Energy - Key
Vocabulary
Term
Potential Energy
Definition
The energy an object possesses due to its
position.
PE = mgh
Kinetic Energy
The energy an object possesses when it is in
motion.
KE = ½mv2
Joules
The units used to measure energy and work
output
Gravity
The acceleration due to gravity is always
constant. The value is 10 m/s2.
Conservation of Energy The energy in a closed system will remain
constant throughout. (i.e. – the potential energy
at the top of a hill will equal the kinetic energy
at the bottom when friction is ignored.)
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Potential Energy
Ep= mgh
Mass
if you double the
mass then the PE
will
Double
Where is the Potential
Gravity
Height
the value for
gravity is
10 m/s2
if you double the
height then the PE
will
Double
energy the least in the picture below?
The person on the swing in the middle because they
have the least height.
Identify two ways you could increase the potential energy.
1.
Increase the mass
2.
Increase the height
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Kinetic Energy
Mass
Velocity
if you double the
velocity then the
KE will
if you double the
mass then the KE
will
Double
Quadruple
Ek= ½ mv2
Symbols:
Ek means Kinetic
Energy
Units: Joules
m means mass
v means velocity
Units: kilograms
Units: m/s
If I want to find:
Then I need to
know:
My formula will
be:
My unit will be:
Kinetic energy
mass & velocity
½ mv2
Joules
Mass
velocity & kinetic
energy
m=2Ek/v2
kg
Velocity
mass & kinetic
energy
v=√2Ek/m
m/s
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Energy is one of the fundamental quantities in our universe.
The workings of the universe can be viewed from the perspective of energy flowing from one place to another
and changing back and forth from one form to another.
Examples of Energy
1. A gust of wind.
2. Batteries.
3. A ball at rest on top of a hill.
4. Thermal Energy
5. Kinetic Energy
6. Electrical Energy
Units of Energy
The Joule is the energy needed to push with a force of one newton over a distance of one meter.
Work
Work is the transfer of energy that results from applying a force over a distance.
Can you create
a triangle to
help you use
this formula?
An object that has Energy is able to do work; without energy, it is impossible
to do work. In fact, one way to think about energy is as stored work.
Sample Problems
A person travels 30 meters dragging a suitcase using 100 N of force. How much work is done?
d=30 m
W = Fd
F=100 N
W = 100 N · 30 m = 3,000 J
1. A car uses 200 N of force from the engine going 1000 meters.
How much work is done? (200,000 J)
2. A person travels 30 meters walks with a 100 N suitcase in their arms.
How much work is done? (0 J)
Potential Energy
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Potential Energy: energy due to position.
Systems or objects with potential energy are able to exert forces (exchange energy) as they change to other
arrangements.
The term Gravitational Potential Energy describes the energy of an elevated object.
Unless otherwise stated, you can assume “potential energy” means gravitational potential energy (GPE). (We
will often abbreviate it as PE)
The units of energy are the same as the units for Work.
Sample Problems
A spoon is raised 0.2 m above a table. If the spoon has a mass of 0.1 kg, what is the gravitational potential
energy associated with the spoon relative to the surface of the table?
h=0.2 m
Ep=mgh
m=0.1 kg
= 0.1 kg x 10 m/s2 x 0.2 m = 0.2 Joules
2
g=10 m/s
Sean stands on the roof of the school holding his egg drop project, 12 m above the ground. If his device has a
mass of 0.5 kg, calculate the potential energy of his device.
h=12 m
Ep=mgh
m=0.5 kg
= 0.5 kg x 10 m/s2 x 12 m = 60 Joules
2
g=10 m/s
Kinetic Energy
Energy of motion is called kinetic energy.
Objects that are moving also have the ability to cause change.
Kinetic energy can easily be transformed into potential energy.
The kinetic energy of a basketball tossed upward converts into potential energy as the height increases and
therefore loses kinetic energy.
The amount of kinetic energy an object has equals the amount of work the object can do by exerting force as it
stops.
Kinetic energy is related to both an object’s mass and its speed.
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Kinetic energy increases as the square of the speed
.
This means that if you go twice as fast, your energy increases by four times (22 = 4).
If your speed is three times as fast, your energy is nine times bigger (32 = 9).
Sample Problems
1. Calculate the kinetic energy of Mr. Beatty’s 4 kilogram dog Dakota running at 5 m/s.
m= 4 kg
v = 5 m/s
Ek = ½ mv2
= ½ 4 kg x (5 m/s)2 = 50 Joules
2. What is the kinetic energy of a 2000 kg race car that is traveling at 45 m/s?
m= 2000 kg
v= 45 m/s
Ek = ½ mv2
=½ (2000) kg x (45 m/s)2 = 2,025,000 Joules
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Conservation of Energy
The idea that energy converts from one form into another without a change in the total amount is called the law
of conservation of energy.
The law states that energy can never be created nor destroyed just converted from one form into another.
**The law of conservation of energy is one of the most important laws in physics.**
(It applies to not only kinetic and potential energy, but to all forms of energy)
THE WAY UP
As the ball in picture moves upward, it slows down and loses kinetic energy.
Eventually it reaches a point where all the kinetic energy has been converted to potential energy. The ball has
moved as high as it will go and its upward speed has been reduced to zero.
THE WAY DOWN
As the ball falls, its speed increases and its height decreases. The potential energy decreases as it converts into
kinetic energy.
Sample Problems
A 2 kg car moving with a speed of 2 m/sec starts up a hill. How high does the car roll before
it stops?
KE in the beginning = PE at the end
Ek = Ep
½ mv2 = mgh
½ (2) kg x (2 m/s)2 = 2 kg x 10 m/s2 x ???
4 Joules = 20 x ???
Height = 0.2 meters
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Class Work
1. Theresa’s 5.45 kg dog, Mr. Muggles is napping on top of 2 meter high couch. What is the potential
energy of Mr. Muggles?
Looking For
Potential energy
Given
m=5.45 kg
h=2m
g=10 m/s2
Relationship
Solution
PE=mgh
109 Joules
2. Garfield (mass = 10.5 kg) is sleeping on top of the 3 meter high couch. What is Garfield’s potential
energy?
Looking For
Potential energy
Given
m=10.5 kg
h=3 m
g=10 m/s2
Relationship
Solution
PE=mgh
315 Joules
3. A 200 kg pig is standing on top of a 40 meter high muddy hill. What is the pig’s potential energy?
Looking For
Potential energy
Given
m=200 kg
h=40 m
g=10 m/s2
Relationship
Solution
PE=mgh
80,000 Joules
4. Tyler (mass=50-kg) is riding in a go-kart down maple avenue.
a. What is Tyler’s kinetic energy if he travels at 2 m/s?
Looking For
Kinetic energy
Given
m=50 kg
v= 2 m/s
Relationship
Solution
KE=1/2 mv2
100 Joules
b. What is Tyler’s kinetic energy if he travels at 4 m/s?
Looking For
Given
Relationship
Solution
Kinetic energy
m=50 kg
v= 4 m/s
KE=1/2 mv2
400 Joules
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Group Work
1. Alan, a hot dog vendor, is selling hot dogs on top of a hill (height = 20 m) outside of Petco Park in San
Diego California. While talking to a customer, Alan’s hot dog cart (m=35 kg) starts to roll down the
hill.
a. What is the kinetic energy of the cart as it rolls down the hill with a velocity of 3.25 m/s?
Looking For
Kinetic energy
Given
m=35 kg
v= 3.25 m/s
Relationship
Solution
KE=1/2 mv2
184.84 Joules
Relationship
Solution
PE=mgh
7,000 Joules
b. What is the potential energy at the top of the hill?
Looking For
Potential energy
Given
m=35 kg
h=20m
g=10 m/s2
mass = 35 kg
2. True or False: If the speed of an object doubles, the kinetic energy of the object doubles.
False, the kinetic energy would quadruple.
3. At Six Flags there is a 625-kg roller coaster car moving at 57.97 m/s.
a. Determine the kinetic energy of the car.
Looking For
Kinetic energy
Given
m=625 kg
v = 57.97 m/s
Relationship
Solution
KE=1/2 mv2
1,050,162.78 Joules
b. If the velocity of the coaster were to double to 115.94 m/s what would its new Kinetic Energy
be?
Looking For
Kinetic energy
Given
m=625 kg
v = 115.94 m/s
Relationship
Solution
KE=1/2 mv2
4,200,651.13 Joules
4. Mister Diwater, the former platform diver for the Ringling Brother's Circus, had a mass of 70 kg. If her
velocity was 20 m/s just prior to hitting the bucket of water then what is her Kinetic Energy?
Looking For
Kinetic energy
Given
m=70 kg
v=20 m/s
Relationship
Solution
KE=1/2 mv2
Ek = 14000 J
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HomeWork
1. In 1987, the fastest auto race in the United States was the Busch Clash in Daytona, Florida. That year,
the winner’s average speed was about 88 m/s. If the mass of the car and its driver was 981 kg determine
their kinetic energy?
Looking For
Given
Relationship
Solution
Kinetic energy
m=981 kg
v=88 m/s
KE=1/2 mv2
Ek = 3,798,432 J
2. In 1994, Leroy Burrell of the United States set what was then a new world record for the men’s 100 m
run. He ran the 100 m distance with an average speed of 10.2 m/s. Assuming that he ran with constant
speed, and his mass was 65-kg, what was Burrell’s kinetic energy?
Looking For
Given
Relationship
Solution
Kinetic energy
m=65 kg
v= 10.2 m/s
KE=1/2 mv2
3381.3 J
3. The fastest helicopter, the Westland Lynx, has a top speed of 111 m/s. If its mass was 3400 kg, what is
the helicopter’s kinetic energy?
Looking For
Given
Relationship
Solution
Kinetic energy
m=3400 kg
v= 111 m/s
KE=1/2 mv2
20,945,700 J
4. Susie Maroney from Australia set a women’s record in long-distance swimming by swimming 93,625 m
in 24.00 h(convert to seconds). What was Maroney’s average speed (in m/s)? If Maroney’s mass was 55
kg, what was her kinetic energy?
24 hours = 86,400 seconds
V = d/t
93,625 m/86,400 s = 1/08 m/s
Looking For
Given
Relationship
Solution
Kinetic energy
m=55 kg
v= 1.08 m/s
KE=1/2 mv2
32.076 J
5. Does doubling the mass OR doubling the speed have the most effect on kinetic energy?
Doubling the speed because it would Quadruple the Kinetic Energy
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Challenge Section!
1. A 20 kg rock is on the edge of a 100 meter cliff.
a. Calculate the potential energy of the rock.
(
)(
⁄ )(
)
b. If the rock falls off the cliff, what is its kinetic energy just
before striking the ground?
c. What speed does the rock have as it strikes the ground?
(
√
)
√
√
2. Tarzan (mass = 75 kg) has an initial velocity of 12 m/s before he jumps off the ground (hi=0). Once in the
air he reaches the apex of his swing (vf = 0 m/s). How high does Tarzan swing assuming no external forces
act on him?
⁄
⁄ (
⁄ (
)
)(
)(
(
)
)
3. A large chunk of ice with mass 15 kg falls from a roof 8 meters above the ground. Find the kinetic energy
of the ice when it reaches the ground. What is the speed of the ice when it reaches the ground?
⁄
(
)
⁄ ( )( )
( )( )
( )
√
√( )
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4. A 74 kg student, starting from rest, slides down an 11.8 meter high water slide. How fast is he going at the
bottom of the slide?
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(
)
⁄ ( )( )
( )( )
( )
√
√( )
5. The diagram below shows a 10,000 kg bus traveling on a straight road which rises and falls. The speed of
the bus at point A is 26.82 m/s (60 mph). The engine has been disengaged and the bus is coasting. Friction
and air resistance are assumed negligible. The numbers on the left show the altitude above sea level in
meters. The letters A-F correspond to points on the road at these altitudes.
1. Find the speed of the bus at point B.
⁄
⁄ (
)(
⁄
)
(
)
(
)( )
⁄ (
)( )
( )
√
√( )
2. An evil villian has planted a bomb on the bus. If the speed of the bus falls below 22.35 m/s
(50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If
you feel the bus will explode, identify the interval in which this occurs.
( )
⁄
(
)
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(
√
√( )
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Name: __________________________ Period: ________________ Date: ________
The Snickers Bar
Research Question
How many times must I climb the stairs to use the stored energy of a snickers bar?
Introduction
Introduction:
In class we will be discussing work and energy. Energy is the ability to do work. Released energy is called
kinetic energy while stored energy is called potential energy.
The foods we eat contain stored energy. This energy is in chemical form and is released when we digest the
food. The basic unit of food energy is measured in calories.
All calories are not equal. There are calories and there are Calories. Calories with the capital C are actually
kilocalories and are called large Calories. One Calorie actually equals 1000 calories! The caloric content of food
is measured in Calories.
Purpose
In this activity you will be investigating how much chemical energy is in the food that you eat.
Do I really want to eat a Snickers?
1) Your weight in pounds must be converted into Newtons. This is accomplished by multiplying your
weight in pounds using the conversion factor 4.45N/pound.
Your weight (Fg) in Newtons = Your weight (Fg) in Pounds x 4.45N/pounds
=(
pounds) (4.45 N/pound)
2) What was the work done by your legs getting you up the steps?
Work Done = Your Weight (N) x 4.16 meters = _________ x 4.16 = _____ J
3) Convert the stored energy in a snickers bar (266 calories) from calories to Joules.
1 calorie = 4186 Joules
266 calories x 4186 Joules = __________ Joules
4) Calculate the number of times you would have to climb the steps to expend the amount of energy stored
in a Snickers bar.
__________ Joules (joules of energy from step #3) / __________ (work done in step #2)
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