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Energy of Objects in Motion
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Energy of Objects in Motion
· Energy and its Forms
Click on the topic to go to that section
· Mechanical Energy
· Types of Energy Resources· Conservation of Energy
· Energy of Motion· Stored Energy
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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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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. The more work that is done by an object, the more energy it exerts.
Since energy is equal to work, the unit for both is the same, the Joule (J).
1 Joule = 1 Newton-meter
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Work can only be done to a system by an external force; a force from something that is not a part of the system.
Work
So let's say our system is a plane and the gate assistance vehicle. When the vehicle comes along and pushes back the plane, it increases the energy of the plane.
The assistance truck is essentially doing work on the plane.
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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
Work
· When a force is applied which causes the object to speed up and move a distance, the work is _______________. · If a resistive force was applied which caused the object to slow down over a distance, or not move at all, the work would be ____________.
(think about acceleration)
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If the object moves in the same direction as the direction of the force,
the energy of the system is increased.
The work is positive: W > 0.
Positive Work
They can push the truck to get it to move!
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If the object moves in the direction opposite the direction of the force then the work is negative: W < 0.
The energy of the system is reduced.
Pushing on the wall as hard as they can won't ever move the wall!
Negative Work
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Mechanical vs. Non-Mechanical Energy
Mechanical Energy - The Energy of an object due to its motion and position. Mechanical Energy is the sum of the Kinetic and Potential Energy of an object. Mechanical Energy is usually used to describe a large object.
Non-Mechanical Energy - The Energy of an object that is not due to it's motion or position. Non-Mechanical Energy usually describes an object at it's atomic level.
Energy exists in many forms, but can be broken down into two major forms:
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1 Which of the following is the unit for energy?
A Meter
B Newton
C Second
D Joule
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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?
A positive
B negative
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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?
A positive
B negative
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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 Ans
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__________ Energy
__________ Energy __________ Energy
Forms of Mechanical EnergyMechanical 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 underlined words into the
correct place in the diagram.
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5 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 type of energy which is used to describe the motion of an object?
A Electrical Energy
B Nuclear Energy
C Potential Energy
D All of the above
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Energy of Motion
In order for an object to move, one of two scenarios has to occur:
The object uses some of the potential energy that it had stored.
The object is being given energy from an outside source.
In either case, now that the object is in motion, the object is experiencing Kinetic Energy.
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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.
Kinetic Energy
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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The amount of Kinetic Energy that an object possesses is dependent on two factors: mass and velocity.
Kinetic Energy
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?
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Kinetic Energy, Mass, Velocity
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.
The larger the mass, the more energy is needed to move the object,
therefore the _______________ the kinetic energy.
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How Does Kinetic Energy Depend on Mass?If two identical objects are moving at the same velocity then they will have the same 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. If they were both to move at the same velocity, which ball would have more kinetic energy?
If however, one object has more mass than the other while traveling at the same velocity, the heavier object will have more kinetic energy.
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Velocity vs. Speed
Remember that velocity is another way to measure motion. Simply put, velocity 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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What is Kinetic Energy?
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.
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v = 5 m/s
v = 10 m/s
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. If however, one of the object's is moving faster, the one which is moving faster will have more kinetic energy.
In the diagram above, two identical tennis balls are moving. Which tennis ball has more kinetic energy and why?
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7 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?
A a police car
B an ambulance
C a Firetruck
D they all have the same kinetic energy
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8 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
B a high school pitcher
C a major league pitcher
D they all had the same kinetic energy
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9 Which of the following situations has the lowest kinetic energy? Be ready to explain your answer.
A a man sitting on a park bench
B a child riding a bike
C a woman driving a car
D it is impossible to tell
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Calculating Kinetic Energy
Kinetic Energy can be solved for by using the equation:
12KE = mv2
Fill in the table below.
variable unitsName
Kinetic Energy
mm/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?
KE = mv2
KE = (0.5)(1000 kg)(5 m/s)2
KE = (0.5)(1000 kg)(25 m2/s2)KE = 125,000 J
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10 A 10 kg snowball is rolling down a hill. Just before reaching the bottom, it's velocity is measured to be 10 m/s. What is the Kinetic Energy of the ball at this position?
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11 A 100 kg man running back in football is running with a velocity of 2 m/s. What is his Kinetic Energy?
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12 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?
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13 A 50kg 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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Thinking Mathematically
KE = mv212
We have already said that mass and velocity are directly proportional to
kinetic energy. This means that if the mass of the object doubles, the
kinetic energy ___________. If the mass of the object increases by a
factor of 5, then the kinetic energy___________ by ______________.
If the mass of the object decreases by half, then the kinetic
energy will ____________ by ___________.
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Thinking Mathematically
Kinetic Energy can be solved by using the equation:
KE = mv212
Looking at this equation again, 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
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14 If the mass of a wagon is doubled, by what factor does the KE increase?
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15 If the velocity of a wagon is tripled, by what factor does the KE increase?
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16 Two balls are moving with the same velocity, ball A has a mass of 10kg and ball B has a mass of 40kg. How much more KE does ball B have?
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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?
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 that an object has stored within it due to it's position, in this case, the car's height.
There are two forms of Potential Energy that we will be looking at in this unit:
Gravitational Potential Energyand
Elastic Potential Energy
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Gravitational Potential Energy
An object has a certain amount of energy naturally associated with it.
If the object has a force acting on it from a distance (like gravity) and there is no object supporting the object, then the amount of energy that the object has is called the Gravitational Potential Energy.
This energy is stored energy and means that it can be used at a later time to cause an object to move.
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Gravitational Potential EnergyGravitational Potential Energy is determined by three factors: mass, gravity, and height. All three factors are directly proportional to energy.
Mass: The heavier the object is, the _______ gravitational potential energy the object has.
Gravity: The larger the gravity, the _________ gravitational potential energy the object has. Since gravity on Earth is considered a constant, this will not change.
Height: The higher the object is off the ground, the _________ gravitational potential energy the object has.
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h = 2 m h = 2 m
m = 2 kg m = 1 kg
In this picture, the mass of a tennis ball was doubled when it was at the same height off of the ground.
How Does Mass Affect Gravitational Potential Energy
How does the gravitational potential energy compare
for the two objects?
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h = 2 m h = 2 m
m = 2 kg m = 1 kg mass: double = doubledgravity: stayed the same = no changeheight: stayed the same = no change
Since the only thing that changed was the mass, which doubled, the gravitational potential energy also doubled.
How Does Mass Affect Gravitational Potential Energy
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h = 4 m
h = 2 m
In this picture, the same object, a tennis ball, is lifted to a height that is twice as high.
How Does Height Affect Gravitational Potential Energy
How would the Gravitational Potential Energy compare at the
higher height?
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h = 4 m
h = 2 m
mass: stayed the same = no changegravity: stayed the same = no changeheight: doubled = doubled
Since the only thing that changed was the height which doubled, the gravitational potential energy also doubled.
How Does Height Affect Gravitational Potential Energy
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17 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 much larger is the Gravitational Potential Energy for the bowling ball compared to the softball?A they are the same
B twice as large
C ten times as large
D thirty times as large
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18 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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Calculating Gravitational Potential Energy
Gravitational Potential Energy can be solved by using the equation:
variable unitsNameGravitational
Potential Energy
mm
Gravity
GPE = mgh
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Example - Calculating Gravitational Potential Energy
A basketball, whose mass is 0.5 kg, is held at a height of 2 m above the ground. How much Gravitational Potential Energy does the basketball possess?
GPE = mghGPE = (0.5 kg)(9.8 m/s2)(2 m)
GPE = 9.8 J
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19 A 50 kg diver is standing on top of the 10 m platform. How much Gravitational Potential Energy does he have?
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20 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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Thinking Mathematically
GPE = mgh
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. If any of these decrease, then the GPE decreases by the same factor.
GPE = mgh
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21 A ball is dropped from 30m, it is then dropped from 60m. By what factor does the GPE increase?
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22 A 3kg object and a 9kg object are both dropped from the same height. Which has more GPE?
A 3kg objectB 9kg object
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23 A 3kg object and a 9kg object are dropped from the same height. How much less is the GPE of the 3kg object than the 9kg object?
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Elastic Potential EnergySometimes it is not possible to take advantage of gravity's pull on an object to change it's Kinetic Energy, such as if the object is on a flat surface.
One type of Potential 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?
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Elastic Potential Energy is determined by two factors: the elasticity of the material and how far it is stretched or compressed.
Elastic Potential Energy
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.
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Elasticity: The more elastic that a material is, the more elastic potential energy the object has.
Distance of stretch (or compression): The larger the distance of the elastic material is stretched (or compressed) the more elastic potential energy it has.
Elastic Potential Energy
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What is the Difference Between Stretching and Compression in a Spring
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 distance, as shown in figure (a) is called the relaxed length.
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)
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What is the Difference Between Stretching and Compression in a Spring
Compressing a spring is caused when the spring is squeezed which causes a decrease in the length of the spring compared to the relaxed length, as shown in figure (c).
In this diagram, both figures (b) and (c) would have the same elastic potential energy because both springs are displaced the same distance, x.
(a) (b) (c)
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How Does Elastic Potential Energy Depend Upon Compression
In the diagram to the right, both pictures show a spring, which is an elastic material.
In the top picture however, the spring is not stretched or compressed, and therefore there is no potential energy stored in the spring.
In the bottom picture, the spring is compressed and therefore elastic potential energy is stored in the spring.
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24 A child jumps on a trampoline in his backyard. At which of the following will she have more elastic potential energy?
A When she is standing on the trampoline
B When she is in the air
C When she lands on the trampoline after jumping
D she will always have the same elastic potential energy
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Calculating Elastic Potential Energy
Elastic Potential Energy can be solved by using the equation:
EPE = kx212
EPE = Elastic Potential Energy (J) k = spring constant (N/m) x = distance of stretch or compression (m)
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Spring Constant
The energy and distance variables in this equation are likely familiar.
12EPE = kx2
But what is the spring constant (k)? Look at the two springs to the right. Which would be easier to stretch?
Every spring has a different degree of stretchiness and that is what the spring constant represents.
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Spring Constant12EPE = kx2
Breaking down the units for spring constant also explains what the variable represents.
Can you explain what Newtons per Meter (N/m) means?
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Example - Calculating Elastic Potential Energy
A spring, which has a spring constant of 10 N/m, is stretched a distance of 1 m. How much Elastic Potential Energy is stored in the spring?
EPE = kx2
EPE = ( )(10 N/m)(1 m)2
EPE = ( )(10 N/m)(1 m2)EPE = (5 N*m)
EPE = 5 J
1212
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25 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?
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26 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?
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27 Which of the following would you expect to have the smallest spring constant?
A a garage door spring
B a slinky
C a spring in a pen
D a trampoline spring
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Thinking Mathematically
EPE = kx212
12KE = mv2
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?
What do you think is the relationship between EPE and the distance the spring is stretched or compressed?
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Thinking Mathematically
EPE = kx212
EPE is _________________________ to the spring constant.
EPE is _________________________ to the square of the
distance the spring is compressed or stretched.
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28 If the spring constant is tripled, by what factor does the EPE increase?
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29 If the spring constant is halved, by what factor does the EPE decrease?
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30 If the distance a spring is stretched is increased by a factor of 6, by what factor is the EPE increased?
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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 more energy from somewhere. But where would it get that energy?
Conservation of Energy
Hint: think back to the roller coaster. What kind of
energy did it have at the top of the hill?
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In order for an object's Kinetic Energy to increase, it must take Energy from it's stored energy, which we call Potential Energy. When this happens, the Potential Energy that an object possesses decreases.
When this happens, the Total Energy (TE) in that closed system contains does not change. This is called the Conservation of Energy.
TEi = TEf
Conservation of Energy
i = initialf= final
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If the amount of energy that we start with "Ei" and the amount we end up with as "Ef" then we would say that if no energy is added to or taken away from a system.
TEi = TEf
When looking at the Mechanical Energy, the total energy possible is the Potential Energy (PE) and the Kinetic Energy (KE) added together.
(PE + KE)i = (PE + KE)f
Conservation of Energy
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If any object at any height is being supported, then the Gravitational Potential Energy is 0 J.
If a spring is not stretched or compressed, then the Elastic Potential Energy is 0 J.
If the object is not moving at any position, then the Kinetic Energy is 0 J.
Conservation of Energy
(PE + KE)i = (PE + KE)f
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What is Meant by a Closed System?
A closed system involves only the material that is being measured. Everything else is called the surroundings.
In the diagram of the ball falling shown to the right, the ball and Earth make up the system as the Gravitational Potential Energy that is stored in the ball due to it's height from Earth's surface is transferred to Kinetic Energy as the ball falls.
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What If Both Types of Mechanical Energy Are Present at the Same Location?
In the case when an object is moving at some height above the ground, the object has both Gravitational Potential Energy and Kinetic Energy are present.
Using the transfer of mechanical energy equation, the total energy at that position is the sum of the two individual energies.
(PE + KE)
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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.
40 J
15 J25 J
How much Kinetic Energy does the car possess at Point A?
0 J
How much Gravitational Potential Energy does the car possess at Point A?
40 J
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At position B in the diagram below, the roller coaster car has a Gravitational Potential Energy equal to 15 J.
40 J
15 J25 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
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At position C in the diagram below, the roller coaster car has a Gravitational Potential Energy equal to 25 J.
40 J
15 J25 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
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31 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 = 0 m
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32 At what position in the diagram below does the object have only Kinetic Energy?
A W
B X
C Y
D Z
E None of the above
h = 0 m
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33 At what position in the diagram below does the object have only Gravitational Potential and Kinetic Energy?
A W B X C Y D Z
E None of the above h = 0 m
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Transfer of Kinetic Energy to Elastic Potential Energy
What must be true is that the Total Energy of the object must be always the same.
Kinetic Energy can be transferred into Potential Energy the same way.
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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. Because the spring is at the relaxed length there is no Elastic Potential Energy present. All of the block's energy is Kinetic Energy.
In the bottom picture, the block has compressed the spring and is no longer moving, meaning the block has no Kinetic Energy. All of the Kinetic Energy has been transformed into Elastic Potential Energy.
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34 In which position of the block would the system have only EPE?
A B C
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35 In which position of the block would the system have only KE?
A B C
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36 In which position of the block would the system have both KE and EPE?
A B C
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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 mechanical energy is not naturally conserved.
TEi = TEf
Because of this, the system is not a closed system, and the surroundings are allowed to interact with the system. This means that there is an outside for that is acting on the system over some distance.
We talked about this in the last unit. What term did we use for the energy used when a force acts over a distance?
What if the Total Mechanical Energy is not equal at the beginning and the end?
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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.
Energy Resources
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Types of Energy Resources
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Energy Production from the Sun
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.
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Energy Production from the Wind
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 of a Wind Turbine as they rotate. Inside the column of the turbine there is a drive shaft which is connected to a generator.
As the blades spin, the drive shaft converts the kinetic energy into mechanical energy. A generator that is connected to the drive shaft then converts the mechanical energy into electrical energy.
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Energy Production From Water
Water is a renewable resource that can be used to create electricity in dams such as the Hoover Dam. Dams are used to convert the kinetic energy possessed by moving water into electricity by moving a turbine connected to a generator.
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Energy Production From Water
The water at the top of the reservoir possesses Gravitational Potential Energy.
As the water moves through intake and down the penstock, the water's Gravitational Potential Energy is converted into Kinetic Energy.
As the water moves past the turbine, the Kinetic Energy that the water possesses is converted into Mechanical Energy as the turbine moves.
The Mechanical Energy that is created by the turbine is then transformed into Electrical Energy by the generator.
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Energy Production from Fossil FuelsFossil 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 turbine producing energy similar to the way that energy is produced in a hydroelectric dam.
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Effects of Using Fossil Fuels As An Energy Resource
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.
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37 Which of the following is not considered a renewable energy resource?
A Solar
B Wind
C Hydroelectric
D Fossil Fuels
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