copyright © 2008 pearson education, inc., publishing as pearson addison-wesley conceptual physics...

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

Conceptual Physics Fundamentals

Chapter 5:

MOMEMTUM AND ENERGY

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This lecture will help you understand:

Momentum Impulse Impulse Changes Momentum Bouncing Conservation of Momentum Collisions Energy Work Potential Energy Work-Energy Theorem Conservation of Energy Power Machines Efficiency Sources of Energy

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Momentum and Energy

“Human history becomes more and more a race between education and catastrophe.”

—H. G. Wells

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Momentum

a property of moving things means inertia in motion more specifically, mass of an object multiplied by

its velocity in equation form: mass velocity

(momentum = mv)

4


Momentum

example: A moving boulder has more

momentum than a stone rolling at the same speed.

A fast boulder has more momentum than a slow boulder.

A boulder at rest has no momentum.

5


A moving object has ________________.

A. momentum

B. energy

C. speed

D. all of the above

MomentumCHECK YOUR NEIGHBOR

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A moving object has ________________.

A. momentum

B. energy

C. speed

D. all of the above

MomentumCHECK YOUR ANSWER

7


When the speed of an object is doubled, its momentum ________________.

A. remains unchanged in accord with the conservation of momentum

B. doubles

C. quadruples

D. decreases

MomentumCHECK YOUR NEIGHBOR

8


When the speed of an object is doubled, its momentum ________________.

A. remains unchanged in accord with the conservation of momentum

B. doubles

C. quadruples

D. decreases

MomentumCHECK YOUR ANSWER

9


Impulse

Impulse product of force and time (force time) in equation form: impulse = Ft

example: o A brief force applied over a short time interval produces a

smaller change in momentum than the same force applied over a longer time interval.

oro If you push with the same force for twice the time, you impart

twice the impulse and produce twice the change in momentum.

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Impulse Changes Momentum

The greater the impulse exerted on something, the greater the change in momentum. in equation form: Ft = (mv)

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When the force that produces an impulse acts for twice as much time, the impulse is ________________.

A. not changed

B. doubled

C. quadrupled

D. halved

Impulse Changes MomentumCHECK YOUR NEIGHBOR

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When the force that produces an impulse acts for twice as much time, the impulse is ________________.

A. not changed

B. doubled

C. quadrupled

D. halved

Impulse Changes MomentumCHECK YOUR ANSWER

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Impulse Changes Momentum Case 1: increasing momentum

o Apply the greatest force for as long as possible, and you extend the time of contact.

o Force can vary throughout the duration of contact.examples:

• golfer swings a club and follows through• baseball player hits a ball and follows through

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A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater ________________.

A. average force

B. impulse

C. both of the above

D. neither of the above


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A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater ________________.

A. average force

B. impulse


D. neither of the above

Explanation:

The force on the cannonball will be the same for a short- or long-barreled cannon. The longer barrel provides for a longer time for the force to act, and therefore, a greater impulse. (The long barrel also provides a longer distance for the force to act, providing greater work and greater kinetic energy of the cannonball.)


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Case 2: decreasing momentum over a long timeo extend the time during which momentum is

reduced

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A fast-moving car hitting a haystack or a cement wall produces vastly different results.1. Do both experience the same change in momentum?2. Do both experience the same impulse?3. Do both experience the same force?

A. yes for all three

B. yes for 1 and 2

C. no for all three

D. no for 1 and 2


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A fast-moving car hitting a haystack or hitting a cement wall produces vastly different results.1. Do both experience the same change in momentum?2. Do both experience the same impulse?3. Do both experience the same force?

A. yes for all three

B. yes for 1 and 2

C. no for all three

D. no for 1 and 2

Explanation: Although stopping the momentum is the same whether done slowly or quickly, the force is vastly different. Be sure to distinguish between momentum, impulse, and force.


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When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!)

A. no, both are the same

B. yes, less if it lands on the carpet

C. no, less if it lands on a hard floor

D. no, more if it lands on a hard floor


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When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!)

A. no, both are the same

B. yes, less if it lands on the carpet

C. no, less if it lands on a hard floor

D. no, more if it lands on a hard floor

Explanation:

The momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended. Be careful to distinguish between force, impulse, and momentum.


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examples: When a car is out of control, it is better to hit a haystack than a concrete wall.

physics reason: same impulse either way, but extension of hitting time reduces the force

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example (continued):

In jumping, bend your knees when your feet make contact with the ground because the extension of time during your momentum decrease reduces the force on you.

In boxing, ride with the punch.

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Impulse Changes Momentum Case 3: decreasing momentum over a short time

o short time interval produces large forceexample: Karate expert splits astack of bricks by bringing her arm and hand swiftly againstthe bricks with considerablemomentum. Time of contact is brief and force of impact is huge.

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Bouncing

Impulses are generally greater when objects bounce. example:

Catching a falling flower pot from a shelf with your hands: You provide the impulse to reduce its momentum to zero. If you throw the flower pot up again, you provide an additional impulse. This “double impulse” occurs when something bounces.

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BouncingPelton wheel designed to “bounce” water when it makes a U-turn as it impacts the curved paddle

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Conservation of Momentum

Law of conservation of momentum:In the absence of an external force, the momentum of a system remains unchanged.

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examples: When a cannon is fired, the force on cannonball

inside the cannon barrel is equal and opposite to the force of the cannonball on the cannon.

The cannonball gains momentum, while the cannon gains an equal amount of momentum in the opposite direction—the cannon recoils.

When no external force is present, no external impulse is present, and no change in momentum is possible.

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examples (continued): Internal molecular forces within a baseball come in

pairs, cancel one another out, and have no effect on the momentum of the ball.

Molecular forces within a baseball have no effect on its momentum.

Pushing against a car’s dashboard has no effect on its momentum.

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Collisions

For all collisions in the absence of external forces

net momentum before collision equals net momentum after collision

in equation form:

(net mv)before = (net mv)after

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Collisions

elastic collisiono occurs when colliding objects rebound without

lasting deformation or any generation of heat

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Collisions

inelastic collisiono occurs when colliding objects result in

deformation and/or the generation of heat

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Collisions

example of elastic collision:

single car moving at 10 m/s collides with another car of the same mass, m, at rest

From the conservation of momentum,

(net mv)before = (net mv)after

(m 10)before = (2m V)after

V = 5 m/s

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Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is ________________.

A. the same

B. half

C. twice

D. none of the above

CollisionsCHECK YOUR NEIGHBOR

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Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is ________________.

A. the same

B. half

C. twice


Explanation:

After the collision, the mass of the moving freight cars has doubled. Can you see that their speed is half the initial velocity of freight car A?

CollisionsCHECK YOUR ANSWER

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Energy

A combination of energy and matter make up the universe.

Energy mover of substances both a thing and a process observed when it is being transferred or being

transformed a conserved quantity

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Energy

property of a system that enables it to do work anything that can be turned into heat

example: electromagnetic waves from the Sun

Matter substance we can see, smell, and, feel occupies space

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Work

Work• involves force and distance• is force distance• in equation form: W = Fd

Two things occur whenever work is done:• application of force• movement of something by that force

38


If you push against a stationary brick wall for several minutes, you do no work ________________.

A. on the wall

B. at all



WorkCHECK YOUR NEIGHBOR

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If you push against a stationary brick wall for several minutes, you do no work ________________.

A. on the wall

B. at all



Explanation:

You may do work on your muscles, but not on the wall.

WorkCHECK YOUR ANSWER

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Work

examples: twice as much work is done in lifting two loads one-

story high versus lifting one load the same vertical distance

reason: force needed to lift twice the load is twice as much

twice as much work is done in lifting a load two stories instead of one story

reason: distance is twice as great

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Workexample: A weightlifter raising a barbell from

the floor does work on the barbell.

Unit of work:Newton-meter (Nm)or Joule (J)

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Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance?

A. twice as much

B. half as much

C. the same

D. depends on the speed of the lift


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Work is done in lifting a barbell. How much work is done in lifting a barbell that is twice as heavy the same distance?

A. twice as much

B. half as much

C. the same

D. depends on the speed of the lift

Explanation:

This is in accord with work = force distance. Twice the force for the same distance means twice the work done on the barbell.


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You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is ________________.

A. less than twice as much

B. twice as much

C. more than twice as much

D. zero


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You do work when pushing a cart with a constant force. If you push the cart twice as far, then the work you do is ________________.

A. less than twice as much

B. twice as much

C. more than twice as much

D. zero


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Potential Energy

Potential Energy stored energy held in readiness with a potential

for doing work

example: o A stretched bow has stored energy that can do work

on an arrow.o A stretched rubber band of a slingshot has stored

energy and is capable of doing work.

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Potential Energy

Gravitational potential energy potential energy due to elevated position

example: o water in an elevated reservoiro raised ram of a pile driver

equal to the work done (force required to move it upward the vertical distance moved against gravity) in lifting it

in equation form: PE = mgh

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Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?

A. yes

B. no

C. sometimes

D. not enough information

Potential EnergyCHECK YOUR NEIGHBOR

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Does a car hoisted for repairs in a service station have increased potential energy relative to the floor?

A. yes

B. no

C. sometimes

D. not enough information

Comment:

If the car were twice as heavy, its increase in potential energy would be twice as great.

Potential EnergyCHECK YOUR ANSWER

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Potential Energy

example: Potential energy of 10-N ball is the same in all 3 cases because work done in elevating

it is the same.

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Kinetic Energy

Kinetic Energy energy of motion depends on the mass of the object and its speed include the proportional constant 1/2 and KE =

1/2 mass speed squared If object speed is doubled kinetic energy is

quadrupled

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Must a car with momentum have kinetic energy?

A. yes, due to motion alone

B. yes, when motion is nonaccelerated

C. yes, because speed is a scalar and velocity is a vector quantity

D. no

Kinetic EnergyCHECK YOUR NEIGHBOR

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Must a car with momentum have kinetic energy?

A. yes, due to motion alone

B. yes, when momentum is nonaccelerated

C. yes, because speed is a scalar and velocity is a vector quantity

D. no

Explanation:

Acceleration, speed being a scalar, and velocity being a vector quantity, are irrelevant. Any moving object has both momentum and kinetic energy.

Kinetic EnergyCHECK YOUR ANSWER

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Kinetic Energy

Kinetic energy and work of a moving object equal to the work required to bring it from rest to

that speed, or the work the object can do while being brought to rest

in equation form: net force distance =

kinetic energy, or Fd = 1/2 mv2

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Work-Energy Theorem

Work-energy theorem gain or reduction of energy is the result of work in equation form: work = change in kinetic

energy (W = KE) doubling speed of an object requires 4 times the

work also applies to changes in potential energy

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Work-Energy Theorem applies to decreasing speed

o reducing the speed of an object or bringing it to a halt

example: applying the brakes to slow a moving car, work is done on it (the friction force supplied by the brakes distance)

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Consider a problem that asks for the distance of a fast-moving crate sliding across a factory floor and then coming to a stop. The most useful equation for solving this problem is ________________.

A. F = ma

B. Ft = mv

C. KE = 1/2mv2

D. Fd = 1/2mv2

Work-Energy TheoremCHECK YOUR NEIGHBOR

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Consider a problem that asks for the distance of a fast-moving crate sliding across a factory floor and then coming to a stop. The most useful equation for solving this problem is ________________.

A. F = ma

B. Ft = mv

C. KE = 1/2mv2

D. Fd = 1/2mv2

Comment:

The work-energy theorem is the physicist’s favorite starting point for solving many motion-related problems.

Work-Energy TheoremCHECK YOUR ANSWER

59


The work done in bringing a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is ________________.

A. actually less

B. about the same

C. twice


Work-Energy TheoremCHECK YOUR NEIGHBOR

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The work done in bringing a moving car to a stop is the force of tire friction stopping distance. If the initial speed of the car is doubled, the stopping distance is ________________.

A. actually less

B. about the same

C. twice


Explanation:

Twice the speed means four times the kinetic energy and four times the stopping distance.

Work-Energy TheoremCHECK YOUR ANSWER

61


Conservation of Energy

Law of conservation of energy Energy cannot be created or destroyed; it may

be transformed from one form into another, but the total amount of energy never changes.

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Conservation of Energy

example: energy transforms without net loss or net gain in the operation of a pile driver

63


Conservation of EnergyA situation to ponder…

Consider the system of a bow and arrow. In drawing the bow, we do work on the system and give it potential energy. When the bowstring is released, most of the potential energy is transferred to the arrow as kinetic energy, and some as heat to the bow.

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Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then ________________.

A. energy is not conserved

B. 10 joules go to warming the bow

C. 10 joules go to warming the target

D. 10 joules are mysteriously missing

A situation to ponder…CHECK YOUR NEIGHBOR

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Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then ________________.

A. energy is not conserved

B. 10 joules go to warming the bow

C. 10 joules go to warming the target

D. 10 joules are mysteriously missing

Explanation:

The total energy of the drawn bow, which includes the poised arrow is 50 joules. The arrow gets 40 joules and the remaining 10 joules warms the bow—still in the initial system.

A situation to ponder…CHECK YOUR ANSWER

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Kinetic Energy and Momentum Compared

Similarities between momentum and kinetic

energy Both are properties of moving things.

Difference between momentum and kinetic energy

Momentum is a vector quantity; therefore it is directional and can be cancelled.

Kinetic energy is a scalar quantity and can never be cancelled.

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Kinetic Energy and Momentum Compared

velocity dependenceoMomentum depends on velocity.o Kinetic energy depends on the square of

velocity.

example: An object moving with twice the velocity of another with the same mass, has twice the momentum but four times the kinetic energy.

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Power

Power measure of how fast work is done in equation form:

Power = work donetime interval

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Power

example: A worker uses more power running up the stairs than

climbing the same stairs slowly. Twice the power of an engine can do twice the work

of one engine in the same amount of time, or twice the work of one engine in half the time or at a rate at which energy is changed from one form to another.

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Power

Unit of powerjoule per second, called the watt after James Watt, developer of the steam engine

o 1 joule/second = 1 watto 1 kilowatt = 1000 watts

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A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of ________________.

A. energy

B. momentum

C. power

D. impulse

PowerCHECK YOUR NEIGHBOR

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A job can be done slowly or quickly. Both may require the same amount of work, but different amounts of ________________.

A. energy

B. momentum

C. power

D. impulse

Comment:

Power is the rate at which work is done.

PowerCHECK YOUR ANSWER

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Machines

Machine device for multiplying forces or changing the

direction of forces cannot create energy but can transform energy

from one form to another, or transfer energy from one location to another

cannot multiply work or energy

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Machines

Principle of a machine conservation of energy concept:

work input = work output input force input distance =

output force output distance

(force distance)input = (force distance)output

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MachinesSimplest machine lever

o rotates on a point of support called the fulcrum

o allows small force over a large distance and large force over a short distance

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Machines

pulleyo operates like a lever with equal arms— changes

the direction of the input force

example: This pulley arrangement can allow a load to be lifted with half the input force.

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Machines operates as a system of pulleys (block and

tackle) multiplies force

78


In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises ________________.

A. 50 centimeters

B. 45 centimeters

C. 25 centimeters


MachinesCHECK YOUR NEIGHBOR

79


In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises ________________.

A. 50 centimeters

B. 45 centimeters

C. 25 centimeters


Explanation:

Work in = work out; Fd in = Fd out.

One-fourth of 1 m = 25 cm.

MachinesCHECK YOUR ANSWER

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Efficiency

Efficiency percentage of work put into a machine that is

converted into useful work output in equation form:

=

useful energy outputefficiencytotal energy input

81


A certain machine is 30% efficient. This means the

machine will convert ________________.

A. 30% of the energy input to useful work—70% of the energy input will be wasted

B. 70% of the energy input to useful work—30% of the energy input will be wasted



EfficiencyCHECK YOUR NEIGHBOR

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A certain machine is 30% efficient. This means the

machine will convert ________________.

A. 30% of the energy input to useful work—70% of the energy input will be wasted

B. 70% of the energy input to useful work—30% of the energy input will be wasted



EfficiencyCHECK YOUR ANSWER

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Sources of Energy

Sun

example: Sunlight evaporates water; water falls as rain; rain

flows into rivers and into generator turbines, then back to the sea to repeat the cycle.

Sunlight can transform into electricity by photovoltaic cells.

Wind power turns generator turbines.

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Sources of Energy

Concentrated energy nuclear power

o stored in uranium and plutoniumo byproduct is geothermal energy

• held in underground reservoirs of hot water to provide steam that can drive turbogenerators

85


Sources of Energy

dry-rock geothermal power is a producer of electricity oWater is put into cavities in deep, dry, hot

rock. Water turns to steam and reaches a turbine, at the surface. After exiting the turbine, it is returned to the cavity for reuse.

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copyright © 2008 pearson education, inc., publishing as pearson addison-wesley conceptual physics...

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