Download 8th Grade Energy of Objects in Motion

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8th Grade
Energy of Objects of Motion
2015-10-28
www.njctl.org
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Energy of Objects in Motion
Click on the topic to go to that section
· Energy and its Forms
· Mechanical Energy
· Energy of Motion
· Stored Energy
· Conservation of Energy
· Types of Energy Resources
Review from Last Unit
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In the previous units we have been studying the motion of objects.
We talked about how far and fast an object goes if a force is applied
to it.
Why does a force cause an object to accelerate?
Review from Last Unit
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Answer
In the previous units we have been studying the motion of objects.
We talked about how
and fast
an object
goes
if a energy
force is applied
Byfar
applying
a force
onto an
object,
it.
is given to thetoobject.
This energy is
added to the amount of energy the object
Why does already
a forcepossessed.
cause an object to accelerate?
If a resistive force is applied onto an
object, then the force is taking energy
away from the object causing it to
decelerate.
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Energy and its Forms
Return to Table
of Contents
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What is Energy?
Energy is a measurement of an object's ability to do work.
How would you
define work?
How would you
know if any work
was being done?
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What is Energy?
Energy is a measurement of an object's ability to do work.
Work is defined as applying a force in order to move an object in a
given direction. When work is done on an object by another object,
there is a transfer of energy between objects.
Since energy is equal to work, the unit for both is the same, the
Joule (J).
1 Joule = 1 Newton-meter
Work
Work can only be done to a system by an external force; a
force from something that is not a part of the system.
So let's say our system is
a plane. The gate
assistance vehicle is not
part of the system. When
the vehicle comes
along and pushes back
the plane, it increases
the energy of the plane.
The assistance truck is
an outside force doing
work on the plane.
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Work
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The amount of work done is the change in the amount of energy
that the system will experience. This is given by the equation:
W = E final - Einitial
Fill in the blanks with "positive" or "negative". HINT: Think about how
these statements relate to acceleration.
· When a force is applied to an object that causes it to speed up and
move a distance, the work is _______________.
· When a resistive force is applied to an object that causes it to slow
down over a distance, or not move at all, the work would be
____________.
Positive Work
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If an object moves in
the same direction as
the direction of the
force applied to it,
the energy of the
system is increased.
The work is positive:
W > 0.
They can push the truck to get it to move!
Negative Work
If an object moves in the direction
opposite to the direction of the
force applied to it, then the work is
negative: W < 0.
The energy of the system is
reduced.
The parachute moves downwards,
while air resistance acts upwards
on the parachute.
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Zero Work
If an object does not move even
when there is a force applied to it,
then no work is done on the object!
W=0 J
The people exert a force onto the
wall, but the wall does not move!
Mechanical vs. Non-Mechanical Energy
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Energy exists in many forms, but can be broken down into two major
forms:
Mechanical Energy - The
energy of an object due to its
motion and position.
Mechanical energy is usually
used to describe a large
object.
It is the sum of kinetic and
potential energy.
Non-Mechanical Energy
The energy of an object
that is not due to its
motion or position. Nonmechanical energy usually
describes an object at its
atomic level.
Examples:
electrical energy
chemical energy
thermal energy
sound energy
1 Which of the following is the unit for energy?
A Meter
B Newton
C Second
D Joule
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1 Which of the following is the unit for energy?
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A Meter
C Second
D Joule
Answer
B Newton
D
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2 A wagon is rolling down a hill. A man tries to stop the
wagon by trying to push it back up the hill, but he is
unsuccessful. Is the man doing positive or negative
work?
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A positive
B negative
A positive
B negative
Answer
2 A wagon is rolling down a hill. A man tries to stop the
wagon by trying to push it back up the hill, but he is
unsuccessful. Is the man doing positive or negative
work?
B
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3 A boy kicks a soccer ball into a net. Did the boy do
positive or negative work on the ball?
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A positive
B negative
3 A boy kicks a soccer ball into a net. Did the boy do
positive or negative work on the ball?
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B negative
Answer
A positive
A
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4 A woman walks across an icy sidewalk that has been
covered in salt to help make it less slippery. Is the salt
doing positive or negative work on the woman's shoes?
A positive
B negative
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A positive
B negative
Answer
4 A woman walks across an icy sidewalk that has been
covered in salt to help make it less slippery. Is the salt
doing positive or negative work on the woman's shoes?
B
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5 Jill is waiting for the bus and she forgot her mittens. She
rubs her hands together to keep them warm. In this
situation, there is ______________ energy due to the
movement of her hands. There is also _______________
energy due to the heat she generates by rubbing her
hands together.
A mechanical, non-mechanical
B non-mechanical, mechanical
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Answer
5 Jill is waiting for the bus and she forgot her mittens. She
rubs her hands together to keep them warm. In this
situation, there is ______________ energy due to the
movement of her hands. There is also _______________
energy due to the heat she generates by rubbing her
hands together.
A mechanical, non-mechanical A
B non-mechanical, mechanical
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Mechanical Energy
Return to Table
of Contents
Forms of Mechanical Energy
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Mechanical Energy can be broken down into two different types of
Energy: energy of motion, which is called Kinetic Energy and stored
energy, which is called Potential Energy. Potential Energy has two
forms, Gravitational and Elastic, depending upon how the energy is
stored.
Write the
__________ Energy
underlined words
into the correct
place in the
diagram.
__________ Energy
__________ Energy
6 Which of the following is a form of mechanical
energy?
A Kinetic
B Thermal
C Chemical
D Solar
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6 Which of the following is a form of mechanical
energy?
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B Thermal
Answer
A Kinetic
A - Kinetic
C Chemical
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D Solar
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Energy of Motion
Return to Table
of Contents
7 Which of the following is a type of energy which is used
to describe the motion of an object?
A Electrical Energy
B Nuclear Energy
C Kinetic Energy
D All of the above
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7 Which of the following is a type of energy which is used
to describe the motion of an object?
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B Nuclear Energy
C Kinetic Energy
Answer
A Electrical Energy
D All of the above
C - Kinetic
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Energy of Motion
In order for an object to move, one of two scenarios has to occur:
1.
The object uses some of the potential energy that it had stored.
2.
Energy is transferred to the object from an outside source.
In either case, now that the object is in motion, the object is
experiencing kinetic energy.
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Kinetic Energy
An object's state of motion can be described by looking at the
amount of kinetic energy that the object has at that moment in time.
Since the state of motion
of an object can change
with time, the kinetic
energy of an object can
also change with time.
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Kinetic Energy
The amount of kinetic energy that an object possesses is
dependent on two factors:
mass
and
velocity
Both of these factors are directly proportional to the kinetic
energy. We talked about this mathematical relationship in the
last chapter. What did directly proportional mean?
Kinetic Energy, Mass, Velocity
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The larger the mass, the more energy is needed to move the object,
therefore the _______________ the kinetic energy.
Since kinetic energy is the energy of motion,
the object has to have a velocity to have kinetic energy. The larger the
velocity, the __________________ the kinetic energy.
How Does Kinetic Energy Depend on Mass?
If two identical objects are moving at the same velocity, they will
have the same kinetic energy.
However, if one object has more
mass than the other, the heavier
object will have more kinetic
energy.
v = 5 m/s
v = 5 m/s
A tennis ball and a bowling ball are both shown above. The bowling
ball is heavier than the tennis ball. Which ball would have more
kinetic energy?
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Velocity vs. Speed
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Remember that velocity is another way to measure motion. V elocity is
the speed of an object with direction. Speed does not have a direction,
so we call speed a scalar quantity.
Since velocity has both magnitude and direction, it is a vector quantity.
Runner's speed: 10 km/hr
Runner's velocity: 10 km/hr to the East
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How Does Kinetic Energy Depend on
Velocity?
In this picture, the hare is moving faster
than the tortoise at this point.
If we assumed that they had the same mass, who would have
more kinetic energy? Why? Discuss this with a partner.
How Does Kinetic Energy Depend upon
Velocity?
If two identical objects are moving at the same velocity then they will
have the same kinetic energy. However, if one of the objects is
moving faster, the faster one will have more kinetic energy.
v = 5 m/s
v = 10 m/s
In the diagram above, two identical tennis balls are moving. Which
tennis ball has more kinetic energy and why?
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8 Three different emergency vehicles are noticed driving on
the highway at a speed of 25 m/s. Which of the following
cars have the most kinetic energy at that moment?
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A a police car
B an ambulance
C a firetruck
D they all have the same kinetic energy
8 Three different emergency vehicles are noticed driving on
the highway at a speed of 25 m/s. Which of the following
cars have the most kinetic energy at that moment?
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B an ambulance
Answer
A a police car
C
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C a firetruck
D they all have the same kinetic energy
9 Three different baseball pitchers had the speed of their
fastball measured by a radar gun. Which of the following
pitcher's fastball had the smallest amount of kinetic
energy?
A a little league pitcher (22 m/s)
B a high school pitcher (33 m/s)
C a major league pitcher (41m/s)
D they all had the same kinetic energy
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9 Three different baseball pitchers had the speed of their
fastball measured by a radar gun. Which of the following
pitcher's fastball had the smallest amount of kinetic
energy?
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Answer
A a little league pitcher (22 m/s)
B a high school pitcher (33 m/s)
C a major league pitcher (41m/s)
A
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D they all had the same kinetic energy
10 Which of the following situations has the least kinetic
energy? Be ready to explain your answer.
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A a man sitting still on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
10 Which of the following situations has the least kinetic
energy? Be ready to explain your answer.
A a man sitting still on a park bench
C a woman driving a car
D it is impossible to tell
Answer
B a child riding a bike
A
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Calculating Kinetic Energy
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Kinetic energy can be solved for by using the equation:
KE =
1
2
mv2
Let's fill in the table below.
variable
Name
units
Kinetic Energy
m
m/s
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Example - Calculating Kinetic Energy
A car, which has a mass of 1,000 kg, is moving with a velocity of 5
m/s. How much kinetic energy does the car possess? Calculate
the car's kinetic energy.
1
KE = 2 mv2
KE = (0.5)(1000 kg)(5 m/s)2
KE = (0.5)(1000 kg)(25 m2/s2)
KE = 125,000 J
Click on the box to see the solution.
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Example - Calculating Kinetic Energy
Teacher Notes
A car, which has a mass of 1,000 kg, is moving with a velocity of 5
m/s. How much kinetic energy does the car possess? Calculate
Please note that there are multiple
the car's kinetic energy.
ways to model the math of this
problem. We suggest showing your
students at least two ways and then
1
continuing
KE to
= 2use
mv2the model that a
majority
of
your
students
2
KE = (0.5)(1000 kg)(5
m/s)prefer.
KE = (0.5)(1000 kg)(25 m2/s2)
KE = 125,000 J
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Click on the
box to see the solution.
11 A 10 kg snowball is rolling down a hill. Just before
reaching the bottom, its velocity is measured to be 10
m/s. What is the kinetic energy of the ball at this
position?
Answer
11 A 10 kg snowball is rolling down a hill. Just before
reaching the bottom, its velocity is measured to be 10
m/s. What is the kinetic energy of the ball at this
position?
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Slide 37 (Answer) / 122
KE= 1/2 mv2
KE= 1/2 (10 kg) (10 m/s)2
KE= 1/2 (10 kg) (100m2/s2)
KE= 500 J
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12 A 100 kg running back in football is running with a
velocity of 2 m/s. What is his kinetic energy?
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Answer
12 A 100 kg running back in football is running with a
velocity of 2 m/s. What is his kinetic energy?
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KE= 1/2 mv2
KE= 1/2 (100 kg) (2 m/s)2
KE= 1/2 (100 kg) (4m2/s2)
KE= 200 J
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13 A 2000 kg car with a velocity of 20 m/s slows down and
stops at a red light. What is the change in kinetic
energy?
Answer
13 A 2000 kg car with a velocity of 20 m/s slows down and
stops at a red light. What is the change in kinetic
energy?
KE= 1/2 mv2
KEf = 0 J (stopped)
KEi= 1/2 (2000 kg) (20 m/s)2
KEi= 1/2 (2000 kg) (400 m2/s2)
KEi= 400,00J
KEf-KEi= 0J-400,000J
= - 400,000J
negative because
it decreased
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Slide 39 (Answer) / 122
14 A 50 kg girl rode her 12 kg bicycle in a race. She started
from rest and peddled with a velocity of 10 m/s. What is the
change in kinetic energy of the girl and her bicycle?
Answer
14 A 50 kg girl rode her 12 kg bicycle in a race. She started
from rest and peddled with a velocity of 10 m/s. What is the
change in kinetic energy of the girl and her bicycle?
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Slide 40 (Answer) / 122
KE= 1/2 mv2
KEi = 0 J (stopped)
KEf= 1/2 (50 kg +12 kg) (10 m/s)2
KEf= 1/2 (62 kg) (100 m2/s2)
KEf= 3100 J
KEf-KEi= 3100J-0J
= 3100 J
positive because it increased
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Thinking Mathematically
1
KE = 2 mv2
We have already said that mass is directly proportional to kinetic energy.
This means that if the mass of the object doubles, the
doubles
kinetic energy ___________.
If the mass of the object increases by a
a factor of 5
increases by ______________.
factor of 5, then the kinetic energy___________
If the mass of the object decreases by half, then the kinetic
decrease
half
energy will ____________
by ___________.
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15 If the mass of a wagon is doubled, its kinetic energy:
A increases
B decreases
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15 If the mass of a wagon is doubled, its kinetic energy:
A increases
Answer
B decreases
A
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16 If the mass of a wagon is doubled, by what factor does
the kinetic energy increase?
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Answer
16 If the mass of a wagon is doubled, by what factor does
the kinetic energy increase?
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2
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Thinking Mathematically
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Kinetic energy can be solved by using the equation:
KE =
1
mv2
2
From the equation, we can see that the kinetic energy is also
directly proportional to the square of the velocity.
This means that if the velocity doubles, the kinetic energy
increases by a factor of 4.
22=4
If the velocity is quadrupled, then the kinetic energy increases
by a factor of 16.
42= 16
17 If the velocity of a wagon is tripled, its kinetic energy:
A increases
B decreases
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17 If the velocity of a wagon is tripled, its kinetic energy:
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A increases
Answer
B decreases
A
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18 If the velocity of a wagon is tripled, by what factor does
the kinetic energy increase?
Answer
18 If the velocity of a wagon is tripled, by what factor does
the kinetic energy increase?
9
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19 Two balls are moving with the same velocity, ball A has a
mass of 10 kg and ball B has a mass of 40 kg. How
much more kinetic energy does ball B have?
Answer
19 Two balls are moving with the same velocity, ball A has a
mass of 10 kg and ball B has a mass of 40 kg. How
much more kinetic energy does ball B have?
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4 times
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20 A cart halves its mass and at the same time doubles its
speed. Does the kinetic energy increase or decrease? By
what factor does the kinetic energy change?
A increase, 2
B increase, 4
C decrease, 2
D decrease, 4
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20 A cart halves its mass and at the same time doubles its
speed. Does the kinetic energy increase or decrease? By
what factor does the kinetic energy change?
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A increase, 2
Answer
· half the4mass gives 1/2 the KE,
B increase,
· double the speed gives 4 x KE
· therefore (1/2)(4)= 2
C decrease, 2
D decrease, 4
A
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Stored Energy
Return to Table
of Contents
Where does Kinetic Energy Come From?
Imagine a roller coaster car that is at the top of the first hill and is
stopped.
Does the car stay
stopped at the top
of the hill for the
entire ride?
What happens?
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Where does Kinetic Energy Come From?
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Once the car leans over the
edge, gravity pulls it down.
The ride is taking advantage
of the gravitational attraction
between the car and Earth to
give the car kinetic energy
and make it go faster as it
falls.
The kinetic energy the car is
receiving is coming from
another type of energy called
potential energy.
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Where does Kinetic Energy Come From?
Potential energy is energy stored in an object due to the object's
position. The roller coaster car on the previous slide had stored
energy due to its height above the ground.
There are two forms of potential energy that we will be looking at in
this unit:
Gravitational Potential Energy
and
Elastic Potential Energy
Gravitational Potential Energy
The potential energy due to
elevated positions is called
gravitational potential energy.
Gravitational potential energy is
stored energy and it can be used at
a later time to cause an object to
move.
Once the person steps off the
diving board, the gravitational
potential energy is converted into
kinetic energy and the person falls
(moves!)
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Gravitational Potential Energy
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Work is required to elevate objects against Earth's
gravity.
For example, work is done on the truck to elevate it
off the ground. The amount of work done on the
truck is equal to the truck's gravitational potential
energy at this new height.
Gravitational Potential Energy
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Gravitational potential energy is determined by three factors: mass,
gravitational acceleration, and height. All three factors are directly
proportional to energy.
more
Mass: The heavier the object is, the _______
gravitational potential energy the object has.
more
Gravitational Acceleration: The larger the 'g', the _________
gravitational potential energy the object has. Since gravity on Earth
is considered a constant, this will not change.
more
Height: The higher the object is off the ground, the _________
gravitational potential energy the object has.
How Does Mass Affect Gravitational
Potential Energy?
In this picture, the mass of a tennis ball was doubled when it was at
the same height off of the ground.
m = 2 kg
h=2m
m = 1 kg
h=2m
How does the gravitational
potential energy compare
for the two objects?
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How Does Mass Affect Gravitational
Potential Energy?
m = 2 kg
Slide 57 / 122
Mass: doubled
m = 1 kg
Gravitational Acceleration:
stayed the same, no change
h=2m
h=2m
Height: stayed the same, no change
Since the only thing that changed was the mass, which doubled,
the gravitational potential energy also doubled.
How Does Height Affect Gravitational
Potential Energy?
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In this picture, a tennis ball is lifted to a height that is twice as high.
How would the gravitational
potential energy compare at the
higher height?
h=4m
h=2m
How Does Height Affect Gravitational
Potential Energy?
Mass: stayed the same, no change
Gravitational Acceleration: stayed the
same, no change
h=4m
h=2m
Height: doubled
Since the only thing that changed was the height which doubled,
the gravitational potential energy also doubled.
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21 A bowling ball, which has a mass that is 30 times larger
than a softball, is lifted to the same height as the softball.
How does the gravitational potential energy of the
bowling ball compare to the softball?
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A they are the same
B thirty times smaller
C ten times as large
D thirty times as large
21 A bowling ball, which has a mass that is 30 times larger
than a softball, is lifted to the same height as the softball.
How does the gravitational potential energy of the
bowling ball compare to the softball?
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B thirty times smaller
C ten times as large
D thirty times as large
Answer
A they are the same
D
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22 Two balloons are floating in the sky. If one balloon is
floating at a height of 30 m and the other identical
balloon, is floating at a height of 45 m, how much larger is
the gravitational potential energy of the higher balloon
compared to the lower one?
A half as large
B they are the same
C 1.5 times larger
D twice as large
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22 Two balloons are floating in the sky. If one balloon is
floating at a height of 30 m and the other identical
balloon, is floating at a height of 45 m, how much larger is
the gravitational potential energy of the higher balloon
compared to the lower one?
Slide 61 (Answer) / 122
A half as large
Answer
B they are the same
C 1.5 times larger
D twice as large
C
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Calculating Gravitational Potential Energy
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Gravitational potential energy can be solved by using the
equation:
GPE = mgh
Let's fill in the table below.
variable
Name
units
Gravitational
Potential Energy
m
m
Gravity
Example - Calculating Gravitational
Potential Energy
A basketball with a mass of 0.5 kg, is held at a height of 2 m
above the ground. How much gravitational potential energy
does the basketball possess?
GPE = mgh
GPE = (0.5 kg)(9.8 m/s2)(2 m)
GPE = 9.8 J
Click on the box to see the solution.
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23 A 50 kg diver is standing on top of a 10 m platform. How
much gravitational potential energy does he have?
Answer
23 A 50 kg diver is standing on top of a 10 m platform. How
much gravitational potential energy does he have?
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Slide 64 (Answer) / 122
GPE= mgh
= 50 kg(9.8 m/s 2)(10 m)
= 4,900 J
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24 A 3,000 kg hot air balloon is hovering at a height of 100
m above Earth's surface. How much gravitational
potential energy does it possess?
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Answer
24 A 3,000 kg hot air balloon is hovering at a height of 100
m above Earth's surface. How much gravitational
potential energy does it possess?
Slide 65 (Answer) / 122
GPE= mgh
= 3000 kg(9.8 m/s2)(100 m)
= 294,000,000 J
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Thinking Mathematically
GPE = mgh
GPE = mgh
GPE = mgh
If any of these decrease,
then the GPE decreases
by the same factor.
We know that GPE is directly
proportional to mass, to
gravity, and to height. This
means that as any of these
increase, the GPE increases
by the same factor.
GPE
= mgh
GPE
= mgh
GPE
= mgh
25 A ball is at a height of 30 m. It is then moved to a height
of 60m. By what factor does the GPE increase?
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Answer
25 A ball is at a height of 30 m. It is then moved to a height
of 60m. By what factor does the GPE increase?
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2
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26 A 3 kg object and a 9 kg object are elevated from the
same height. Which has more GPE?
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A 3 kg object
B 9 kg object
26 A 3 kg object and a 9 kg object are elevated from the
same height. Which has more GPE?
A 3 kg object
Answer
B 9 kg object
B
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27 A 3 kg object and a 9 kg object are dropped from the
same height. How much less is the GPE of the 3 kg
object than the 9 kg object?
Answer
27 A 3 kg object and a 9 kg object are dropped from the
same height. How much less is the GPE of the 3 kg
object than the 9 kg object?
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Slide 69 (Answer) / 122
1/3
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28 An object is 5 m above the ground. The object triples its
mass and doubles its height. By what factor does the
object's GPE change?
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Answer
28 An object is 5 m above the ground. The object triples its
mass and doubles its height. By what factor does the
object's GPE change?
Slide 70 (Answer) / 122
6
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Elastic Potential Energy
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Another type of stored energy is
called elastic potential energy.
Looking at the picture to the right,
can you come up with an idea about
what elastic potential energy is?
Elastic Potential Energy
Elastic potential energy is determined by two factors: the elasticity
of the material and how far it is stretched or compressed.
Think about what you know
about rubber bands.
Do you think elasticity and
distance stretched are directly
proportional or indirectly
proportional to the energy?
Talk about this at your table.
Slide 72 / 122
Slide 73 / 122
Elastic Potential Energy
Elasticity: The more elastic a material is, the more elastic potential
energy the object has.
Distance of stretch (or compression): The larger
the distance the elastic material is stretched (or
compressed) the more elastic potential energy
it has.
What is the Difference Between Stretching
and Compression in a Spring?
Slide 74 / 122
Think about a slinky sitting
on a desk. A spring has no
potential energy stored in it
if it is neither stretched nor
compressed. This relaxed
state is shown in figure (a).
Stretching a spring is
caused when the spring is
pulled increasing the length
of the spring compared to
the relaxed length, as shown
in figure (b).
(a)
(b)
(c)
What is the Difference Between Stretching
and Compression in a Spring?
Compressing a spring is caused when the spring is squeezed. This
causes a decrease in the length of the spring compared to the relaxed
length, as shown in figure (c).
The stretched and compressed spring below store the same elastic
potential energy because both springs are displaced the same
distance, x.
relaxed
no EPE stored
(a)
stretched compressed
(b)
(c)
Slide 75 / 122
How Does Elastic Potential Energy Depend
Upon Compression and Stretching?
Slide 76 / 122
Both pictures to the right show a spring, which
is an elastic material.
In the top picture the spring is stretched from
its relaxed state.
In the bottom picture, the spring is compressed
from its relaxed state.
For each case, is elastic potential energy stored in the
spring?
29 A child jumps on a trampoline. When will the trampoline
have more elastic potential energy?
Slide 77 / 122
A When the child is standing on the trampoline
B When the child is in the air
C When the child lands on the trampoline after
jumping
D The trampoline will always have the same elastic
potential energy
29 A child jumps on a trampoline. When will the trampoline
have more elastic potential energy?
A When the child is standing on the trampoline
Answer
B When the child is in the air
C
C When the child lands on the trampoline after
jumping
[This object is a pull
tab]
D The trampoline will always have the same elastic
potential energy
Slide 77 (Answer) / 122
Calculating Elastic Potential Energy
Slide 78 / 122
Elastic potential energy can be solved by using the equation:
EPE = 1 kx2
2
EPE = Elastic Potential Energy (J)
k = spring constant (N/m)
x = distance of stretch or compression (m)
Spring Constant
Slide 79 / 122
1
EPE = 2 kx2
The energy and distance variables in this equation are likely familiar.
But what is the spring constant
(k)? Look at the two springs to
the right. Which do you think
would be easier to stretch?
Every spring has a different
degree of stretchiness and
that is what the spring
constant represents.
Spring Constant
1
EPE = 2 kx2
Breaking down the units for
spring constant also
explains what the variable
represents.
Can you explain what
Newtons per Meter (N/m)
means?
Slide 80 / 122
Example - Calculating Elastic Potential
Energy
Slide 81 / 122
A spring that has a spring constant of 10 N/m, is stretched a
distance of 1 m from its relaxed length. How much elastic
potential energy is stored in the spring?
1
EPE =2 kx2
EPE = (
EPE = (
1
2
1
2
)(10 N/m)(1 m)2
)(10 N/m)(1 m2)
EPE = (5 N*m)
EPE = 5 J
Click on the box to see the solution.
Example - Calculating Elastic Potential
Energy
Slide 81 (Answer) / 122
Teacher Notes
A spring that has a spring constant of 10 N/m, is stretched a
Please
note that
there
aremuch
multiple
distance of 1 m from
its relaxed
length.
How
elastic
ways toinmodel
the math of this
potential energy is stored
the spring?
problem. We suggest showing your
students at least two ways and then
continuing to use the model that a
1
majorityEPE
of your
prefer.
=2 students
kx2
EPE = (
EPE = (
1
2
1
2
)(10 N/m)(1 m)2
)(10 N/m)(1 m2)
EPE = (5 N*m)
EPE = 5 J
[This object is a teacher notes pull
tab]
Click on the box to see the solution.
30 A child bouncing on a pogo stick compresses the spring
by 0.25 m. If the spring constant of the spring on the
bottom of the pogo stick is 200 N/m, what is the elastic
potential energy stored in the spring when it is
compressed?
Slide 82 / 122
Answer
30 A child bouncing on a pogo stick compresses the spring
by 0.25 m. If the spring constant of the spring on the
bottom of the pogo stick is 200 N/m, what is the elastic
potential energy stored in the spring when it is
compressed?
Slide 82 (Answer) / 122
EPE= 1/2 kx 2
= 1/2 (200 N/m) (0.25 m) 2
= 1/2 (200 N/m)(0.0625 m 2)
= 100 N/m (0.0625 m2)
EPE = 6.25 J
[This object is a pull
tab]
31 A rubber band with a spring constant of 40 N/m is pulled
back 0.5 m. How much elastic potential energy is stored
in the elastic band?
Answer
31 A rubber band with a spring constant of 40 N/m is pulled
back 0.5 m. How much elastic potential energy is stored
in the elastic band?
EPE= 1/2 kx2
= 1/2 (40 N/m) (0.5 m)2
= 20 N/m (0.25 m2)
EPE = 5 J
[This object is a pull
tab]
Slide 83 / 122
Slide 83 (Answer) / 122
32 Which of the following would you expect to have the
smallest spring constant?
Slide 84 / 122
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
32 Which of the following would you expect to have the
smallest spring constant?
Slide 84 (Answer) / 122
B a slinky
C a spring in a pen
Answer
A a garage door spring
C
D a trampoline spring
[This object is a pull tab]
Thinking Mathematically
EPE = 1 kx2
2
KE =
1 mv2
2
Notice that the equation for EPE is similar to the equation for KE.
Remember that in the equation for KE, energy was directly
proportional to the mass and it was also directly proportional to
the square of the velocity.
What do you think the relationship is between EPE and the
spring constant, k?
What do you think is the relationship between EPE and the
distance, x, the spring is stretched or compressed?
Slide 85 / 122
Thinking Mathematically
Slide 86 / 122
1
EPE = 2 kx2
directly proportional
EPE is _________________________
to the spring constant.
directly proportional
EPE is _________________________
to the square of the
distance the spring is compressed or stretched.
33 If the spring constant, k, is tripled, by what factor does
the EPE increase?
Answer
33 If the spring constant, k, is tripled, by what factor does
the EPE increase?
3
[This object is a pull
tab]
Slide 87 / 122
Slide 87 (Answer) / 122
34 If the spring constant, k, is halved, by what factor does
the EPE decrease?
Answer
34 If the spring constant, k, is halved, by what factor does
the EPE decrease?
Slide 88 / 122
Slide 88 (Answer) / 122
1/2
[This object is a pull
tab]
35 If the distance a spring is stretched is increased by a
factor of 6, by what factor is the EPE increased?
Slide 89 / 122
Answer
35 If the distance a spring is stretched is increased by a
factor of 6, by what factor is the EPE increased?
Slide 89 (Answer) / 122
36
[This object is a pull
tab]
Slide 90 / 122
Conservation of Energy
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of Contents
Slide 91 / 122
Conservation of Energy
What we have looked at so far is that an object has kinetic energy if
the object is in motion. The faster that the object is going, the more
kinetic energy it has.
In order for an object's kinetic energy to increase, it must get energy
from somewhere. But where would it get that energy?
Hint: think back to the roller
coaster. What kind of
energy did it have at the
top of the hill?
Conservation of Energy
Slide 92 / 122
In order for an object's kinetic energy to increase, it must take
energy from its stored energy, which we call potential energy.
When this happens, the potential energy that an object
possesses decreases.
Even though kinetic and potential energy are changing, the Total
Energy (TE) in that closed system contains does not change.
This is called the Conservation of Energy.
initial Total Energy = final Total Energy
TEi = TEf
Conservation of Energy
Slide 93 / 122
When energy is conserved, no energy is added or taken away from
the system. The total energy you start with is the total energy you
end with.
TEi = TEf
In other words, energy can not be created or destroyed. It can only
be transformed from one form to another.
Click here to see conservation of energy
explained in roller coasters!
Conservation of Energy
When looking at the mechanical energy of a system, the total
energy possible is the Potential Energy (PE) and the Kinetic
Energy (KE) added together. Therefore, another way to write
conservation of energy is like this:
(PE + KE)i = (PE + KE)f
When would PE be zero?
When would KE be zero?
· the object is on the
ground (GPE)
· the object is not moving
· when a spring or other
elastic material is not
stretched or compressed
(EPE)
Slide 94 / 122
Conservation of Energy
Slide 95 / 122
Let's see if we can determine the total energy of a ball that isdropped
from rest. The figure below shows the ball at different positions as it
falls, starting with when it's at rest at 1 m before being dropped. Use
the idea of conservation of energy to determine the missing values.
Remember that the total
mechanical energy at
that position is the sum of
the two individual
energies: (PE + KE)
v= 0 m/s
Height = 1 m
TE = 0.5 J
PE = 0.5 J
KE = 0 J
Height = 0.5 m
TE = 0.5 J
PE = 0.25 J
KE = 0.25 J
Height = 0 m
TE = 0.5 J
PE = 0 J
KE = 0.5 J
At position A in the diagram below, the roller coaster car has 40 J of
total energy and has a velocity equal to 0 m/s.
Slide 96 / 122
How much kinetic energy does the car possess at Point A?
0J
How much gravitational potential energy does the car possess at
Point A?
40 J
40 J
15 J
25 J
Slide 97 / 122
At position B in the diagram below, the roller coaster car has a
gravitational potential energy equal to 15 J.
How much total energy does the car possess at Point B?
40 J
How much kinetic energy does the car possess at Point B?
25 J
40 J
15 J
25 J
Slide 98 / 122
At position C in the diagram below, the roller coaster car has a
gravitational potential energy equal to 25 J.
How much total energy does the car possess at Point C?
40 J
How much kinetic energy does the car possess at Point C?
15 J
40 J
15 J
25 J
Slide 99 / 122
36 At what position in the diagram below does the object
have only gravitational potential energy?
A W
B X
C Y
D Z
E None of the above
h=0m
Slide 99 (Answer) / 122
36 At what position in the diagram below does the object
have only gravitational potential energy?
B X
C Y
D Z
Answer
A W
A
[This object is a pull
tab]
E None of the above
h=0m
Slide 100 / 122
37 At what position in the diagram below does theobject
have only kinetic energy?
A W
B X
C Y
D Z
E None of the above
h=0m
Slide 100 (Answer) / 122
37 At what position in the diagram below does theobject
have only kinetic energy?
B X
C Y
D Z
Answer
A W
B
[This object is a pull
tab]
E None of the above
h=0m
38 At what position in the diagram below does the
object have both gravitational potential and kinetic
energy? Choose all that apply.
A W
B X
C Y
D Z
E None of the above
h=0m
Slide 101 / 122
38 At what position in the diagram below does the
object have both gravitational potential and kinetic
energy? Choose all that apply.
Slide 101 (Answer) / 122
A W
Answer
B X
C and D
C Y
[This object is a pull
tab]
D Z
E None of the above
h=0m
Transfer of Kinetic Energy to Potential
Energy
Slide 102 / 122
Transfer of Kinetic Energy to Potential
Energy
Slide 103 / 122
Just as potential energy can be transferred to kinetic energy, kinetic
energy can be transferred into potential energy.
The total energy of the object must always be the
same due to conservation of energy. Let's look at the
ball that is dropped from 1 m again. Suppose the ball
bounces after it hits the ground. What will happen to
v= 0 m/s
the KE?
Height = 1 m
TE = 0.5 J
PE = 0.5 J
Height = 0.5 m
KE = 0 J
TE = 0.5 J
PE = 0.25 J
KE = 0.25 J
Height = 0 m
TE = 0.5 J
PE = 0 J
KE = 0.5 J
The kinetic energy at the bottom will be transferred to gravitational
potential energy as the ball gains height. Because of conservation of
energy, the total energy stays the same!
Height = 0 m
TE = 0.5 J
PE = 0 J
KE = 0.5 J
Height = 0.5 m
TE = 0.5 J
PE = 0.25 J
KE = 0.25 J
v= 0 m/s
Height = 1 m
TE = 0.5 J
PE = 0.5 J
KE = 0 J
Transfer of Kinetic Energy to Potential
Energy
Slide 104 / 122
In reality, the ball will not bounce as high as it was dropped. Does this
mean energy was lost?
No. It just means that some of the KE that
the ball had when it first hits the ground was
transferred to the ground as heat and sound
energy (aka Non-Mechanical Energy). If we
consider the ball and the ground to be a
closed system, then the system's total
energy stays the same!
TE = 0.5 J
PE = 0.25 J
KE = 0.15 J
TE = 0.5 J
PE = 0 J
KE = 0.5 J
Sound Energy!
NME = 0.10 J
TE = 0.5 J
PE = 0.4 J
KE = 0 J
v= 0 m/s
Height < 1 m
NME=0.10 J
Transfer of Kinetic Energy to Potential
Energy
Slide 105 / 122
Kinetic energy can also be transferred to elastic potential energy.
Conservation of energy of
still applies, which means the
total energy remains
constant.
Let's consider a system that
is composed of a block and a
spring as shown to the right.
Transfer of Kinetic Energy to Elastic
Potential Energy
In the top picture, the block is travelling
at 10 m/s, meaning that it has kinetic
energy. The spring is relaxed and
therefore has no elastic potential
energy. The total energy of the blockspring system is entirely due to the KE
of the block right now.
In the bottom picture, the block has
compressed the spring and is no
longer moving. The block has
transferred its kinetic energy to elastic
potential energy in the spring. The total
energy of the block-spring system is
entirely due to the elastic potential
energy in the spring.
Slide 106 / 122
39 In which position of the block would the system have
only EPE?
A
B
C
B
Answer
39 In which position of the block would the system have
only EPE?
A
Slide 107 / 122
C
Slide 107 (Answer) / 122
C
[This object is a pull
tab]
40 In which position of the block would the system have
both KE and EPE?
A
B
C
Slide 108 / 122
A
Answer
40 In which position of the block would the system have
both KE and EPE?
C
B
Slide 108 (Answer) / 122
B
[This object is a pull
tab]
41 In which position of the block would the system have
only KE?
A
B
C
B
C
Answer
41 In which position of the block would the system have
only KE?
A
Slide 109 / 122
A
[This object is a pull
tab]
Slide 109 (Answer) / 122
What if the Total Energy is not
equal at the beginning and the end?
Slide 110 / 122
If the total amount of energy that we start with, Ei, does not equal
the total amount of energy that we end up with, "Ef ", then energy
was not conserved
TEi
TEf
This means that there was an outside force that acted on the
system. Let's look at the dropping ball again. Last time we
considered the ball and the ground as the system together. What if
we just considered the ball as the system by itself?
What if the Total Energy is not
equal at the beginning and the end?
Slide 111 / 122
The total energy of the ball before the bounce and after the bounce
would be different. This is because the ground would now be an
outside force acting on the system, the ball.
TE = 0.4 J
PE = 0.4 J
KE = 0 J
TE = 0.5 J
TE = 0.5 J
PE = 0 J
KE = 0.5 J
Sound Energy!
TE = 0.4 J
PE = 0.25 J
KE = 0.15 J
NME = 0.10 J
v= 0 m/s
Height < 1 m
NME=0.10 J
Slide 112 / 122
Types of Energy Resources
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of Contents
Energy Resources
Slide 113 / 122
Electrical energy can be produced through the conservation of
energy by using the mechanical energy contained in energy
resources.
Energy resources can be broken down into two categories:
Renewable and Non-Renewable.
Renewable Energy Resources are natural resources that can
replenish themselves over time.
Non-Renewable Energy Resources are natural energy resources
that exist in limited supply and cannot be replenished in a timely
manner.
Types of Energy Resources
Slide 114 / 122
Energy Production from the Sun
Slide 115 / 122
Solar energy is a renewable form of
energy that is produced when
photons that are contained in sunlight
are absorbed by specially designed
plates that are angled towards the
sun.
When the photons hit the solar panels, charged particles are free to
move which causes a current to be produced. This current is
converted to usable electricity by the home.
Solar energy is converted to electrical energy!
Energy Production from the Wind
Slide 116 / 122
Wind is a renewable energy resource
that is used to create electricity by
wind turbines, such as in the Alta
Wind Energy Center in California, the
world's largest wind farm.
As the wind blows past the blades of
the turbine, the kinetic energy of the
wind is transferred to the blades.
Inside the column of the turbine,
there is a drive shaft which is
connected to a generator.
As the blades spin, it spins the drive shaft that is connected to a
generator. The generator converts the kinetic energy (mechanical
energy) into electrical energy!
Energy Production From Water
Slide 117 / 122
Water is a renewable resource that can be used to
create electricity in dams such as the Hoover Dam.
Gravitational potential energy is stored in elevated
water. When the water is released downward
towards a turbine, the GPE is converted to kinetic
energy and spins the turbine.
The turbine is connected to a generator that
converts this mechanical energy to electrical
energy!
Energy Production from Fossil Fuels
Fossil fuels are a non-renewable energy
resource that can be used to produce
electricity when it is burned.
Fossil fuels include: natural gas, oil, and coal
(shown to the right).
When the fuel is burned, the heat
turns water into steam which turn
the blades of a turbine (kinetic
energy!). The turbine is connected
to a generator that converts the
mechanical energy into electrical
energy!
Slide 118 / 122
Effects of Using Fossil Fuels As An Energy
Resource
Slide 119 / 122
Fossil fuels are non-renewable
energy resources due to how long
it takes for them to be produced
compared to how much is used to
create energy.
Fossil fuels take millions of years
to be produced.
Fossil fuels are also not considered
"Clean" energy resources as they
produce Carbon Dioxide (CO2) when
burned. Carbon dioxide is
considered a greenhouse gas, which
many believe is a cause global
warming.
42 Which of the following is not considered a renewable
energy resource?
Slide 120 / 122
A Solar
B Wind
C Hydroelectric (water)
D Fossil Fuels
42 Which of the following is not considered a renewable
energy resource?
B Wind
Answer
A Solar
D
C Hydroelectric (water)
[This object is a pull
tab]
D Fossil Fuels
Slide 120 (Answer) / 122
43 The production of energy by wind, water, the sun, and
fossil fuels relies on the principle of conservation of
energy.
Slide 121 / 122
True
False
43 The production of energy by wind, water, the sun, and
fossil fuels relies on the principle of conservation of
energy.
Slide 121 (Answer) / 122
False
Answer
True
TRUE
[This object is a pull
tab]
44 The spinning of a generator in wind turbines and
hydroelectric dams converts non-mechanical energy into
electrical energy.
True
False
Slide 122 / 122
44 The spinning of a generator in wind turbines and
hydroelectric dams converts non-mechanical energy into
electrical energy.
True
Answer
False
FALSE
they convert
mechanical energy
into electrical energy
[This object is a pull
tab]
Slide 122 (Answer) / 122