Chapter 5 Work, Energy, and Power. Work W = F x This equation applies when the force is in the same direction as the displacement are in the same direction.

Chapter 5

Work, Energy, and Power

Work W = F x

This equation applies when the force is in the same direction as the displacement

are in the same direction

and F x

A linebacker pushes against the blocker but the blocker does not move. The work is:

Positive

Negative

Zero

Not e

nough in

fo

0% 0%0%0%

1. Positive2. Negative3. Zero4. Not enough info

Answer Now

When doing a bench press, you gradually lower the bar down to your chest. The work done by you is:

Positive

Negative

Zero

Not e

nough in

fo

0% 0%0%0%

1. Positive2. Negative3. Zero4. Not enough info

Answer Now

When doing a bench press, you gradually lower the bar down to your chest. The work done by gravity is:

Positive

Negative

Zero

Not e

nough in

fo

0% 0%0%0%

1. Positive2. Negative3. Zero4. Not enough info

Answer Now

When doing a curl, you exert a force to raise the dumbbell to your shoulder. The work done by you is:

Positive

Negative

Zero

Not e

nough in

fo

0% 0%0%0%

1. Positive2. Negative3. Zero4. Not enough info

Answer Now

Because your two-year old cousin refuses to move, you pull him along the ground while tugging at an angle. The work done is:

Positive

Negative

Zero

Not e

nough in

fo

0% 0%0%0%

1. Positive2. Negative3. Zero4. Not enough info

Answer Now

If there exists a force on an object an the object moves, work must have been done.

True

False

0%0%

1. True2. False

Work Can Be Positive or Negative Work is positive

when lifting the box

Work would be negative if lowering the box The force would

still be upward, but the displacement would be downward

When Work is Zero Displacement is

horizontal Force is vertical cos 90° = 0

Units of Work SI

Newton • meter = Joule N • m = J J = kg • m2 / s2

Work W = (F cos )x

q is the angle between

If = 0, cos = 1, and W = F Δx

If = 90o, cos = 0, and W = 0

and F x

More About Work The work done by a force is zero

when the force is perpendicular to the displacement cos 90° = 0

Limitations of Work This gives no information about:

the time it took for the displacement to occur

-or- the velocity or acceleration of the

object

Work is a Scalar Even though the sign matters (like

vectors), the sign does not indicate the direction if travel.

Let’s try some practice problems:

Kinetic Energy Energy associated with the motion

of an object Scalar quantity measured in Joules

2mv2

1KE

Work-Kinetic Energy Theorem

The net work done on an object is equal to the change in the object’s kinetic energy

Speed will increase if work is positive Speed will decrease if work is negative

net fiW KE KE KE

Gravitational Potential Energy Gravitational potential energy is

associated with the vertical position of the object

PEgrav = mgy y = vertical position (relative to a

reference point – usually ground) g = acceleration due to gravity

Conservation of Mechanical Energy Total mechanical energy is the sum

of the kinetic and potential energies in the system and is stays constant (if closed system)

ffii

fi

PEKEPEKE

EE

On which track does the marble have the largest initial potential energy?

Gre

en

Yellow

Red Blue

All the sa

me

0% 0% 0%0%0%

1. Green2. Yellow3. Red4. Blue5. All the same

On which track will the marble have the largest final velocity?

Gre

en

Yellow

Red Blue

All the sa

me

0% 0% 0%0%0%

1. Green2. Yellow3. Red4. Blue5. All the same

On which track does the marble have the largest total mechanical energy at the beginning?

Gre

en

Yellow

Red Blue

All the sa

me

0% 0% 0%0%0%

1. Green2. Yellow3. Red4. Blue5. All the same

If a steel marble is released down the green track and a plastic marble goes down the blue track, which will have the greater velocity at the end of the track?

Steel

Plastic

Same

0% 0%0%

1. Steel2. Plastic3. Same

If a steel marble is released down the green track and a plastic marble goes down the blue track, which will have the greater kinetic energy at the end of the track?

Steel

Plastic

Same

0% 0%0%

1. Steel2. Plastic3. Same

On which track did the marble have the largest average velocity?

Gre

en

Yellow

Red Blue

All the sa

me

0% 0% 0%0%0%

1. Green2. Yellow3. Red4. Blue5. All the same

On which track did the marble have the second largest average velocity?

Gre

en

Yellow

Red Blue

All the sa

me

0% 0% 0%0%0%

1. Green2. Yellow3. Red4. Blue5. All the same

Notes About Conservation of Energy We can neither create nor destroy

energy Another way of saying energy is

conserved If the total energy of the system does

not remain constant, the energy must have crossed the boundary by some mechanism (friction, heat, sound, …)

When graphing F vs. –x, what was the relationship?

Linear

Quadratic

Power Functi

on

Inverse

No re

lationshi...

0% 0% 0%0%0%0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1. Linear2. Quadratic3. Power Function4. Inverse5. No relationship

Springs – Hooke’s Law

One of the simplest type of simple harmonic motion is called Hooke's Law. This is primarily in reference to SPRINGS.

kxorkxF

k

k

xF

s

s

N/m):nitConstant(U Spring

alityProportion ofConstant

The negative sign only tells us that “F” is what is called a RESTORING FORCE, in that it works in the OPPOSITE direction of the displacement.

Hooke’s Law

Felas = -kx

Felas = Elastic force of the spring (force points back to equilibrium position.) (N)

k = Spring constant (N/m)x = displacement from equilibrium (m)

(note:opposite to direction of the elastic force)

Hooke’s Law from a Graphical Point of View

x(m) Force(N)

0 0

0.1 12

0.2 24

0.3 36

0.4 48

0.5 60

0.6 72

graph x vs.F a of Slope

kx

Fk

kxF

s

sSuppose we had the following data:

Force vs. Displacement y = 120x + 1E-14

R2 = 1

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Displacement(Meters)

Fo

rce(

New

ton

s) k =120 N/m

We have seen F vs. x Before!!!!

Force vs. Displacement y = 120x + 1E-14

R2 = 1

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Displacement(Meters)

Fo

rce(

New

ton

s)

Work or ENERGY = FDx

Since WORK or ENERGY is the AREA, we must get some type of energy when we compress or elongate the spring. This energy is the AREA under the line!

Area = ELASTIC POTENTIAL ENERGY

Since we STORE energy when the spring is compressed and elongated it classifies itself as a “type” of POTENTIAL ENERGY, Us. In this case, it is called ELASTIC POTENTIAL ENERGY.

Elastic Potential Energy

The graph of F vs.x for a spring that is IDEAL in nature will always produce a line with a positive linear slope. Thus the area under the line will always be represented as a triangle.

NOTE: Keep in mind that this can be applied to WORK or can be conserved with any other type of energy.

Elastic potential energy

20

2

00

21|

2|

)(

)()(

kxUWx

kW

dxxkdxkxW

dxkxdxxFW

springxx

x

x

x

x

Elastic “potential” energy is a fitting term as springs STORE energy when there are elongated or compressed.

Conservation of Energy in Springs

Strain PE vs. Gravitational PE

The area under the curve on the left equals the energy stored in a linear spring, or the amount of work required to deform the spring.

The area under the curve on the right equals the potential energy due to the constant force of gravity (mg), or the work required to lift an object x m.

Note that one area is square and the other triangular.

Force (N)

x (m)0

Strain

Force (N)“mg”

x (m) “h”

0Gravitational

½Fx Fxor

mgh

Power Often also interested in the rate at

which the energy transfer takes place Power is defined as this rate of energy

transfer

SI units are Watts (W)

WFv

t

2

2

J kg mW

s s

Power, cont. US Customary units are generally hp

Need a conversion factor

W746s

lbft550hp1

Work is done when

the disp

lacement is

not ...

the disp

lacement is

zero

.

the fo

rce is

zero

.

the fo

rce and disp

laceme..

0% 0%0%0%

1. the displacement is not zero.

2. the displacement is zero.

3. the force is zero.4. the force and

displacement are perpendicular.

If both the mass and the velocity of a ball are tripled, the kinetic energy of the ball is increased by a factor of

3. 6. 9.27.

0% 0%0%0%

1. 3.2. 6.3. 9.4. 27.

Of the following examples, the one that represents work as defined by a scientist is:

lifting a

book from your..

.

leaning o

n a sh

ovel w

hil...

pushing hard

against

a w...

carry

ing a heavy

box on...

0% 0%0%0%

1. lifting a book from your desk.

2. leaning on a shovel while others labor.

3. pushing hard against a wall for an hour.

4. carrying a heavy box on your head.

The ability to do work is defined as:

force

and measu

red in

j...

energy a

nd measu

red in

...

power and m

easured in

...

energy a

nd measu

red in

...

0% 0%0%0%

1. force and measured in joules.

2. energy and measured in watts.

3. power and measured in watts.

4. energy and measured in joules.

A rolling wagon has 50 joules of kinetic energy. If the wagon’s velocity is doubled, the kinetic energy of the wagon:

is re

duced to

25 joules.

is in

creas

ed to 100 jo

ules.

is in

creas

ed to 200 jo

ules.

remains t

he same.

0% 0%0%0%

1. is reduced to 25 joules.

2. is increased to 100 joules.

3. is increased to 200 joules.

4. remains the same.