Ch 7, Energy; Ex 4, 7, 13, 14, 44, 46; Pb 2, 6

**Ex7.4 When a rifle with a long barrel is fired, the force of expanding gases
acts on the bullet for a longer distance. What effect does this have on the
velocity of the emerging bullet? (Do you see why long-range cannons have such
long barrels?)**

Work = force x distancework = change in KE = change in [

^{1}/_{2}m v^{2}]The expanding gases exert a force on the bullet. This force is exerted over a distance so

workis done on the bullet. This work done on the bullet means its KE (kinetic energy) increases. If thedistanceover which the force acts increases, then the amount of work done on the bullet increases and the final value of its KE increases -- more KE means more speed! Long-rang cannons on naval ships are 10 or 15 meters long.

** **

**Ex 7.7 Can something have energy without having momentum? Explain. Can something
have momentum without having energy? Defend your answer.**

An object

at resthasnomomentum; its velocity iszero.But it can still have potential energy -- PE -- because of work we have done on it. We canliftan object and give it gravitational PE = m g h. It has PE because it cando workon something else as it falls -- or it can increase its own KE. Lifting the object, to give it PE, requires that work be done on it. If wecompress a spring, we must do work on it. That work is thenstoredin the compressed spring and is available to do work on something else. That means there isPEstored in acompressed spring. If we bend a bow we must do work on it. That work is thenstoredin the bent bow and is available to do work on something else. That means there isPEstored in abent bow. In all these cases, on object can haveenergy-- potential energy -- even though it is at rest; an object at rest has no momentum.However, if an object has momentum it has a velocity. And, if it has a velocity, it has

KE-- kinetic energy or energy of motion. So, if an object has momentum, it must also have energy.

** **

**Ex 7.13 At what point in its motion is the KE of a pendulum bob a maximum?
At what point is its PE a maximum? When its KE is half its maximum value, how
much PE does it have?**

The KE of a pendulum ismaximumat thebottomof its swing where its PE is minimum (or where we often take its PE to be zero).The PE of a pendulum is

maximumat thetopof its swing where it momentarily stops and its KE is zero.The total energy remains constant,

E = KE + PE So when the pendulum's KE is half its maximum value, its PE is half its maximum value if we have counted its PE as zero at the bottom of its swing.

**Ex 7.14 A Physics instructor demonstrates energy conservation by releasing
a heavy pendulum bob, as shown in the sketch, allowing it to swing to and fro.
What would happen if, in his exuberance, he gave the bob a slight shove as it
left his nose? Why?**

Ouch!If the bob starts off from rest, it will convert its PE into KE going down to the bottom of the swing and then convert KE back to PE and come to rest at the other end of its swing and then start back. On the way back, it increases its KE by reducing its PE until it comes to the bottom of the swing. On the last part of its swing, this KE decreases as it rises and increases its PE until the KE finally goes to zero and the pendulum comes to rest. With KE = 0, the PE must be equal to the total energy which is the original PE and it is back at its original height.

However,if the bob starts off with some KE because of a shove, then its total energy is greater than for the case just described. At the bottom of its swing, the pendulum will have a greater speed due to this increased energy. At the other end of the swing, it will come to rest at a greater height so its PE is greater. On the way back, that great height means it will smash our exuberant physicist in the nose!Ouch!

** **

**Ex 7.44 Scissors for cutting paper have long blades and short handles, whereas
metal-cutting shears have long handles and shout blades. Bolt cutters have very
long handles and very short blades. Why is this so?**

Scissors are levers. A longer blade with the short handles means that the longer blade moves a

greater distancebut withless forcewhen compared to the handles. Metal-cutting shears have blades that move asmallerdistancebut withmore force. The bolt cutters, with very short blades and very long handles, have blades that move andeven smaller distancebut witheven greater force.Input work is done by the "operator" as she or he exerts a force on the handles and moves them through a distance. Output work is done by the blade as it exerts a force and moves through a distance. These devices trade off moving a small force through a large distance, as with the scissors, or moving a greater force through a smaller distance.

** **

**Ex 7.44 Consider the swinging-balls apparatus, also known as Newton's pendulum.
If two balls are lifted and released, momentum is conserved as two balls pop
out the other side with the same speed as the released balls at impact. But
momentum would also be conserved if one ball popped out at twice the speed.
Can you explain why this never happens? (And why is this exercise in Chapter
6, on Energy, rather than Chapter 5, on Momentum?)**

Indeed,momentumwould be conserved if a single ball popped out with twice the original, incoming speed. We might write that asinitial momentum = (2 m) (v _{o}) = (m) (2 v_{o}) = final momentumBut what does that do to the KE? Remember that KE = (

^{1}/_{2}) m v^{2}initial KE = 2 [ ( ^{1}/_{2}) m v_{o}^{2}] =?= 1 [ (^{1}/_{2}) m (2 v_{o})^{2}] = final KEinitial KE = 2 [ (

^{1}/_{2}) m v_{o}^{2}] =?= 1 [ (^{1}/_{2}) m (4 v_{o}^{2})] = final KEinitial KE = 2 [ (

^{1}/_{2}) m v_{o}^{2}] =?= 4 [ (^{1}/_{2}) m v_{o}^{2}] = final KEinitial KE = 2 [ (

^{1}/_{2}) m v_{o}^{2}] =/= 4 [ (^{1}/_{2}) m v_{o}^{2}] = final KEBecause of the way KE is defined, this situation would make the final KE

twice as muchas the initial KE. So this doenothappen!

**
**

Work done by the brakes changes the car's KE from its initial value to zero. This work is equal to the force of friction causing the skid marks multiplied by the length of the skid marks sincework = force x distance When the car's speed is increased from 50 km/h to 150 km/h, its KE is increased by

nine times!Remember that KE is given byKE = ( ^{1}/_{2}) m v^{2}so increasing v by

threemeans that KE increases bynine. The force of friction between the road and the skidding tires does not change appreciably so thedistanceor length over which the force is applied must increasenine timesas well. That means we would expect skid marks to be about 9 x 15 m or135 mlong.

**Pb 7.6 Consider the inelastic collision between the two freight cars in
the last chapter (Figure 6.11). The momentum before and after the collision
is the same. The KE, however, is less after the collision than before the collision.
How much less, and what becomes of this energy?**

momentum = mass x velocity The two freight cars have the same mass -- just call it M -- so the

momentum is conserved.We can see that frominitial momentum = M (10) + M (0) = M (10) initial momentum = M (10) = (2 M) (5) = final momentum

But what has happened to the KE?

initial KE = (1/2) M v _{o}^{2}= (1/2) M (10)^{2}= (1/2) M (100)(1/2) M

_{total}v_{f}^{2}= (1/2) (2 M) (5)^{2}= (1/2) M (50) = final KEinitial KE = 2 x final KE

The final Kinetic Energy is only

one-halfthe initial Kinetic Energy (even though the final momentum is equal to the initial momentum). In an accidental collision, kinetic energy will be "lost" (that is, converted intoheat) by bending and breaking parts of the cars. In a designed collision, like this, kinetic energy will be "lost" (or turned into heat) by heating up thecouplingsthat hold the cars together.

Here's an "extra" one.

Pb 7.* Your monthly electric bill is probably expressed in kilowatt-hours (kWh), a unit of energy delivered by the flow of 1 kW of electricity for 1 hr. How many joules of energy do you get when you buy 1 kWh?1 watt = 1 W = 1 J/sTherefore,

1 J = (1 W) x (1 s) = (1 W) (1 s) = 1 W s

1 kWh = [1 kW] [ h ]

1 kWh = [1 kW (

^{1000 W}/_{kW})] [ h (^{60 min}/_{h}) (^{60 s}/_{min})] = 3,600,000 Ws = 3,600,000 J1 kWh = 3,600,000 J

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Typical or possible multiple-guess questions for this material:

1. If you push an object twice as far while applying the same force you do

A) half as much workB) the same amount of work

C) twice as much work

D) four times as much work

2. If you push an object just as far while applying twice the force you do

A) half as much workB) the same amount of work

C) twice as much work

D) four times as much work

3. Exert 1 N for a distance of 1 m in 1 s and you deliver a power of

A) 0.5 WB) 1.0 W

C) 2.0 W

D) 3.0 W

4. Exert 100 J in 50 s and your power output is

A) 0.5 WB) 1.0 W

C) 2.0 W

D) 4.0 W

5. An object is raised above the ground gaining a certain amount of potential energy. If the same object is raised twice as high it gains

A) half as much energyB) the same amount of energy

C) twice as much energy

D) four times as much energy

6. An object that has kinetic energy must be

A) elevatedB) falling

C) moving

D) at rest

7. An object that has potential energy may have this energy because of its

A) speedB) acceleration

C) momentum

D) position

8. A clerk can lift containers a vertical distance of 1 meter or can roll them up a 2 meter-long ramp to the same elevation. With the ramp, the applied force required is about

A) one-fourth as muchB) half as much

C) the same

D) twice as much

9. When a car is braked to a stop, its kinetic energy is transformed to

A) energy of motionB) heat energy

C) stopping energy

D) potential energy

10. For which position above does the ball on the end of the
string have **the greatest gravitational
potential energy**?

11. For which position above does the ball on the end of the
string have **the greatest kinetic
energy**?

12. Which requires more work: lifting a 5 kg sack vertically 2 meters or lifting a 10 kg sack vertically 4 meters?

A) lifting the 5 kg sackB) both require the same amount of work

C) lifting the 10 kg sack

D) both require the same amount of force

13. A 10 kg sack is lifted 2 meters in the same time as a 5 kg sack is lifted 4 meters. The power expended in raising the 10 kg sack compared to the power used to lift the 5 kg sack is

A) half as muchB) the same

C) twice as much

D) four times as much

14. A 2 kg mass is held 4 m above the ground. What is the approximate potential energy of the mass with respect to the ground?

A) 8 JB) 40 J

C) 80 J

D) 160 J

15. A 2 kg mass has 40 J of potential energy with respect to the ground. Approximately how far is it located above the ground?

A) 1 mB) 2 m

C) 3 m

D) 4 m

16. Using 1,000 J of work, a model elevator is raised from the ground floor to the second floor in 20 seconds. How much power does the elevator use?

A) 50 WB) 500 W

C) 2 kW

D) 20 kW

17. A car moves 4 times as fast as another identical car. Compared to the slower car, the faster car has

A) the same kinetic energyB) 4 times the kinetic energy

C) 8 times the kinetic energy

D) 16 times the kinetic energy

18. A car moving at 50 km/hr skids 20 m with locked brakes. How far will the car skid with locked brakes if it is traveling at 150 km/hr?

A) 40 mB) 60 m

C) 90 m

D) 180 m

19. When a rifle is fired it recoils so both the bullet and rifle are set in motion. The rifle and bullet ideally acquire equal but opposite amounts of

A) kinetic energyB) momentum

C) potential energy

D) all of the above

20. What does an object have when moving that it doesn`t have when at rest?

A) momentumC) mass

D) all of the above

21. If an object has kinetic energy, then it also must have

A) momentumB) velocity

C) speed

D) all of the above

|Back to 3050's Home Page|Back to Calendar|ToC, Ch 7|Ch 8, Rotation|

Answers to the typical or possible multiple-choice questions for this material:

1. If you push an object twice as far while applying the same force you do

A) half as much workB) the same amount of work

C) twice as much workW = F s

W= FsD) four times as much work

2. If you push an object just as far while applying twice the force you do

A) half as much workB) the same amount of work

C) twice as much workW = F s

W=FsD) four times as much work

3. Exert 1 N for a distance of 1 m in 1 s and you deliver a power of

A) 0.5 W

B) 1.0 WPower is the rate at which work is done

P = W /t

P = [(1 N) ( 1 m)] / (1 s)

P = 1 J / 1 s

P = 1 WC) 2.0 W

D) 3.0 W

4. Exert 100 J in 50 s and your power output is

A) 0.5 WB) 1.0 W

C) 2.0 WPower is the rate at which work is done

P = W / t

P = 100 J / 50 s

P = 2 WD) 4.0 W

5. An object is raised above the ground gaining a certain amount of potential energy. If the same object is raised twice as high it gains

A) half as much energyB) the same amount of energy

C) twice as much energyPE = m g hD) four times as much energy

6. An object that has kinetic energy must be

A) elevatedB) falling

C) movingKE = (^{1}/_{2}) m v^{2}D) at rest

7. An object that has potential energy may have this energy because of its

A) speedB) acceleration

C) momentum

D) position

8. A clerk can lift containers a vertical distance of 1 meter or can roll them up a 2 meter-long ramp to the same elevation. With the ramp, the applied force required is about

A) one-fourth as much

B) half as muchW_{ramp}= W_{lift}

F_{ramp}x 1 m = F_{lift}x 2m

F_{ramp}= (^{1}/_{2}) F_{lift}C) the same

D) twice as much

9. When a car is braked to a stop, its kinetic energy is transformed to

A) energy of motion

B) heat energyC) stopping energy

D) potential energy

10. For which position above does the ball on the end of the
string have **the greatest gravitational
potential energy**?

A) PE = m g h

The height is greatest at position A.

11. For which position above does the ball on the end of the
string have **the greatest kinetic
energy**?

D) KE = (^{1}/_{2}) m v^{2}

E_{Tot}= PE + KE

KE = maximum when PE = minimum

PE = minimum at D

Therefore, KE = maximum at D

12. Which requires more work: lifting a 5 kg sack vertically 2 meters or lifting a 10 kg sack vertically 4 meters?

A) lifting the 5 kg sackB) both require the same amount of work

C) lifting the 10 kg sackW = m g h

W_{5}= (5 kg) ( 10 m/s^{2}) ( 2 m) = 100 J

W_{10}= (10 kg) (10 m/s^{2}) (4 m) = 400 JD) both require the same amount of force

13. A 10 kg sack is lifted 2 meters in the same time as a 5 kg sack is lifted 4 meters. The power expended in raising the 10 kg sack compared to the power used to lift the 5 kg sack is

A) half as much

B) the sameP = W / t

P = m g h / t

P_{5}= (10 kg) (10 m/s^{2}) (2 m) / t = 200 J / t

P_{10}= (5 kg) (10 m/s^{2}) (4 m) / t = 200 J / tC) twice as much

D) four times as much

14. A 2 kg mass is held 4 m above the ground. What is the approximate potential energy of the mass with respect to the ground?

A) 8 JB) 40 J

C) 80 JPE = m g h

PE = (2 kg) (10 m/s^{2}) (4 m)

PE = 80 JD) 160 J

15. A 2 kg mass has 40 J of potential energy with respect to the ground. Approximately how far is it located above the ground?

A) 1 m

B) 2 mPE = m g h

PE = (2 kg) (10 m/s^{2}) (2 m)

PE = 40 JC) 3 m

D) 4 m

16. Using 1,000 J of work, a model elevator is raised from the ground floor to the second floor in 20 seconds. How much power does the elevator use?

A) 50 WP = W / t

P = 1,000 J / 20 s

P = 50 J / s

P = 50 WB) 500 W

C) 2 kW

D) 20 kW

17. A car moves 4 times as fast as another identical car. Compared to the slower car, the faster car has

A) the same kinetic energyB) 4 times the kinetic energy

C) 8 times the kinetic energy

D) 16 times the kinetic energyKE = (^{1}/_{2}) m v^{2}

If v is 4 times greater then v^{2}is 4^{2}= 16 times greater.

18. A car moving at 50 km/hr skids 20 m with locked brakes. How far will the car skid with locked brakes if it is traveling at 150 km/hr?

A) 40 mB) 60 m

C) 90 m

D) 180 mW = F s = KE

Increasing the speed by a factor of three means KE has increased by a factor of nine.

The brakes only exert so much force as they skid; the force is constant.

The stopping distance must increase by a factor of nine.

This was also a homework problem, Pb 6.1 .

19. When a rifle is fired it recoils so both the bullet and rifle are set in motion. The rifle and bullet ideally acquire equal but opposite amounts of

A) kinetic energy

B) momentumMomentum is always conservedC) potential energy

D) all of the above

20. What does an object have when moving that it doesn`t have when at rest?

A) momentumAt rest, an object's momentum must be zero.

But an object can have potential energy while it is at rest.

And an object certainly has mass while it is at rest.B) energy

C) mass

D) all of the above

21. If an object has kinetic energy, then it also must have

A) momentumB) velocity

C) speed

D) all of the aboveIf it has KE, it has velocity and that means it also has momentum and speed.|Back to 3050's Home Page|Back to Calendar|ToC, Ch 7|Ch 8, Rotation|

(C) 2003, Doug Davis; all rights reserved