Conceptual Physics Fundamentals - Chap5.pdf · 2015. 8. 23. · The momentum becomes zero in both...

Conceptual Physics

Fundamentals

Chapter 5:

MOMEMTUM AND ENERGY

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

Momentum and Energy

“Human history becomes more and more a

race between education and catastrophe.”

—H. G. Wells

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)

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.

A moving object has

A. momentum.

B. energy.

C. speed.

D. all of the above

Momentum

CHECK YOUR NEIGHBOR

A moving object has

A. momentum.

B. energy.

C. speed.

D. all of the above

Momentum

CHECK YOUR ANSWER

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.

Momentum

CHECK YOUR NEIGHBOR

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.

Momentum

CHECK YOUR ANSWER

Impulse

• product of force and time (force time)

• in equation form: impulse = Ft

example: • 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.

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

twice the impulse and produce twice the change in momentum.

Impulse Changes Momentum

The greater the impulse exerted on

something, the greater the change in

momentum. • in equation form: Ft = (mv)

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.

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

• Case 1: increasing momentum – apply the greatest force for as long as possible and

you extend the time of contact

– force can vary throughout the duration of contact

examples: • golfer swings a club and follows through

• baseball player hits a ball and follows through

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

CHECK YOUR NEIGHBOR

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.)

CHECK YOUR ANSWER

• Case 2: decreasing momentum over a long time

– extend the time during which momentum is

reduced

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

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

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

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

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

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

• Case 3: decreasing momentum over a short time

– short time interval produces large force

example: Karate expert splits a

stack of bricks by bringing her

arm and hand swiftly against

the bricks with considerable

momentum. Time of contact is

brief and force of impact is huge.

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.

Bouncing

Pelton wheel designed to “bounce” water when it

makes a U-turn when it impacts the curved

paddle

Conservation of Momentum

Law of conservation of momentum:

In the absence of an external force, the

momentum of a system remains unchanged.

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.

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.

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

Collisions

• elastic collision

– occurs when colliding objects rebound without

lasting deformation or any generation of heat

Collisions

• inelastic collision

– occurs when colliding objects result in

deformation and/or the generation of heat

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

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

Collisions

CHECK YOUR NEIGHBOR

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?

Collisions

CHECK YOUR ANSWER

Momemtum Video

Conservation of momentum in space

http://www.youtube.com/watch?v=4IYDb6K5

Physics class room explanation

http://www.physicsclassroom.com/class/mo

mentum/u4l2b.cfm

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

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

• 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

If you push against a stationary brick wall for several

minutes, you do no work

A. on the wall.

B. at all.

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

examples:

• twice as much work is done in lifting 2 loads 1- story

high versus lifting 1 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 2 stories

instead of 1 story

reason: distance is twice as great

Work example:

• a weightlifter raising a barbell from

the floor does work on the barbell

Unit of work:

Newton-meter (Nm)

or Joule (J)

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

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

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.

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

Potential Energy

• stored energy held in readiness with a potential

for doing work

example:

• a stretched bow has stored energy that can do work

on an arrow

• a stretched rubber band of a slingshot has stored

energy and is capable of doing work

Potential Energy

Gravitational potential energy

• potential energy due to elevated position

example:

• water in an elevated reservoir

• 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

Does a car hoisted for repairs in a service station have

increased potential energy relative to the floor?

A. yes

C. sometimes

D. not enough information

Potential Energy

CHECK YOUR NEIGHBOR

Does a car hoisted for repairs in a service station have

increased potential energy relative to the floor?

A. yes

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 Energy

CHECK YOUR ANSWER

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

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

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

Kinetic Energy

CHECK YOUR NEIGHBOR

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

Explanation:

Acceleration, speed being a scalar, and velocity being a vector

quantity, are irrelevant. Any moving object has both momentum

and kinetic energy.

Kinetic Energy

CHECK YOUR ANSWER

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

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

• also applies to changes in potential energy

Work-Energy Theorem • applies to decreasing speed

– 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)

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

A. F = ma.

B. Ft = mv.

C. KE = 1/2mv2.

D. Fd = 1/2mv2.

Work-Energy Theorem

CHECK YOUR NEIGHBOR

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

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 Theorem

CHECK YOUR ANSWER

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 Theorem

CHECK YOUR NEIGHBOR

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.

D. none of the above.

Explanation:

Twice the speed means four times the kinetic energy and four

times the stopping distance.

Work-Energy Theorem

CHECK YOUR ANSWER

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.

example: energy transforms without net loss or net

gain in the operation of a pile driver

A 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.

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.

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

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 and therefore is

directional and can be cancelled

• kinetic energy is a scalar quantity and can never

be cancelled

Kinetic Energy and Momentum

Compared • velocity dependence

– momentum depends on velocity

– 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 4 times the kinetic energy.

• measure of how fast work is done

Power = work donetime interval

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.

Unit of power

— joule per second, called the watt after James

Watt, developer of the steam engine

• 1 joule/second = 1 watt

• 1 kilowatt = 1000 watts

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.

CHECK YOUR NEIGHBOR

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.

CHECK YOUR ANSWER

Energy, Work and Power

http://www.youtube.com/watch?v=pDK2p1QbPKQ&feature

=related

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

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

Machines Simplest machine

• lever

– rotates on a point of support called the

fulcrum

– allows small force over a large distance and

large force over a short distance

Machines

• pulley

– 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

Machines

• operates as a system of pulleys (block and tackle)

• multiplies force

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.

Machines

CHECK YOUR NEIGHBOR

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.

Machines

CHECK YOUR ANSWER

Efficiency

• percentage of work put into a machine that is

converted into useful work output

useful energy outputefficiencytotal energy input

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.

Efficiency

CHECK YOUR NEIGHBOR

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.

Efficiency

CHECK YOUR ANSWER

Sources of Energy

Sources of energy

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.

Sources of Energy

Concentrated energy

• nuclear power

– stored in uranium and plutonium

– byproduct is geothermal energy

• held in underground reservoirs of hot water to

provide steam that can drive turbogenerators

Sources of Energy

• dry-rock geothermal power is a producer of

electricity

– Water 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.

Conceptual Physics Fundamentals - Chap5.pdf · 2015. 8. 23. · The momentum becomes zero in both...

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