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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 =magh 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 – 1/2mvi2
Since W= Fd;
Fd = 1/2mvf2 – 1/2mvi2
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 +1/2mvf2
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)