Chapter 8

Work, Energy, and Power

Chapter Warm Up

1. What is a non-science meaning of the term “work”? Give an example.

2. What is the scientific meaning of the term “work”? Give an example.

3. What is a non-science meaning of the term “energy”? Give an example.

4. What is the scientific meaning of the term “energy”? Give an example.

5. What are two different types of energy?

6. What is the Law of Conservation of Energy?

Section 1: Work

Definition: The product of the force on an object

and the distance through which the object is

moved.

Work is done when a force moves an object

through a distance.

Work is done by the force on the object.

The force and direction must be parallel.

Symbol: W

Units: kgm2/s2= Joule (J)

Equation: W Force; W distance (d)

W Fd; if force in kgm/s2 and distance in m,

Then W=Fd

Not a vector quantity(it’s something called a dot

product)

1J = work done lifting 1 kg a height of 1 meter.

Example Problems

1. A tugboat pulls a ship with a constant horizontal

force of 5.00 x 103 N across a harbor. How much

work is done on the ship if it moves 3.00 km?

1.50 x 107 J

2. What net force is required to do 2.55 x 103 J

of work on a crate to move it 5.00 m?

5.10 x 102 N

3. How far will a car move if 4.58 x 107 J of

work is done on it by a net force of 362 N?

1.27 x 105 m

Section 2: Energy

Definition: Capacity or ability to do work

Ways to classify energy:

Source:

Nuclear, chemical, mechanical, magnetic, electrical, gravitational, solar, hydrodynamic, thermal, wind, geothermal

Physical Form

Mechanical

Nonmechanical

We will deal with mechanical energy only

Two Types of Mechanical Energy:

Potential

Kinetic

Potential Energy

Energy of position

Energy an object has due to its

position in a field

3 classifications

Gravitational Potential Energy

Magnetic Potential Energy

Electrical Potential Energy

Gravitational Potential Energy

Definition: The energy an object has due

to its position in a gravitational field

The amount of gravitational potential

energy an object has is independent of the

path it took to get to its position

Example

The amount of potential energy a hiker

gains climbing a mountain.

Symbol: PEg

Units: kgm2/s2 (Joule)

Equation: PEg mass, height, and acceleration

PEg = magh use h instead of y -- convention

Example Problems

1. How much gravitational potential energy does

a 1,000. kg roller coaster car have when it is

stopped at the top of a 55 m lift hill?

5.4 x 105 J

2. A ski lift has a vertical elevation change of

1390 m. If a skier rides to the top of the lift and

gains1152 kJ of gravitational potential energy,

what is the skier’s mass?

8.45 x 101 kg

3. An apple with a mass of 95.0 g is carried from

the street level of a building to its roof and gains

355 J of gravitational potential energy. How tall

is the building?

3.81 x 102 m

Kinetic Energy

Definition: The energy an object has due its

motion.

Example: The energy a baseball has as it is

flying through the air towards home plate.

Symbol: KE

Units: kgm2/s2 (Joule) – it is energy after all!

Equation:

KE mass; KE velocity – after a lot of

algebra, get

KE = ½ mv2

Example Problems:

1. How much kinetic energy does an 850. kg car

have if it is traveling at 35.0 m/s?

5.21 X 105 J

2. A cheetah is traveling at a speed of 31.3 m/s.

If it has 3.11x 104 J of kinetic energy, what is the

mass of the cheetah?

63.5 kg

3. An emperor penguin has a mass of 35 kg. The

penguin has 149 J of kinetic energy. How fast is

the penguin swimming?

2.9 m/s

Section 3: Work and Energy

How can work and energy be related?

Work is the amount of PEg an object gains when

moved in a gravitational field,

And

KE is the amount of work an object can do while

changing velocity

Mathematically

Work and Potential Energy:

W = PEg and PEg = magh

so

W =magh or W = magh

also

Since W = Fd, then

Fd = magh

Example Problems

1. How much work is done by a hiker on a 15.0

kg backpack that is lifted up a height of 10.0

m?

1.47 x 103 J

2. How far does a 2.50 kg book have to be raised

to do 12.5 J of work on the book?

0.510 m

3. 1.25 J of work is done on a Teddy Bear by

raising it 1.10 m in to the air. What is the mass

of the Teddy Bear?

0.116 kg

Work and Kinetic Energy:

Work – Kinetic Energy Theory

W = KE

W = KEf - KEi

W = 1/2mvf2 – 1/2mvi

2

Since W= Fd;

Fd = 1/2mvf2 – 1/2mvi

2

Example Problems;

1. 75 kg bobsled is pushed from rest along a

horizontal surface by two athletes. After the

bobsled has been pushed a distance of 4.5 m,

its speed is 6.0 m/s. What is the magnitude of

the net force on the bobsled?

3.0 x 102 N

2. A 30.0 kg box initially sliding at 5.00 m/s on a

rough surface is brought to rest by 20.0 N of

friction. What distance does the box slide?

18.8m

3. A space ship of mass 5.00×104 kg is traveling

at a speed 1.15 × 104 m/s in outer space. Except

for the force generated by its own engine, no

other force acts on the ship. As the engine exerts

a constant force of 4.00 × 105 N, the ship moves

a distance of 2.50 × 106 m in the direction of the

force of the engine. Determine the final speed of

the ship.

1.31 x 104 m/s

4. A car experiences a net force of 57.7 N while

it is slowing down from 25.0 m/s to 20.0 m/s

over a distance of 325m. What was the car’s

mass?

1.67 x 102 kg

Section 4: Conservation of Energy

LAW OF CONSERVATION OF ENERGY:

Energy may not be created nor destroyed, it only

changes form.

OR

The amount of energy in a closed system is

constant.

Conservation of Mechanical Energy

Mechanical energy is the energy an object has

due to its position or motion.

Mechanical energy is not always conserved –

some may be converted to heat energy(friction)

But, if friction is negligible, mechanical energy

is conserved.

This means

initial mechanical energy = final mechanical energy

MEi = MEf

MEi = PEi + KEi

MEi = maghi +1/2mvi2

MEf = PEf + KEf

MEf = maghf +1/2mvf2

maghi +1/2mvi2 = maghf +1/2mvf

2

Example Problems

1. Donald Duck is at the top of Mt. Gushmore, at an elevation of 28.0 meters. Donald has a mass of 52.5 kg. He goes down the waterslide to the bottom of Mt. Gushmore. How fast is Donald going when he is at the bottom of the slide?

23.4 m/s

2. A pendulum bob is released from some initial

height such that the speed of the bob at the

bottom of its swing is 1.9 m/s. What is the initial

height of the bob?

0.18m

3. Starting from rest, a 25.0 kg child goes down a

3.00 m tall slide. How fast is she going when she

is halfway down the slide?

5.42 m/s

Section 5: Power

Definition: The rate at which energy is

transferred from one form to another.

Rate at which work is done.

Rate implies time

Symbol: P

Unit: kgm2/s3 = Watt (W) – J/s

Equations

Power = P = work/t

If vertical motion:

P = mag(hf –hi)/t

If horizontal motion:

P = Fd/t

Example Problems:

1. A 193 kg curtain must be raised 7.5 m in no

more than 5.0 seconds. How much power is

needed to do this?

2.8 X 103 kgm2/s3 (W)

2. A rain cloud contains 2.66 x 107 kg of water

vapor. How long would it take for a 2.00 x 103

W pump to raise the same amount of water to the

cloud’s altitude, 2.00 km?

2.61 x 108 s

3. A ship generates 5.6 x 107 W of power. How

much work can this ship do in 1.0 hour?

2.0 x 1011 kgm2/s2 (J)