Kinetic Energy Lecturer: Professor Stephen T. Thornton

Kinetic Energy

Lecturer: Professor Stephen T. Thornton

Reading Quiz:Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has A) the same kinetic energy as the lighter one.B) half as much kinetic energy as the lighter one.C) twice as much kinetic energy as the lighter one.D) four times as much kinetic energy as the lighter one.

Answer: C

The velocities will be the same in this case, so the only difference in the kinetic energy is due to the mass. Because the mass is twice as much, the kinetic energy is twice as much.

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K mv

Last Time

Discussed the concept of work

TodayDiscuss kinetic energy

Work-energy theorem

In a baseball game, the

catcher stops a 90-mph

pitch. What can you say

about the work done by

the catcher on the ball?

A) catcher has done positive work

B) catcher has done negative work

C) catcher has done zero work

Conceptual QuizConceptual Quiz

In a baseball game, the

catcher stops a 90-mph

pitch. What can you say

about the work done by

the catcher on the ball?

A) catcher has done positive work

B) catcher has done negative work

C) catcher has done zero work

The force exerted by the catcher is oppositeopposite in direction to the in direction to the

displacement of the ball, so the work is negativedisplacement of the ball, so the work is negative. Or using the

definition of work (WW = = F d cos F d cos ), because = = 180180ºº, then W < W <

00. Note that because the work done on the ball is negative, its

speed decreases.


Follow-up:Follow-up: What about the work done by the ball on the catcher? What about the work done by the ball on the catcher?

Previous kinematic equation:2 2

2 2

2 2net

2 2

net

2 2

net total

2 or rearranging,

2

2 multiply by / 2

1 1

2 21 1

2 2

,

f i

f i

f i

f i

f i

v v ad

ad v v

Fd v v m

m

F d mv mv

W W mv mv

Definition of kinetic energy

Unit of kinetic energy is the joule, J.

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2K mv

Q. Why do we define this?

A. It turns out to make our calculations easier!

Work-Energy Theorem

The total work done on an object is equal to the change in its kinetic energy:

2 2

total

1 1

2 2f if iW K K mv mvK

This is a general result, even for a force not constant in magnitude and direction. Do spring demo.

Copyright © 2009 Pearson Education, Inc.

Kinetic Energy and the Work-Energy Principle

Energy was traditionally defined as the ability to do work. We now know that not all forces are able to do work; however, we are dealing in these chapters with mechanical energy, which does follow this definition.

Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules. Energy can be considered as the ability to do work:

To find work, we have to be sure about what force is exerting the effort. Here we might ask about the work done by friction, gravity, air resistance, or the engine. Not a good figure. Forces are not accurate.

We need to make sure we can find the work done by every force. (sloppy diagram)

engine

friction friction friction

gravity gravity

air resis air resis air resis

(don't like)

sin

W Fd

W F d F d

W F d mgd

W F d F d

Doing Work Against Gravity

Energy is reclaimed in this case.

Doing Work Against Friction

Energy is not reclaimed in this case.

Does the Earth do work on the moon?

The Moon revolves around the Earth in a nearly circular orbit, with approximately constant tangential speed, kept there by the gravitational force exerted by the Earth. Gravity does no work, because the displacement and force are perpendicular.

Cable Tension, Work. A 265-kg load is lifted 23.0 m vertically with an acceleration a = 0.150g by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

Crate Friction. A 46.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?

Paintball. In the game of paintball, players use guns powered by pressurized gas to propel 33-g gel capsules filled with paint at the opposing team. Game rules dictate that a paintball cannot leave the barrel of a gun with a speed greater than 85 m/s. Model the shot by assuming the pressurized gas applies a constant force F to a 33-g capsule over the length of the 32-cm barrel. Determine F (a) using the work-energy principle, and (b) using the kinematic equations and Newton’s second law.

A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?

A) positive work was done B) negative work was

done C) zero work was done

Conceptual Quiz

A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child?

A) positive work was done B) negative work was

done C) zero work was done

The kinetic energy of the child increased because her The kinetic energy of the child increased because her speed increasedspeed increased. This increase in KEincrease in KE was the result of positive work being donepositive work being done. Or, from the definition of work, because W = KE = KEf – KEi and we know that KEKEff > KE > KEii in this case, then the work work WW must be must be positivepositive.

Conceptual Quiz

Follow-up:Follow-up: What does it mean for negative work to be done on the child? What does it mean for negative work to be done on the child?

Conceptual QuizA) 20 mB) 30 mC) 40 mD) 60 m E) 80 m

If a car traveling If a car traveling 60 km/hr60 km/hr can brake to a stop within can brake to a stop within 20 20 mm, what is its stopping , what is its stopping distance if it is traveling distance if it is traveling 120 120 km/hrkm/hr? Assume that the ? Assume that the braking force is the same in braking force is the same in both cases.both cases.

F d = Wnet = KE = 0 – mv2, and thus, |F| d = mv|F| d = mv22..

Therefore, if the speed doublesdoubles, the stopping distance gets fourfourtimes largertimes larger.

Conceptual QuizA) 20 mB) 30 mC) 40 mD) 60 m E) 80 m

If a car traveling If a car traveling 60 km/hr60 km/hr can brake to a stop within can brake to a stop within 20 20 mm, what is its stopping , what is its stopping distance if it is traveling distance if it is traveling 120 120 km/hrkm/hr? Assume that the ? Assume that the braking force is the same in braking force is the same in both cases.both cases.

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Copyright © 2009 Pearson Education, Inc.

Work Done by a Constant ForceSolving work problems:

1. Draw a free-body diagram.

2. Choose a coordinate system.

3. Apply Newton’s laws to determine any unknown forces.

4. Find the work done by a specific force.

5. To find the net work, either

a) find the net force and then find the work it does, or

b) find the work done by each force and add.

By what factor does

the kinetic energy of

a car change when

its speed is tripled?

A) no change at all

B) factor of 3

C) factor of 6

D) factor of 9

E) factor of 12


By what factor does the

kinetic energy of a car

change when its speed

is tripled?

A) no change at all

B) factor of 3

C) factor of 6

D) factor of 9

E) factor of 12

Because the kinetic energy is mvmv22, if the speed increases speed increases

by a factor of 3by a factor of 3, then the KE will increase by a factor of 9KE will increase by a factor of 9.


Follow-up:Follow-up: How would you achieve a KE increase of a factor of 2? How would you achieve a KE increase of a factor of 2?

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A) quarter as much

B) half as much

C) the same

D) twice as much

E) four times as much

Two stones, one twice the Two stones, one twice the

mass of the other, are dropped mass of the other, are dropped

from a cliff. Just before hitting from a cliff. Just before hitting

the ground, what is the kinetic the ground, what is the kinetic

energy of the heavy stone energy of the heavy stone

compared to the light one?compared to the light one?

Consider the work done by gravity to make the stone

fall distance d:

KE = Wnet = F d cos

KE = mg d

Thus, the stone with the greater massgreater mass has the greatergreater

KEKE, which is twicetwice as big for the heavy stone.


A) quarter as much

B) half as much

C) the same

D) twice as much

E) four times as much

Two stones, one twice the Two stones, one twice the

mass of the other, are dropped mass of the other, are dropped

from a cliff. Just before hitting from a cliff. Just before hitting

the ground, what is the kinetic the ground, what is the kinetic

energy of the heavy stone energy of the heavy stone

compared to the light one?compared to the light one?

Follow-up:Follow-up: How do the initial values of gravitational PE compare? How do the initial values of gravitational PE compare?


A) 0 30 mph

B) 30 60 mph

C) both the same

A car starts from rest and accelerates to 30

mph. Later, it gets on a highway and

accelerates to 60 mph. Which takes more

energy, the 0 30 mph, or the 30 60

mph?

The change in KE ( mv mv22 ) involves the velocityvelocity squaredsquared.

So in the first case, we have: m (30 m (3022 −− 0 022) = m (900)) = m (900)

In the second case, we have: m (60 m (6022 −− 30 3022) = m (2700)) = m (2700)

Thus, the bigger energy changebigger energy change occurs in the second casesecond case.


A car starts from rest and accelerates to 30

mph. Later, it gets on a highway and

accelerates to 60 mph. Which takes more

energy, the 0 30 mph, or the 30 60

mph?

A) 0 30 mph

B) 30 60 mph

C) both the same

Follow-up:Follow-up: How much energy is required to stop the 60-mph car? How much energy is required to stop the 60-mph car?

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The work W0 accelerates a car from

0 to 50 km/hr. How much work is

needed to accelerate the car from

50 km/hr to 150 km/hr?


A) 2 W0

B) 3 W0

C) 6 W0

D) 8 W0

E) 9 W0

The work W0 accelerates a car from

0 to 50 km/hr. How much work is

needed to accelerate the car from

50 km/hr to 150 km/hr?

A) 2 W0

B) 3 W0

C) 6 W0

D) 8 W0

E) 9 W0

Let’s call the two speeds v and 3v, for simplicity.

We know that the work is given by W = KE = KEf – Kei.

Case #1: W0 = m (vv22 – 0022) = m (vv22)

Case #2: W = m ((33vv)2 – vv22) = m (99vv22 – vv22) = m (88vv22) = 8 W0


Follow-up:Follow-up: How much work is required to stop the 150-km/hr car? How much work is required to stop the 150-km/hr car?

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A) m1

B) m2

C) they will go the

same distance

Two blocks of mass m1 and m2 (m1 > m2)

slide on a frictionless floor and have the

same kinetic energy when they hit a long

rough stretch ( > 0), which slows them

down to a stop. Which one goes farther?

m1

m2

With the same same KEKE, both blocks

must have the same worksame work done

to them by friction. The friction

forceforce is lessless for mm22 so stopping

distancedistance must be greatergreater.


A) m1

B) m2

C) they will go the

same distance

Two blocks of mass m1 and m2 (m1 > m2)

slide on a frictionless floor and have the

same kinetic energy when they hit a long

rough stretch ( > 0), which slows them

down to a stop. Which one goes farther?

m1

m2

Follow-up:Follow-up: Which block has the greater magnitude of acceleration? Which block has the greater magnitude of acceleration?

A golfer making a putt gives the ball an initial

velocity of v0, but he has badly misjudged the

putt, and the ball only travels one-quarter of

the distance to the hole. If the resistance

force due to the grass is constant, what speed

should he have given the ball (from its original

position) in order to make it into the hole?

A) 2 v0

B) 3 v0

C) 4 v0

D) 8 v0

E) 16 v0


A golfer making a putt gives the ball an initial

velocity of v0, but he has badly misjudged the

putt, and the ball only travels one-quarter of

the distance to the hole. If the resistance

force due to the grass is constant, what speed

should he have given the ball (from its original

position) in order to make it into the hole?

A) 2 v0

B) 3 v0

C) 4 v0

D) 8 v0

E) 16 v0

In traveling four times the distancefour times the distance, the resistive force

will do four times the workfour times the work. Thus, the ball’s initial KE initial KE

must be four times greatermust be four times greater in order to just reach the

hole—this requires an increase in the initial speed by a increase in the initial speed by a

factor of 2factor of 2, because KE = KE = mvmv22.


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Documents

Kinetic Energy Lecturer: Professor Stephen T. Thornton