that an object or system of objects will maintain its angular momentum unless acted upon by an unbalanced external torque.
** All moving objects have momentum.
** Linear momentum is the product of the mass and velocity of an object.
** Rotating objects have angular momentum. Angular momentum is the product of rotational inertia, I , and rotational velocity, w.
angular momentum = rotational inertia x rotational velocity
angular momentum = I x w
** When a direction is assigned to rotational speed, it is called rotational velocity.
** When an object is small compared with the radial distance to its axis of rotation, its angular momentum is equal to the magnitude of its linear momentum, mv , multiplied by the radial distance, r.
angular momentum = mvr
** A moving bicycle is easier to balance than a bicycle at rest because of the angular momentum provided by the spinning wheels.
Conservation of Angular Momentum – it is conserved when no external torque acts on an object.
** The law of conservation of angular momentum states that if no unbalanced external torque acts on a rotating system, the angular momentum of the system is constant.
** A person who spins with arms extended obtains greater rotational speed when the arms are drawn in. In other words, whenever a rotating body contracts, its rotational speed increases.
** Zero-angular-momentum twists and turns are performed by turning one part of the body against the other.
Simulated Gravity – from within a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.
** Occupants in today’s space vehicles feel weightless because they lack a support force. Future space habitats will probably spin, effectively supplying a support force that simulates gravity.
** We experience 1 g on Earth’s surface due to gravity. Small-diameter space structures would have to rotate at high speeds to provide a simulated gravitational acceleration of 1 g.
PHYSICS CONCEPT #12 – Everything pulls on everything else.
The Falling Apple -- Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree – they are both pulled by Earth’s gravity.
** Newton understood the concept of inertia, that without an outside force, moving objects continue to move at constant speed in a straight line. He knew that if an object undergoes a change in speed or direction, then a force is responsible.
The Falling Moon – the moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.
** Newton reasoned that the moon must be falling around Earth. The moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it. He hypothesized that the moon was a projectile circling Earth under the attraction of gravity.
** Newton compared the motion of the moon to a cannonball fired from the top of a high mountain. If the cannonball were fired with enough speed, its path would become a circle and the cannonball would circle indefinitely.
** both the orbiting cannonball and the moon have a component of velocity parallel to Earth’s surface. This sideways or tangential velocity is sufficient to ensure nearly circular motion around Earth rather than into it.
** Newton reasoned that the mass of the moon should not affect how it falls, just as mass has no effect on the acceleration of freely falling objects on Earth. How far the moon falls should relate only to its distance from Earth’s center.
The Falling Earth – Newton’s theory of gravity confirmed the Copernican theory of the solar system.
** The planets don’t crash into the sun because they have tangential velocities. If the tangential velocities of the planets were reduced to zero, their motion would be straight toward the sun and they would indeed crash into it. Any objects in the solar system with insufficient tangential velocities have long ago crashed into the sun.
Newton’s Law of Universal Gravitation – gravity in universal, everything pulls on everything else in a way that involves only mass and distance.
** Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.
** The law of universal gravitation can be expressed in equation form:
F = G (m1m2/d2), where m1 and m2 are the objects’ masses, and d is the distance between their centers of mass.
** The universal gravitational constant, G, in the equation describes the strength of gravity. In scientific notation, G = 6.67 x 10-11 N-m2/kg2 . The value of G tells us that the force of gravity is a very weak force. It is the weakest of the presently known four fundamental forces.
Gravity and Distance: The Inverse-Square Law – gravity decreases according to the inverse square law. The force of gravity weakens as the square of distance.
** When a quantity varies as the inverse square of its distance from its source, it follows and inverse-square law. For example, the inverse square of 3 is (1/3)2 or 1/9
** This law applies to all cases where the effect from a localized source spreads evenly throughout the surrounding space, such as the weakening of gravity with distance. Other examples are light, radiation, and sound.
Gravitational Field – Earth can be thought of as being surrounded by a gravitational field that interacts with objects and causes them to experience gravitational forces.
** A gravitational field occupies the space surrounding a massive body. A gravitational field is an example of a force field, for any mass in the field space experiences a force.
** Iron filings sprinkled over a sheet of paper on top of a magnet reveal the shape of the magnet’s
magnetic field. The pattern of filings shows the strength and direction of the magnetic field at different locations around the magnet. Earth is a giant magnet and, like all magnets, is surrounded by a magnetic field.
** The strength of Earth’s gravitational field, like the strength of its force on objects, follows the inverse-square law. Earth’s gravitational field is strongest near Earth’s surface and weaker at greater distances from Earth.
Gravitational Field Inside a Planet – the gravitational field of Earth at its center is zero.
** The gravitational field of Earth exists inside Earth as well as outside.
** If you traveled through an imaginary hole drilled completely through Earth, you’d gain speed as you fell from the North Pole toward the center of Earth, and lose speed moving away from the center toward the South Pole.
Weight and Weightlessness – pressure against Earth is the sensation we interpret as weight.
** The force of gravity, like any force, causes acceleration. Because we are almost always in contact with Earth, we think of gravity primarily as something that presses us against Earth rather than something that accelerates us.
** If you stand on a scale, gravity pulls you against the supporting floor and scale, and the floor and scale push upward on you. This pair of forces compresses a spring-like gauge inside the scale. The weight reading on the scale is linked to the amount of compression.
** Weightlessness is not the absence of gravity; rather, it is the absence of a support force. Astronauts in orbit are without a support force and experience weightlessness.
Ocean Tides – Newton showed that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of Earth.
** The moon’s gravitational attraction is stronger on Earth’s oceans closer to the moon, and weaker on the oceans farther from the moon. This difference causes the oceans to bulge out on opposite sides of Earth. Because Earth spins, a fixed point on Earth passes beneath both bulges each day, producing two high tides and two low tides.
** A spring tide is a high or low tide that occurs when the sun, Earth, and moon are all lined up.
The tides due to the sun and the moon coincide, making high tides higher than average and low tides lower than average. Spring tides occur during a new or full moon.
** A neap tide occurs when the moon is halfway between a new moon and a full moon. The pulls of the moon and sun are perpendicular to each other. As a result, the solar and lunar tides do not overlap, so the high tides are not as high and low tides are not as low.
Black Holes – when a massive star collapses into a black hole, there is no change in the gravitational field at any point beyond the original radius of the star.
** Two main processes occur continuously in stars like our sun: gravitation, which tends to pull solar material inward, and thermonuclear fusion, which blows material outward.
** If the fusion rate increases, the sun will get hotter and bigger; if the fusion rate decreases, the sun will get cooler and smaller.
** When the sun runs out of fusion fuel (hydrogen), gravitation will dominate and the sun will start to collapse. The collapse will cause helium to fuse into carbon, and the sun will expand into a red giant. When the helium is used up, the sun will collapse into a black dwarf.
** For stars more massive than the sun, once thermonuclear fusion ends, gravitational collapse will take over, eventually forming a black hole. The density of a black hole is so great that its enormous gravitational field prevents even light from escaping. The gravitational field beyond the original radius of the star is no different after the collapse than before.
Universal Gravitation – The formulation of the law of universal gravitation is one of the major reasons for the success in science that followed, for it provided hope that other phenomena of the world might also be described by equally simple and universal laws.
** Earth is round because of gravitation. Earth attracted itself together before it became solid. Any “corners” of Earth have been pulled in so that Earth is a giant sphere.
** The solar system began when a slightly rotating ball of interstellar gas contracted due to mutual gravitation. To conserve angular momentum, the rotational speed of the ball of gas increased, causing the particles to sweep out into a disk shape.
** The deviation of an orbiting object from its path around a center of force caused by the action of an additional center of force is called a perturbation.
** The planet Neptune was discovered when a perturbation in the orbit of Uranus led scientists to conclude that a disturbing body beyond the orbit of Uranus was the culprit.
** According to current scientific understanding, the universe originated and grew from the explosion of a primordial fireball some 13.7 billon years ago. This is the “Big Bang” theory of the origin of the universe. All the matter of the universe was hurled outward from this event and continues in an outward expansion.
** More recent evidence suggests the universe is not only expanding, but accelerating outward. It is pushed by an antigravity dark energy that makes up an estimated 73 percent of the universe. Twenty-three percent of the universe is composed of the yet-to-be discovered particles of exotic dark matter. Ordinary matter makes up only 4 percent.
Physics Concept #13 -- The path of an Earth satellite follows the curvature of Earth.
Earth Satellites -- A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time of 1 second it takes to fall 4.9 m, will orbit the earth.
** An Earth satellite is a projectile moving fast enough to fall continually around Earth rather than into it.
** A geometric fact about the curvature of Earth is that its surface drops a vertical distance of nearly 5 meters for every 8000 meters tangent to its surface.
** The orbital speed for close orbit about Earth is 8 km/s (29,000 km/h or 18,000 mi/h)
** A satellite must stay about 150 kilometers or more above Earth’s surface to keep from burning due to the friction of the atmosphere.
Circular Orbits -- A satellite in circular orbit around Earth is always moving perpendicularly to gravity and parallel to Earth’s surface at constant speed.
PHYSICS CONCEPT #1: An object in mechanical equilibrium is stable, without changes in motion.
Force:
A force is needed to change an object’s state of motion.
Force is a –
Mechanical Equilibrium:
You can express the equilibrium rule mathematically as ΣF = 0
Mechanical equilibrium is a state wherein no physical changes occur; it is a state of steadiness.
Whenever the net force on an object is zero (ΣF = 0), the object is said to be in mechanical equilibrium – this is known as the ________________ rule.
The symbol Σ stands for “the sum of” and F stands for “forces.”
________________.
The weight of a book sitting on a table is a negative force that squeezes downward on the atoms of the table. The atoms squeeze upward on the book. The compressed atoms produce the positive support force.
Equilibrium for Moving Objects:
Objects at __________ are said to be in ___________ equilibrium; objects moving at constant speed in a straight-line path are said to be in dynamic equilibrium.
Equilibrium is a state of no ______________. An object under the influence of only one force cannot be in __________________. Only when there is no force at all, or when two or more forces combine to zero, can an object be in _______________________.
Both ___________ and ____________ equilibrium are examples of ______________ equilibrium.
Vectors:
The ______________________ Rule: To find the resultant of two nonparallel vectors, construct a parallelogram wherein the two vectors are adjacent sides. The diagonal of the parallelogram shows the resultant.
The sum of two or more vectors is called their ________
** one of Galileo’s greatest contributions to physics was demolishing the notion that a force is necessary to keep an object moving. A force is any push or pull.
** friction is the force that acts between materials that touch as they move past each other.
** Galileo found that a ball rolling on a smooth horizontal plane has almost constant velocity, and if friction were entirely absent, the ball would move forever. Galileo also stated that the tendency of a moving body to keep moving is natural and that every object resists change to its state of motion.
** the property of a body to resist changes to its state of motion is called ________________.
NEWTON’S LAW OF INERTIA-- Newton’s first law – states that every object continues in a state of rest or of uniform speed in a straight line, unless acted on by a nonzero net force.
** forces are needed to overcome any friction that may be present. Forces are also needed to set objects in motion initially.
** once an object is moving in a force-free environment, it will move in a straight line indefinitely.
Measure of Inertia -- the more mass an object has, the greater its inertia and the more force it takes to change its state of motion.
** Mass is the quantity of matter in an object. Mass is a measure of the inertia of an object. Mass is measured in kilograms.
** Weight is the force of gravity on an object. Weight depends on an object’s location. The mass of an object is the same whether the object is located on Earth, on the moon, or in outer space.
** Mass and weight are proportional to each other in a given place. Objects with great mass have great weight; objects with little mass have little weight.
** In most parts of the world, the measure of matter is commonly expressed in units of mass. The SI unit of mass is the kilogram and its symbol is kg.
** The SI unit of force is the Newton. The SI symbol for the Newton is N and is written with a capital letter because it is named after a person.
** Objects within moving vehicles move with the vehicles.
PHYSICS CONCEPT #3 -- You can describe the motion of an object by its position, speed, direction, and acceleration.
Motion is Relative:
** An object is moving if its position relative to a fixed point is changing.
** When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object.
** Unless stated otherwise, when we discuss the speeds of things in our environment, we mean speed with respect to the surface of Earth.
Speed – You can calculate the speed of an object by dividing the distance covered by time.
** Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes.
** Speed is how fast an object is moving.
** Any combination of units for distance and time that are useful and convenient are legitimate for describing speed.
** Some units that describe speed are miles per hour (mi/h) and kilometers per hour (km/h). The slash symbol (/) is read as “per”.
** The speed of an object at any instant is called the instantaneous speed.
** The average speed of an object is the total distance covered divided by the time.
** Average speed does not indicate variations in the speed that may take place during the trip.
** A simple rearrangement of the definition of average speed gives the total distance covered:
Total distance covered = average speed x travel time
Velocity – Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves.
** Velocity is speed in a given direction.
** A quantity such as velocity, which specifies direction as well as magnitude, is called a vector quantity.
** Quantities that require only magnitude for a description are ______________ quantities.
** Constant speed means steady speed.
** Constant velocity means both constant speed and constant direction, which is a straight line.
** If either an object’s speed or its direction (or both) is changing, then the object’s velocity is changing.
Acceleration—you can calculate the acceleration of an object by dividing the change in its velocity by time.
** Acceleration – is the rate at which the velocity is changing
** In Physics, the term acceleration applies to decreases as well as increases in speed.
** Acceleration also applies to change in direction.
** Acceleration is defined as the rate of change in velocity rather than speed.
** Acceleration, like velocity, is a vector quantity because it is directional.
** If an object’s speed, direction, or both, changes, the object changes velocity and accelerates.
** When the direction is not changing, acceleration may be expressed as the rate at which speed changes.
** Since acceleration is the change in velocity or speed per time interval, its units are those of speed per time. m/sec/sec -- which is m/sec2
Free Fall – How Fast? The acceleration of an object in free fall is about 9.8 m/sec2
** Gravity causes objects to accelerate downward once they begin to fall.
** In real life, air resistance affects the acceleration of a falling object.
** An object moving under the influence of the gravitational force only is said to be in _________
__________. Freely falling objects are affected only by gravity.
** The elapsed time is the time that has elapsed, or passed, since the beginning of any motion.
** For free fall, it is customary to use the letter (g) to represent the acceleration because the acceleration is due to gravity.
** Although g varies slightly in different parts of the world, its average value is nearly 9.8 m/s2
** The instantaneous speed of an object falling from rest is equal to the acceleration multiplied by the amount of time it falls(the elapsed time).
** The instantaneous speed (v) of an object falling from rest after an elapsed time (t) can be expressed in equation form as v = gt. Note that the letter (v) symbolizes both speed and velocity.
** At the highest point of a rising object, when the object is changing its direction of motion from upward to downward, its instantaneous speed is zero.
** As an object rises, its speed decreases at the same rate it increases when moving downward—at 9.8 m/sec2
** The instantaneous speed at points of equal elevation in a moving object’s path is the same whether the object is moving upward or downward.
Free Fall – How Far? For each second of free fall, an object falls a greater distance than it did in the previous second.
** The initial speed of the fall is zero and takes a full second to get to 9.8 m/s
** Whenever an object’s initial speed is zero and the acceleration (a) is constant, that is, steady and “non-jerky”, the equations for the velocity and distance traveled are:
v = at d= ½ at2
Graphs of Motion – On a speed-versus-time graph the slope represents speed per time, or acceleration.
** On a speed-versus-time graph, if the line forms a straight line, time and speed are directly proportional to each other.
** The slope of the line is the vertical change divided by the horizontal change for any part of the line.
** On a distance-versus-time graph for a falling object, the relationship is quadratic and the curve is parabolic.
Air Resistance and Falling Objects – Air resistance noticeably slows the motion of things with large surface areas like falling feathers or pieces of paper. But air resistance less noticeably affects the motion of more compact objects like stones and baseballs.
** Air resistance can affect the acceleration of objects outside a vacuum.
** In many cases, however, the effect of air resistance is small enough to be neglected.
** With negligible air resistance, falling objects can be considered to be falling freely.
How Fast, How Far, How Quickly, How Fast Changes – Acceleration is the rate at which velocity itself changes
** When we wish to specify how fast something freely falls from rest after a certain elapsed time, we are talking about speed or velocity. The appropriate equation in these cases is v = gt
** When we wish to specify how far an object has fallen, we are talking about distance. The appropriate equation is these cases is d =1/2 gt2
PHYSICS CONCEPT #4: Projectile motion can be described by the horizontal and vertical components of motion.
Vector and Scalar Quantities: A vector quantity includes both magnitude and direction, but a scalar quantity includes only magnitude.
** Sketches in physics often include arrows, where each arrow represents the magnitude and the direction of a certain quantity.
** Velocity is a vector quantity, as is acceleration.
** Scalars can be added, subtracted, multiplied, and divided like ordinary numbers.
Velocity Vectors: The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.
** An airplane’s velocity is a combination of the velocity of the airplane relative to the air and the velocity of the air relative to the ground ( the wind velocity).
** For two velocity vectors that are perpendicular, the result of adding the two vectors, called the resultant, is the diagonal of the rectangle described by the two vectors.
** To add equal-magnitude vectors, a square is constructed, and the resultant is the diagonal of the square. For any square, the length of the diagonal is √2, or 1.414 times either of its sides.
Components of Vectors – The perpendicular components of a vector are independent of each other.
** two vectors at right angles that add up to a given vector are known as the components of the vector they replace.
** the process of determining the components of a vector is called resolution.
** any vector drawn on a piece of paper can be resolved into vertical and horizontal components that are perpendicular.
Projectile Motion—the horizontal component of motion for a projectile is just like the horizontal motion of a ball rolling freely along a level surface without friction. The vertical component of a projectile’s velocity is like the motion for a freely falling object.
** A cannonball shot from a cannon, a stone thrown into the air, a ball rolling off the edge of a table, a spacecraft circling Earth – all of these are examples of projectiles.
** A projectile is any object that moves through the air or space, acted on only by gravity (and air resistance, if any).
** When no horizontal force acts on a projectile, the horizontal velocity remains constant.
** The horizontal component of motion for a projectile is completely independent of the vertical component of motion.
Projectiles Launched Horizontally – the downward motion of a horizontally launch projectile is the same as that of free fall.
** When projectiles are launched horizontal, gravity acts only downward, so the only acceleration is downward.
** The vertical distance fallen has nothing to do with the horizontal component of motion.
** The path traced by a projectile accelerating only in the vertical direction while moving at constant horizontal velocity is a parabola.
Projectiles Launched at an Angle – the vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 4.9 t2 meters
** the maximum horizontal range for projectiles is attained at a projection angle of 45o
** when the effect of air resistance on a projectile’s motion is significant, the range is diminished and the path is not a true parabola.
** if air resistance is negligible, a projectile hits the ground with the same speed it had originally when it was projected upward from the ground.
PHYSICS CONCEPT #5—An object accelerates when a net force acts on it
Force causes acceleration – unbalanced forces acting on an object cause the object to accelerate.
** the combination of forces acting on an object is the net force; acceleration depends on net force.
** doubling the force on an object doubles its acceleration.
** an object’s acceleration is directly proportional to the net force acting on it.
Mass Resists Acceleration – for a constant force, an increase in the mass will result in a decrease in the acceleration.
** the same force applied to twice as much mass results in only half the acceleration.
** for a given force, the acceleration produced in inversely proportional to the mass. Inversely means that the two values change in opposite directions.
Newton’s Second Law – states that the acceleration produced by a net force on a object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.
** Newton’s second law – describes the relationship among an object’s mass, an object’s acceleration, and the net force on an object.
** In equation form, Newton’s second law is written as follows:
Acceleration = net force/ mass or a = F/m
** acceleration is equal to the net force divided by the mass
Friction – the force of friction between the surfaces depends on the kinds of material in contact and how much the surfaces are pressed together.
** friction acts on materials that are in contact with each other, and it always acts in a direction to oppose relative motion.
** liquids and gases are called fluids because they flow. Fluid friction occurs when an object moves through a fluid.
** Air resistance is the friction acting on something moving through air.
** A diagram showing all of the forces acting on an object is called a free-body diagram.
Applying Force – Pressure -- for a constant force, an increase in the area of contact will result in a decrease in the pressure.
** Pressure is the amount of force per unit of area.
** In equation form, pressure is defined as follows:
Pressure = force/area of application or P = F/A
** Pressure is measured in newtons per square meter, or pascals (Pa). One newton per square meter is equal to one pascal.
** The smaller the area supporting a given force, the greater the pressure on that surface.
Free Fall Explained -- all freely falling objects fall with the same acceleration because the net force on an object is only its weight, and the ratio of weight to mass is the same for all objects.
** A 10-kg cannonball and a 1-kg stone dropped from an elevated position at the same time will fall together and strike the ground at practically the same time.
** Since mass and weight are proportional, a 10-kg cannonball experiences 10 times as much gravitational force as a 1-kg stone.
Falling and Air Resistance – the air resistance force an object experiences depends on the object’s speed and area.
** the force due to air resistance diminishes the net force acting on falling objects
** Terminal speed – is the speed at which the acceleration of a falling object is zero because friction balances the weight.
** Terminal velocity – is terminal speed together with the direction of motion
PHYSICS CONCEPT #6: For every force, there is an equal and opposite force.
Forces and Interactions – a force is always part of a mutual action that involves another force.
** A mutual action is an interaction between one thing and another.
** An example of interaction occurs when a hammer exerts a force on a nail, and the nail exerts a force on the hammer.
Newton’s Third Law – states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
** Newton’s third law – describes the relationship between two forces in an interaction. Newton’s third law is often stated: “ To every action there is always an equal and opposing reaction.”
** In an interaction, one force is called the action force. The other force is called the reaction force. The action and reaction forces are equal in strength and opposite in direction.
** When you walk on a floor, you push against the floor, and the floor simultaneously pushes against you.
Identifying Action and Reaction – to identify a pair of action-reaction forces, first identify the interacting objects A and B, and if the action is A on B, the reaction is B on A.
** When a boulder falls to Earth, the action is Earth exerting a force on the boulder, and the reaction is the boulder simultaneously exerting a force on Earth.
** A rocket accelerates because the rocket pushes exhaust gas and the exhaust gas pushes on the rocket.
Action and Reaction on Different Masses – a given force exerted on a small mass produces a greater acceleration than the same force exerted on a large mass.
** recall that Newton’s second law states that acceleration is proportional to the net force and inversely proportional to the mass.
** when a boulder falls toward Earth, Earth also moves toward the boulder. Because Earth has a huge mass, its acceleration toward the boulder is infinitesimally small. A rocker accelerates because it continually recoils from the exhaust gases ejected from its engine.
PHYSICS CONCEPT #7 – momentum is conserved for all collisions as long as external forces don’t interfere.
Momentum – a moving object can have a large momentum if it has a large mass, a high speed, or both.
** Momentum is the mass of the object multiplied by its velocity.
** A moving truck has more momentum than a car moving at the same speed because the truck has more mass.
** A fast car can have more momentum than a slow truck.
** A truck at rest has no momentum at all.
Impulse Changes Momentum – the change in momentum depends on the force that acts and the length of time it acts.
** The quantity force x time interval is called impulse. In short-hand notation, impulse = F ∆t
** The greater the impulse exerted on something, the greater will be the change in momentum. The exact relationship is impulse = change in momentum or Ft = ∆(mv)
** To increase the momentum of an object, apply the greatest force possible for as long as possible. A golfer teeing off and a baseball player trying for a home run do both of these things when they swing as hard as possible and follow through with their swings.
** In the case of decreasing momentum, a longer contact time reduces the force and decreases the resulting deceleration. A padded dashboard in a car is safer than a rigid, metal one because the padded dashboard increases the time of contact.
Bouncing – the impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop.
** it take a greater impulse to catch a flower pot and throw it back up than merely to catch it.
** A karate expert strikes the bricks in such a way that her hand is made to bounce back, yielding as much as twice the impulse to the bricks.
Conservation of Momentum – law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged.
** the law of conservation of momentum describes the momentum of a system
** if the system undergoes changes wherein all forces are internal – for example, in atomic nuclei undergoing radioactive decay, cars colliding, or stars exploding—the net momentum of the system before and after the event is the same.
** the momentum before firing a cannon is zero. After firing, the momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.
Collisions – whenever objects collide in the absence of external forces, the net momentum of both objects before the collision equals the net momentum of both objects after the collision.
** when objects collide without being permanently deformed and without generating heat, the collision is said to be an elastic collision.
** Colliding objects bounce perfectly in perfect elastic collisions.
** A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision.
** Whenever colliding objects become tangled or couple together, a totally inelastic collision occurs.
** Perfectly elastic collisions are not common in the everyday world. At the microscopic level, however, perfectly elastic collisions are commonplace. For example, electrically charged particles bounce off one another without generating heat.
Momentum Vectors – the vector sum of momenta is the same before and after a collision.
** momentum is conserved even when the interacting objects don’t move along the same straight line.
** The momentum of a car wreck is equal to the vector sum of the momenta of each of the cars before the collision.
** when a firecracker bursts, the vector sum of the momenta of its fragments adds up to the firecracker’s momentum just before bursting.
PHYSICS CONCEPT #8 – Energy can change from one form to another without a net loss or gain
Work – work is done when a force acts on an object and the object moves in the direction of the force.
** Work is the product of the force on an object and the distance through which the object is moved.
** in the simplest case, when the force is constant, the motion takes place in a straight line in the direction of the force: work = force x distance In equation form, W = Fd
** Work generally falls into two categories: work done against another force and work done to change the speed of an object. In both categories, work involves a transfer of energy between something and its surroundings.
The unit of work is the Newton-meter (N-m), also called the joule. One joule (J) of work is done when a force of 1N is exerted over a distance of 1 m.
Power -- power equals the amount of work done divided by the time interval during which the work is done.
** Power is the rate at which work is done: power = work done/ time interval
** a high-power engine does work rapidly. If an engine has twice the power of another engine, this means that it can do twice the work in the same amount of time or the same amount of work in half the time.
** The unit of power is the joule per second, which is also known as the watt. One watt (W) of power is expended when one joule of work is done in one second.
** In the US, we customarily rate engines in units of horsepower and electricity in kilowatts, but either may be used. One horsepower (hp) is the same as 0.75 kW.
Mechanical Energy – the two forms of mechanical energy are kinetic energy and potential energy.
** The property of an object or system that enables it to do work is energy.
** Like work, energy is measured in joules.
** Mechanical energy is the energy due to the position of something or the movement of something.
Potential Energy – three examples of potential energy are elastic potential energy, chemical energy, and gravitational potential energy.
** Energy that is stored and held in readiness is called potential energy. (PE) because in the stored state it has the potential for doing work.
** A stretched or compressed spring, a bow that is drawn back, and a stretched rubber band have elastic potential energy.
** The chemical energy in fuels is potential energy at the submicroscopic level. This energy is available when a chemical change in the fuels takes place.
** The potential energy due to the elevated position of an object is gravitational potential energy.
** The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it. Gravitational potential energy = weight x height. In equation form, PE = mgh The height in this equation is the distance above some chosen reference level.
Kinetic Energy – the kinetic energy of a moving object is equal to the work required to bring it to its speed from rest, or the work the object can do while being brought to rest.
** The energy of motion is kinetic energy (KE)
** The kinetic energy of an object is equal to half the object’s mass multiplied by the square of its speed. In equation form, this is KE = ½ mv2
** The net force on an object multiplied by the distance along which the force acts equals the object’s kinetic energy. In equation form, this is Fd = ½ mv2
Work-Energy Theorem – states that whenever work is done, energy changes
** The work-energy theorem describes the relationship between work and energy.
** Work equals change in kinetic energy. In equation form, Work = ∆KE, where the delta symbol,∆, means “change in”. The work in this equation is the net work.
** if you push a box across a floor at a constant speed, you are pushing just hard enough to overcome friction. In this example, the net force and net work are zero, and KE = 0.
** Kinetic energy often appears hidden in different forms of energy. Random molecular motion is sensed as heat. Sound consists of molecules vibrating in rhythmic patterns. Light energy originates in the motion of electrons in atoms. Electrons in motion make electric currents.
Conservation of Energy – the law of conservation of energy states that energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.
** The study of the various forms of energy and the transformations from one form into another is the law of conservation of energy.
** Everywhere along, the path of a pendulum bob, the sum of potential energy and kinetic energy is the same. At the highest points, the energy is only potential energy. At the lowest point, the energy is only kinetic energy.
** The sun shines because some of its nuclear energy is transformed into radiant energy. In nuclear reactors, nuclear energy is transformed into heat.
** Some electric-generating plants transform the energy of falling water into electrical energy. Electrical energy then travels through wires to homes.
Machines – transfer energy from one place to another or transforms it from one form to another.
** A machine is a device used to multiply forces or to change the direction of forces. A machine cannot put out more energy than is put into it.
** A lever is a simple machine made of a bar that turns about a fixed point.
** If heat from friction is negligible, the work put into a machine equals the work put out by the machine: work input = work output (force x distance)input = (force x distance) output
** The pivot point of a lever is the fulcrum.
** The ratio of output force to input force for a machine is called the mechanical advantage.
** A type 1 lever has the fulcrum between the input force and the load. If the fulcrum is closer to the load, a small input force exerted through a large distance produces a larger output force over a shorter distance. The directions of input and output are opposite.
** For a type 2 lever, the load is between the fulcrum and the input force. Force is increased at the expense of distance. Input and output forces have the same direction.
** In a type 3 lever, the fulcrum is at one end and the load is at the other. The input force is applied between them. The input and output forces have the same direction.
** A pulley is a kind of lever that can be used to change the direction of a force.
** A single pulley with a fixed axis behaves like a type 1 lever. A single pulley with an axis that moves behaves like a type 2 lever.
** A system of pulleys multiplies the force and it may change the direction of the force. The mechanical advantage for a simple pulley system is the same as the number of strands of rope that actually support the load.
Efficiency – in any machine, some energy is transformed into atomic or molecular kinetic energy- making the machine warmer.
** The efficiency of a machine is the ratio of useful energy output to total energy input, or the percentage of the work input that is converted to work output. No real machine can be 100% efficient. The wasted energy is dissipated as heat.
** An inclined plane is a machine. Its theoretical mechanical advantage, assuming negligible friction, is the length of the incline divided by the height of the inclined plane.
** Efficiency can also be expressed as the ration of actual mechanical advantage to the theoretical mechanical advantage.
** To convert efficiency to percent, express it as a decimal and multiply by 100%.
Energy for Life – there is more energy stored in the molecules in food than there is in the reaction products after the food is metabolized. This energy difference sustains life.
** most living organisms on this planet feed on various hydrocarbon compounds that release energy when they react with oxygen. In metabolism of food in the body, carbon combines with oxygen to form carbon dioxide.
** Only green plants and certain one-celled organisms can make carbon dioxide combine with water to produce hydrocarbon compounds such as sugar. This process is called photosynthesis and requires an energy input, which normally comes from sunlight.
Sources of Energy—The sun is the source of practically all our energy on Earth.
** Sunlight is directly transformed into electricity by photovoltaic cells or in the flexible solar shingles on the roofs of buildings. We use the energy in sunlight to generate electricity indirectly as well.
** Wind, caused by unequal warming of Earth’s surface, is another form of solar power. Wind can be used to turn generator turbines within specially equipped windmills.
** Hydrogen is the least polluting of all fuels. Because it takes energy to make hydrogen (to extract it from water and carbon compounds), it is not a source of energy. In a fuel cell, hydrogen and oxygen gas are compressed at electrodes to produce water and electric current.
** The most concentrated form of usable energy is stored in nuclear fuels.
** Earth’s interior is kept hot by producing a form of nuclear power, radioactivity.
** Geothermal energy is held in underground reservoirs of hot water.
PHYSICS CONCEPT #9 —Centripetal force keeps an object in circular motion
Rotation and Revolution – two types of circular motion are rotation and revolution
** An axis is the straight line around which rotation takes place.
** When an object turns about an internal axis – that is, an axis located within the body of the object – the motion is called rotation, or spin. A Ferris wheel rotates about an axis.
** When an object turns about an external axis, the motion is called revolution. Riders revolve about the axis of a Ferris wheel.
** Earth undergoes both types of circular motion. It revolves around the sun once every 365 ¼ days, and it rotates around an axis passing through its geographical poles once every 24 hours.
Rotational Speed – tangential speed depends on rotational speed and the distance from the axis of rotation.
** Linear speed is the distance traveled per unit time. The linear speed is greater on the outer edge of a rotating object, such as a merry-go-round, than it is closer to the axis.
** Tangential speed is the speed of something moving along a circular path. For circular motion, the terms linear speed and tangential speed are interchangeable.
** Rotational speed, which is sometimes called angular speed, is the number of rotations per unit of time. All parts of a merry-go-round have the same rotational speed.
** Tangential speed and rotational speed are related.
Tangential speed ~ radial distance x rotational speed
v ~ rw
** As you move away from the axis of a rotating platform, your tangential speed increases while your rotational speed stays the same.
** Wheels of a train stay on the track because their rims are slightly tapered. So when a train rounds a curve, wheels on the outer track ride on the wider part of the tapered rims (and cover a greater distance in the same time) while opposite wheels ride on their narrow parts (covering a smaller distance in the same time)
Centripetal Force – the centripetal force on an object depends on the object’s tangential speed, its mass, and the radius of its circular path.
** Any object moving in a circle undergoes an acceleration that is directed to the center of the circle. This is centripetal acceleration. Centripetal means “toward the center”.
** The force directed toward a fixed center that causes an object to follow a circular path is called centripetal force.
** Centripetal forces can be exerted in a variety of ways. Anything that moves in a circular path is acted on by a centripetal force.
** Centripetal force can be calculated using the following equation:
Centripetal force = mass x speed 2 / radius of curvature
Fc = mv2/r
** Centripetal force Fc is measured in newtons when mass m is expressed in kilograms, speed v in m/s, and radius of curvature r in meters.
** The centripetal force acting on a circularly moving object is the net force that acts exactly along the radial direction – toward the center of the circular path.
Centripetal and Centrifugal Forces -- The “centrifugal-force effect” is attributed not to any real force but to inertia – the tendency of the moving body to follow a straight-line path.
** The apparent outward force on a rotating or revolving body is called centrifugal force. Centrifugal means “center-fleeing,” or “away from the center.”
** If you are in a car that rounds a sharp corner to the left, you tend to pitch outward against the right door. This happens not because of some outward or centrifugal force, but because there is no centripetal force holding you in a circular motion.
** Likewise, the only force exerted on a whirling can at the end of a string is centripetal force. No outward force acts on the can.
Centrifugal Force in a Rotating Reference Frame—Centrifugal force is an effect of rotation. It is not part of an interaction and therefore it cannot be a true force.
** Because centrifugal force is merely an effect of rotation, it is not a true force like gravitational, electromagnetic, and nuclear forces.
** Physicists refer to centrifugal force as a “fictitious force.”
** To observers in a rotating system, however, centrifugal force is very real.
PHYSICS CONCEPT #10: An object will remain upright if its center of mass is above the area of support.
Torque – to make an object turn or rotate, apply a torque.
** Torque is produced by a turning force and tends to produce rotational acceleration.
** Force and torque are different; forces tend to make things accelerate whereas torques produce rotation.
** A torque is produced when a force is applied with “leverage.” You use leverage when you use a screwdriver to open the lid of a paint can.
** The lever arm is the distance from the turning axis to the point of contact.
** Torque can be calculated using the following equation: torque = force 1 x lever arm
Balanced Torques -- when balanced torques act on an object, there is no change in rotation.
** Children of unequal weight can balance on a seesaw by sitting at different distances from the pivot point.
** Scales balances with sliding weights are based on balanced torques.
Center of Mass – the center of mass of an object is the point located at the object’s average position of mass.
** The point where all of the mass of an object can be considered concentrated is called the center of mass.
** For a symmetrical object, the center of mass is at the geometric center of the object. For irregularly shaped objects, the location of the center of mass varies.
** Spin can be applied to an object by applying a force that does not pass through the object’s center of mass. Kicking a football in the middle, for example, will make it travel without rotating.
Kicking the football above or below its center will make it rotate.
Center of Gravity – for everyday objects, the center of gravity is the same as the center of mass
** The center of gravity, or CG, is the average position of all of the particles of weight that make up an object. For most objects on and near Earth, the terms center of mass and center of gravity are interchangeable.
** If you throw a wrench so that it rotates as it moves through the air, you’ll see it wobble about its CG. The center of gravity itself would follow a parabolic path.
** An object’s CG is its balance point; supporting the CG supports the entire object. A meter stick can be balanced by applying a force at its geometric midpoint – the location of its CG.
** Any object suspended at a single point will hang with its CG directly below the point of suspension.
Torque and Center of Gravity – if the center of gravity of an object is above the area of support, the object will remain upright.
** If the CG extends outside the area of support, an unbalanced torque exists, and the object will topple.
** The Leaning Tower of Pisa does not topple because its CG does not extend beyond its base.
** It is difficult to balance a broom upright in the palm of your hand because the support base is small and far beneath the CG.
Center of Gravity of People – the center of gravity of a person is not located in a fixed place, but depends on body orientation.
** When you stand erect with your arms at your sides, your CG is within your body.
** The CG us slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.
** Raising your arms vertically over your head raises your CG by several centimeters.
** When you stand, your CG is somewhere above your support base, which is the area bounded by your feet.
Stability – when an object is toppled, the center of gravity of that object is raised, lowered, or unchanged.
** An object balanced so that any displacement lowers its center of mass is in unstable equilibrium.
** An object balanced so that any displacement raises its center of mass is in stable equilibrium. Raising the CG of an object in stable equilibrium requires increasing the object’s potential energy, which requires work.
** An object balanced so that any small movement neither raises nor lowers its center of gravity is in neutral equilibrium.
** An object with a low CG is usually more stable than an object with a relatively high CG.
PHYSICS CONCEPT #11 – Rotating objects tend to keep rotating while nonrotating objects tend to remain nonrotating.
Rotational Inertia – the greater the rotational inertia, the more difficult it is to change the rotational speed of an object.
** The resistance of an object to change in its rotational motion is called rotational inertia, or moment of inertia.
** A torque is required to change the rotational state of motion of an object.
** Rotational inertia depends on mass and how the mass is distributed. The greater the distance between an object’s mass concentration and the axis of rotation, the greater the rotational inertia.
** A short pendulum has less rotational inertia and therefore swings back and forth more frequently than a long pendulum. Likewise, bent legs swing back and forth more easily than outstretched legs.
** Formulas to calculate rotational inertia for different objects vary and depend on the shape of an object and the location of the rotational axis.
Rotational Inertia and Gymnastics – The three principal axes of rotation in the human body are the longitudinal axis, the transverse axis, and the medial axes.
** The three axes of rotation in the human body are at right angles to one another. All three axes pass through the center of gravity of the body.
** The vertical axis that passes from the head to toe is the longitudinal axis. Rotational inertia about this axis is increased by extending a leg or the arms.
** You rotate about your transverse axis when you perform a somersault or a flip. Tucking in your arms and legs reduces your rotational inertia about the transverse axis; straightening your arms and legs increases your rotational inertia about this axis.
** The third axis of rotation for the human body is the front-to-back axis, or medial axis. You rotate about the medial axis when executing a cartwheel.
Rotational Inertia and Rolling – Objects of the same shape but different sizes accelerate equally when rolled down an incline.
** An object with a greater rotational inertia takes more time to get rolling than an object with a smaller rotational inertia. A hollow cylinder, for example, rolls down an incline much slower than a solid cylinder.
** All objects of the same shape roll down an incline with the same acceleration, even if their masses are different.
Angular Momentum – Newton’s first law of inertia for rotating systems states that an object or system of objects will maintain its angular momentum unless acted upon by an unbalanced external torque.
** All moving objects have momentum.
** Linear momentum is the product of the mass and velocity of an object.
** Rotating objects have angular momentum. Angular momentum is the product of rotational inertia, I , and rotational velocity, w.
angular momentum = rotational inertia x rotational velocity
angular momentum = I x w
** When a direction is assigned to rotational speed, it is called rotational velocity.
** When an object is small compared with the radial distance to its axis of rotation, its angular momentum is equal to the magnitude of its linear momentum, mv , multiplied by the radial distance, r.
angular momentum = mvr
** A moving bicycle is easier to balance than a bicycle at rest because of the angular momentum provided by the spinning wheels.
Conservation of Angular Momentum – it is conserved when no external torque acts on an object.
** The law of conservation of angular momentum states that if no unbalanced external torque acts on a rotating system, the angular momentum of the system is constant.
** A person who spins with arms extended obtains greater rotational speed when the arms are drawn in. In other words, whenever a rotating body contracts, its rotational speed increases.
** Zero-angular-momentum twists and turns are performed by turning one part of the body against the other.
Simulated Gravity – from within a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.
** Occupants in today’s space vehicles feel weightless because they lack a support force. Future space habitats will probably spin, effectively supplying a support force that simulates gravity.
** We experience 1 g on Earth’s surface due to gravity. Small-diameter space structures would have to rotate at high speeds to provide a simulated gravitational acceleration of 1 g.
PHYSICS CONCEPT #12 – Everything pulls on everything else.
The Falling Apple -- Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree – they are both pulled by Earth’s gravity.
** Newton understood the concept of inertia, that without an outside force, moving objects continue to move at constant speed in a straight line. He knew that if an object undergoes a change in speed or direction, then a force is responsible.
The Falling Moon – the moon is actually falling toward Earth but has great enough tangential velocity to avoid hitting Earth.
** Newton reasoned that the moon must be falling around Earth. The moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it. He hypothesized that the moon was a projectile circling Earth under the attraction of gravity.
** Newton compared the motion of the moon to a cannonball fired from the top of a high mountain. If the cannonball were fired with enough speed, its path would become a circle and the cannonball would circle indefinitely.
** both the orbiting cannonball and the moon have a component of velocity parallel to Earth’s surface. This sideways or tangential velocity is sufficient to ensure nearly circular motion around Earth rather than into it.
** Newton reasoned that the mass of the moon should not affect how it falls, just as mass has no effect on the acceleration of freely falling objects on Earth. How far the moon falls should relate only to its distance from Earth’s center.
The Falling Earth – Newton’s theory of gravity confirmed the Copernican theory of the solar system.
** The planets don’t crash into the sun because they have tangential velocities. If the tangential velocities of the planets were reduced to zero, their motion would be straight toward the sun and they would indeed crash into it. Any objects in the solar system with insufficient tangential velocities have long ago crashed into the sun.
Newton’s Law of Universal Gravitation – gravity in universal, everything pulls on everything else in a way that involves only mass and distance.
** Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.
** The law of universal gravitation can be expressed in equation form:
F = G (m1m2/d2), where m1 and m2 are the objects’ masses, and d is the distance between their centers of mass.
** The universal gravitational constant, G, in the equation describes the strength of gravity. In scientific notation, G = 6.67 x 10-11 N-m2/kg2 . The value of G tells us that the force of gravity is a very weak force. It is the weakest of the presently known four fundamental forces.
Gravity and Distance: The Inverse-Square Law – gravity decreases according to the inverse square law. The force of gravity weakens as the square of distance.
** When a quantity varies as the inverse square of its distance from its source, it follows and inverse-square law. For example, the inverse square of 3 is (1/3)2 or 1/9
** This law applies to all cases where the effect from a localized source spreads evenly throughout the surrounding space, such as the weakening of gravity with distance. Other examples are light, radiation, and sound.
Gravitational Field – Earth can be thought of as being surrounded by a gravitational field that interacts with objects and causes them to experience gravitational forces.
** A gravitational field occupies the space surrounding a massive body. A gravitational field is an example of a force field, for any mass in the field space experiences a force.
** Iron filings sprinkled over a sheet of paper on top of a magnet reveal the shape of the magnet’s
magnetic field. The pattern of filings shows the strength and direction of the magnetic field at different locations around the magnet. Earth is a giant magnet and, like all magnets, is surrounded by a magnetic field.
** The strength of Earth’s gravitational field, like the strength of its force on objects, follows the inverse-square law. Earth’s gravitational field is strongest near Earth’s surface and weaker at greater distances from Earth.
Gravitational Field Inside a Planet – the gravitational field of Earth at its center is zero.
** The gravitational field of Earth exists inside Earth as well as outside.
** If you traveled through an imaginary hole drilled completely through Earth, you’d gain speed as you fell from the North Pole toward the center of Earth, and lose speed moving away from the center toward the South Pole.
Weight and Weightlessness – pressure against Earth is the sensation we interpret as weight.
** The force of gravity, like any force, causes acceleration. Because we are almost always in contact with Earth, we think of gravity primarily as something that presses us against Earth rather than something that accelerates us.
** If you stand on a scale, gravity pulls you against the supporting floor and scale, and the floor and scale push upward on you. This pair of forces compresses a spring-like gauge inside the scale. The weight reading on the scale is linked to the amount of compression.
** Weightlessness is not the absence of gravity; rather, it is the absence of a support force. Astronauts in orbit are without a support force and experience weightlessness.
Ocean Tides – Newton showed that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of Earth.
** The moon’s gravitational attraction is stronger on Earth’s oceans closer to the moon, and weaker on the oceans farther from the moon. This difference causes the oceans to bulge out on opposite sides of Earth. Because Earth spins, a fixed point on Earth passes beneath both bulges each day, producing two high tides and two low tides.
** A spring tide is a high or low tide that occurs when the sun, Earth, and moon are all lined up.
The tides due to the sun and the moon coincide, making high tides higher than average and low tides lower than average. Spring tides occur during a new or full moon.
** A neap tide occurs when the moon is halfway between a new moon and a full moon. The pulls of the moon and sun are perpendicular to each other. As a result, the solar and lunar tides do not overlap, so the high tides are not as high and low tides are not as low.
Black Holes – when a massive star collapses into a black hole, there is no change in the gravitational field at any point beyond the original radius of the star.
** Two main processes occur continuously in stars like our sun: gravitation, which tends to pull solar material inward, and thermonuclear fusion, which blows material outward.
** If the fusion rate increases, the sun will get hotter and bigger; if the fusion rate decreases, the sun will get cooler and smaller.
** When the sun runs out of fusion fuel (hydrogen), gravitation will dominate and the sun will start to collapse. The collapse will cause helium to fuse into carbon, and the sun will expand into a red giant. When the helium is used up, the sun will collapse into a black dwarf.
** For stars more massive than the sun, once thermonuclear fusion ends, gravitational collapse will take over, eventually forming a black hole. The density of a black hole is so great that its enormous gravitational field prevents even light from escaping. The gravitational field beyond the original radius of the star is no different after the collapse than before.
Universal Gravitation – The formulation of the law of universal gravitation is one of the major reasons for the success in science that followed, for it provided hope that other phenomena of the world might also be described by equally simple and universal laws.
** Earth is round because of gravitation. Earth attracted itself together before it became solid. Any “corners” of Earth have been pulled in so that Earth is a giant sphere.
** The solar system began when a slightly rotating ball of interstellar gas contracted due to mutual gravitation. To conserve angular momentum, the rotational speed of the ball of gas increased, causing the particles to sweep out into a disk shape.
** The deviation of an orbiting object from its path around a center of force caused by the action of an additional center of force is called a perturbation.
** The planet Neptune was discovered when a perturbation in the orbit of Uranus led scientists to conclude that a disturbing body beyond the orbit of Uranus was the culprit.
** According to current scientific understanding, the universe originated and grew from the explosion of a primordial fireball some 13.7 billon years ago. This is the “Big Bang” theory of the origin of the universe. All the matter of the universe was hurled outward from this event and continues in an outward expansion.
** More recent evidence suggests the universe is not only expanding, but accelerating outward. It is pushed by an antigravity dark energy that makes up an estimated 73 percent of the universe. Twenty-three percent of the universe is composed of the yet-to-be discovered particles of exotic dark matter. Ordinary matter makes up only 4 percent.
Physics Concept #13 -- The path of an Earth satellite follows the curvature of Earth.
Earth Satellites -- A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time of 1 second it takes to fall 4.9 m, will orbit the earth.
** An Earth satellite is a projectile moving fast enough to fall continually around Earth rather than into it.
** A geometric fact about the curvature of Earth is that its surface drops a vertical distance of nearly 5 meters for every 8000 meters tangent to its surface.
** The orbital speed for close orbit about Earth is 8 km/s (29,000 km/h or 18,000 mi/h)
** A satellite must stay about 150 kilometers or more above Earth’s surface to keep from burning due to the friction of the atmosphere.
Circular Orbits -- A satellite in circular orbit around Earth is always moving perpendicularly to gravity and parallel to Earth’s surface at constant speed.
** In circular orbit the speed of a circling satellite is not changed by gravity.
** A satellite is always moving at a right angle(perpendicular) to the force of
gravity, so that no change in speed occurs -- only a change in direction.
** For a satellite close to Earth, the time for a complete orbit around Earth, its
period, is about 90 minutes.
Elliptical Orbits -- A satellite in orbit around Earth traces an oval-shaped path
called an ellipse.
** An ellipse is the closed path taken by a point that moves is such a way that
the sum of its distances from two fixed points is constant.
** The two fixed points in an ellipse are called foci.
** Satellite speed, which is constant in a circular orbit, varies in a elliptical orbit.
Energy Conservation and Satellite Motion: The sum of the KE and PE of a
satellite is constant at all points along an orbit.
** In an elliptical orbit, the apogee is the point in a satellite's orbit farthest from
the center of Earth, and the perigee is the point in a satellite's orbit closest to
the center of Earth.
** The PE is greatest when the satellite is at the apogee and least when the
satellite is at the perigee.
** The KE will be least when the PE is most, and the KE will be most when the PE
is least. At every point in the orbit, the sum of the KE and PE is constant.
Kepler's Laws of Planetary Motion -- Kepler's 1st law states that the path of each
planet around the sun is an ellipse with the sun at one focus. Kepler's 2nd law
states that each planet moves so that an imaginary line drawn from the sun to
any planet sweeps out equal areas of space in equal time intervals. Kepler's
3rd law states that the square of the orbital period of a planet is directly
proportional to the cube of the average distance of the planer from the sun.
** Kepler's laws apply not only to planets but also to moons or any satellite in
orbit around any body.
** Kepler found that the planets do not go around the sun at uniform speed but
move faster when they are nearer the sun and more slowly when they are
farther from the sun.
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