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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
Vocabulary for these chapters:
ch. 10: section 1 – all
ch. 11: section 1 – potential energy and gravitational potential energy
section 2 – all
Chapter 10
“Doing work on a system changes the system’s energy.”
Work: Remember that impulse is what it took to cause a change in
momentum: Ft
Instead of look at a change in time, we can look at it in a different way:
A change in distance.
When we move something from one place to another, we are doing work
Work causes a change in something’s energy
Work  Force  displacement  cos
W  Fd cos
Units? N  m  Joules
Why displacement and not distance?
“How much work is done by a person on a 10 kg box when that person pushes the box with a
force of 184N, 10.0m across a floor?”
“How much work is done on that same box if a person lifts it up 2 meters?”
Since cos is equal to 0 when  is equal to 90o , work is not done on anything when the
movement is perpendicular (normal force, gravitational force on an object being slid across
the desk)
When  equal to 0o (in the direction of movement – pushing horizontally on a box), cos is equal
to 1 and W=Fd
It’s important to note that when something is not being displaced, there is no work being done.
Ex: Lift a set of barbells (p. 145 in CP book)
Work is done to lift them, but no work is done to hold them
up – does this make sense?
**Work – two categories
1. work done against another force
Ex: archery (against the elastic bowstring), push-ups (against your weight), push a
box across the floor (against friction)
2. change the speed of an object
Ex: changing the speed of a car
Both – transfer of energy between something and its surroundings
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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
What if work is done by different forces? Remember that work is a vector quantity (because
Force is a vector), so it has direction. Work is done in the direction of the net force that is
being exerted on it.
Just calculate the work done by each force and add the results, taking into consideration the
directions of the forces.
Example on bottom of page 266 – you and your friend are both pushing on a box. The box moves
one meter in the positive direction.
What if you push a box across the floor with a force of 3N, then push it back to its original
position by pushing it with a force of 3N. How much work have you done? Be careful!
Even though displacement is zero, you have done 6 J of work because both force and direction
have changed. Remember that Work is a vector!
Example 1 on p. 268 and numbers 1-4
Example 2 on p. 269 and number 5, 6, 8
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Chapter 10 & 11: Work and Energy
Honors Physics Teacher Notes - Grothaus
Energy:
The idea of energy was unknown to Isaac Newton
Its existence was still being debated in the 1850’s
The concept of energy is now ingrained in every branch of science and in every aspect of our
society
Examples of where we find energy
Can we see energy?
We can only observe the effects of energy when something is happening
When energy is being transferred from one place to another or transformed from one form
to another.
Work-Energy Theorem:
Work done on a system is equal to the change in the system’s
energy.
W  E
Since work is measured in joules, energy must also be measured in Joules
Named after James Prescott Joule – who established the relationship between work done
and the change in energy in the nineteenth century
Specifically, work is the transfer of energy that occurs when a force is applied through a
displacement
Power:
Remember when we talked about velocity and acceleration. Acceleration is how fast velocity is
changing.
Like velocity, work doesn’t take into consideration the amount of time it takes to do the work.
Carry the same load up the stairs walking and running
Same amount of work, but why are you more tired when you run?
How fast the work is done is Power (the rate at which work is done)
Power equals the change in energy divided by the time interval required for the change – or
the amount of work done divided by the time interval required to do the work.
A car engine that has twice as much power doesn’t produce twice as much work or go twice as
fast as the other engine, but it can do twice the amount of work in the same amount of time or
do the same amount of work in half the time
𝒑𝒑𝒑𝒑 𝒑𝒑𝒑𝒑/
𝑗𝑗𝑗𝑗𝑗𝑗
𝒑𝒑𝒑𝒑𝒑 = 𝒑𝒑𝒑𝒑 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 = /𝑗𝑗𝑗 = watt = W
W ;
Joule
watt 
t
sec
1 W = one joule of work is done in one second
P
1 W is a relatively small unit of power. Example: If you lift a glass of water (about 2N) a
half meter up to your mouth at a constant speed, you do 1J of work
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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
Space shuttle uses 33,000 megawatts (MW) of power for lift off
In the United States: horsepower (hp) for cars, kW for electricity
0.75 kW = 1 hp 134 hp energy?
Example 3 on p. 272
Do numbers 10 - 13
Mechanical Energy
When you pull a bowstring, stretch a rubber band, wind a spring, you enable these things to do
work
The property of an object or system that enables it to do work is energy
Many forms of energy:
Mechanical Energy is the energy due to the position of
something or the movement of something.
1. kinetic energy
2. potential energy
Mechanical Energy becomes evident only when it changes from one form to another, or
when there is motion
Mechanical Energy is relative to a frame of reference
Depends on the location we choose for our reference
Potential Energy
Just like it sounds, potential energy is energy that is stored and held in readiness.
There are three examples of potential energy: elastic potential energy, chemical energy and
gravitational potential energy
not doing:
Chemical Energy: chemical energy in fuels is potential energy.
Has to do with the energy of position at the subatomic level.
Fossil fuels, electric batteries, digestion of food we eat, conversion of solar energy
to chemical energy in plants
Gravitational Potential Energy: Work is needed to pick things up against Earth’s gravity. (push up)
The potential energy due to elevated positions is called GPE
(CP book – p. 148)
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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
The amount of GPE possessed by an elevated object is equal to the amount of work done against
gravity to get it to that elevation (only vertical distance)
Remember that W = Fd (joules)
Also remember that Weight = mg (ma, where a = g) and that weight is a force
The upward force needed when moving at constant velocity is the weight of the object, so
the work done in lifting it through a height h is the product mgh (weight x height)
Gravitational potential energy = weight x height
PE = mgh (units?)
Height is the distance above some reference level
Floor vs. ground (out window, neg. height)
p. 148 again. Figure 9.3 Doesn’t matter what path got it there
Hydroelectric plants use GPE
Water from an upper reservoir flows thru a long tunnel to an electric generator
GPE of the water is changed to electrical energy
At night, when there isn’t as much demand for energy, these plants might buy energy when
it’s cheap to bring the water back up to the top of the reservoir: pumped storage
(Drop a bowling ball on your toe – from 1 mm or from 1 m
Same mass, same weight, but more GPE – so more work)
Elastic potential energy: A stretched or compressed spring; a bow being drawn back; a stretched rubber
band (part of a slingshot), the stretched strings of a tennis racket or guitar
All have a potential to do work.
Depends on the distance of compression or stretching and the spring constant.
Remember: k = spring constant (spring strength)
The stiffer the spring, the higher k is.
k is measured in N/m
The length of the string, spring, etc when no external forces are acting on it is called the
relaxed length of the spring.
x is the distance the spring is compressed or stretched from its relaxed
length
1
PEe  kx 2
2
What happens if k is increased? What happens when x is increased?
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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
Kinetic Energy
If an object is moving, then it’s capable of doing work. Energy of motion is called Kinetic Energy
(KE comprises thermal energy, sound, and light)
Depends on the mass as well as the speed of the object
1
(relate to momentum)
KE  mv 2 (show units)
2
The kinetic energy of a moving object is equal to the work required to bring it to its
speed from rest, or the work the object can do while being brought to rest.
𝑗𝑗𝑗 𝑗𝑗𝑗𝑗𝑗 𝑗 𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 = 𝑗𝑗𝑗𝑗𝑗𝑗𝑗 𝑗𝑗𝑗𝑗𝑗𝑗
1
W  Fd  mv 2
2
What happens when you double mass?
What happens when you double speed?
It takes four times as much work to double the speed or an object moving twice as
fast takes four times as much work to stop it.
Whenever work is done, energy is changed
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed. It can
be transformed from one form into another, but the total amount of energy never changes.
Bow and arrow: bow’s PE transferred to arrow in KE
W = Fd Force of impact times distance travelled is not quite equal to the
KE. Some energy lost through heat
See page 303 in text
Pendulum, skate park demo, figure 9.9 on p. 154 (CP book)
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Honors Physics Teacher Notes - Grothaus
Chapter 10 & 11: Work and Energy
Bottom line: energy may change form, but total energy stays exactly the same
When you assume no friction on a system, you can say
KEi  PEi  KE f  PE f
With friction, then you have to factor in that energy loss.
But always:
Total energy before = Total energy after
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