8th Grade Energy of Objects of Motion 2015-10-28 www.njctl.org - - PDF document

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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

· 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 Slide 4 (Answer) / 122

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

By applying a force onto an object, energy is given to the object. This energy is added to the amount of energy the object already possessed. If a resistive force is applied onto an

• bject, then the force is taking energy

away from the object causing it to decelerate.

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Energy and its Forms

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Slide 6 / 122 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?

Slide 7 / 122 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

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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. 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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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 = Efinal - Einitial

Work

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 ____________.

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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.

Positive Work

They can push the truck to get it to move!

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If an object moves in the direction

• pposite to the direction of the

force applied to it, then the work is negative: W < 0. The energy of the system is reduced.

Negative Work

The parachute moves downwards, while air resistance acts upwards

• n the parachute.

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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

Zero Work

The people exert a force onto the wall, but the wall does not move!

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Non-Mechanical Energy The energy of an object that is not due to its motion or position. Non- mechanical energy usually describes an object at its atomic level. Examples: electrical energy chemical energy thermal energy sound energy Mechanical Energy - The energy of an object due to its motion and position. Mechanical energy is usually used to describe a large

• bject.

It is the sum of kinetic and potential energy.

Mechanical vs. Non-Mechanical Energy

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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1 Which of the following is the unit for energy? A Meter B Newton C Second D Joule

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Answer

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? A positive B negative

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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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Answer

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? 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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Answer

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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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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Answer

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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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

A

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Mechanical Energy

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__________ Energy __________ Energy __________ Energy

Forms of Mechanical Energy

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 underlined words into the correct place in the diagram.

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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? A Kinetic B Thermal C Chemical D Solar

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Answer

A - Kinetic

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Energy of Motion

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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? A Electrical Energy B Nuclear Energy C Kinetic Energy D All of the above

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Answer

C - Kinetic

Slide 24 / 122 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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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

• f an object can change

with time, the kinetic energy of an object can also change with time.

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velocity mass The amount of kinetic energy that an object possesses is dependent on two factors:

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? and

Slide 27 / 122 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.

Slide 28 / 122 How Does Kinetic Energy Depend on Mass?

If two identical objects are moving at the same velocity, 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. Which ball would have more kinetic energy? However, if one object has more mass than the other, the heavier

• bject will have more kinetic

energy.

Slide 29 / 122 Velocity vs. Speed

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

Slide 30 / 122 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.

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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. However, if one of the objects is moving faster, the faster one 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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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? 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 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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Answer

C

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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? 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? 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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Answer

A

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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 B a child riding a bike C a woman driving a car D it is impossible to tell

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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 B a child riding a bike C a woman driving a car D it is impossible to tell

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Answer

A

Slide 35 / 122 Calculating Kinetic Energy

Kinetic energy can be solved for by using the equation: 1 2

KE = mv2

Let's fill in the table below. variable units Name Kinetic Energy

m m/s

Slide 36 / 122 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. KE = mv2 KE = (0.5)(1000 kg)(5 m/s)2 KE = (0.5)(1000 kg)(25 m2/s2) KE = 125,000 J

1 2

Click on the box to see the solution.

Slide 36 (Answer) / 122 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. KE = mv2 KE = (0.5)(1000 kg)(5 m/s)2 KE = (0.5)(1000 kg)(25 m2/s2) KE = 125,000 J

1 2

Click on the box to see the solution. Teacher Notes

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Please note that there are multiple ways to model the math of this

• problem. We suggest showing your

students at least two ways and then continuing to use the model that a majority of your students prefer.

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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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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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Answer

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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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

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?

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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?

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Answer 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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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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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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Answer 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

Slide 41 / 122 Thinking Mathematically

KE = mv2 1 2 We have already said that mass is 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 ___________. doubles increases a factor of 5 decrease half

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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 B decreases

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Answer

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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16 If the mass of a wagon is doubled, by what factor does the kinetic energy increase?

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Answer

2

Slide 44 / 122 Thinking Mathematically

Kinetic energy can be solved by using the equation: KE = mv2 1 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

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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: A increases B decreases

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Answer

A

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18 If the velocity of a wagon is tripled, by what factor does the kinetic energy increase?

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18 If the velocity of a wagon is tripled, by what factor does the kinetic energy increase?

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Answer

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?

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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?

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Answer

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? A increase, 2 B increase, 4 C decrease, 2 D decrease, 4

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Answer

· half the mass gives 1/2 the KE, · double the speed gives 4 x KE · therefore (1/2)(4)= 2 A

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Stored Energy

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• f Contents

Slide 50 / 122 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

• f the hill for the

entire ride? What happens?

Slide 51 / 122 Where does Kinetic Energy Come From?

Once the car leans over the edge, gravity pulls it down. The ride is taking advantage

• f 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.

Slide 52 / 122 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

Slide 53 / 122 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!)

Slide 54 / 122 Gravitational Potential Energy

Work is required to elevate objects against Earth's gravity. For example, work is done on the truck to elevate it

• ff the ground. The amount of work done on the

truck is equal to the truck's gravitational potential energy at this new height.

Slide 55 / 122 Gravitational Potential Energy

Gravitational potential energy is determined by three factors: mass, gravitational acceleration, and height. All three factors are directly proportional to energy. Mass: The heavier the object is, the _______ gravitational potential energy the object has. 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. Height: The higher the object is off the ground, the _________ gravitational potential energy the object has. more more more

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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: doubled Gravitational Acceleration: stayed the same, no change 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 Mass Affect Gravitational Potential Energy? Slide 58 / 122

h = 4 m h = 2 m

In this picture, 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 change Gravitational Acceleration: stayed the same, no change Height: 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? Slide 60 / 122

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? A they are the same B thirty times smaller C ten times as large D thirty times as large

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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? A they are the same B thirty times smaller C ten times as large D thirty times as large

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D

Answer

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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? A half as large B they are the same C 1.5 times larger D twice as large

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Answer

C

Slide 62 / 122 Calculating Gravitational Potential Energy

Gravitational potential energy can be solved by using the equation: variable units Name

Gravitational Potential Energy

m m

Gravity

GPE = mgh

Let's fill in the table below.

Slide 63 / 122 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?

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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?

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Answer

GPE= mgh = 50 kg(9.8 m/s2)(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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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

GPE= mgh = 3000 kg(9.8 m/s2)(100 m) = 294,000,000 J

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GPE = mgh GPE = mgh GPE = mgh

GPE = mgh GPE = mgh GPE = mgh

Thinking Mathematically

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.

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25 A ball is at a height of 30 m. It is then moved to a height

• f 60m. By what factor does the GPE increase?

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25 A ball is at a height of 30 m. It is then moved to a height

• f 60m. By what factor does the GPE increase?

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Answer

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? A 3 kg object B 9 kg object

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26 A 3 kg object and a 9 kg object are elevated from the same height. Which has more GPE? A 3 kg object B 9 kg object

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Answer

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

• bject than the 9 kg object?

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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

• bject than the 9 kg object?

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Answer

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

• bject's GPE change?

Slide 70 (Answer) / 122

28 An object is 5 m above the ground. The object triples its mass and doubles its height. By what factor does the

• bject's GPE change?

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Answer

6

Slide 71 / 122 Elastic Potential Energy

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?

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Elastic potential energy is determined by two factors: the elasticity

• f 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.

Slide 73 / 122

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.

Elastic Potential Energy Slide 74 / 122 What is the Difference Between Stretching and Compression in a Spring?

Think about a slinky sitting

• n 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

• f the spring compared to

the relaxed length, as shown in figure (b).

(a) (b) (c)

Slide 75 / 122 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.

(a) (b) (c)

relaxed stretched compressed no EPE stored

Slide 76 / 122 How Does Elastic Potential Energy Depend Upon Compression and Stretching?

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?

Slide 77 / 122

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 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

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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 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

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Answer

C

Slide 78 / 122 Calculating Elastic Potential Energy

Elastic potential energy can be solved by using the equation: EPE = kx2 1 2 EPE = Elastic Potential Energy (J) k = spring constant (N/m) x = distance of stretch or compression (m)

Slide 79 / 122 Spring Constant

The energy and distance variables in this equation are likely familiar.

1 2 EPE = kx2

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.

Slide 80 / 122 Spring Constant

1 2 EPE = 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 81 / 122 Example - Calculating Elastic Potential Energy

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? EPE = kx2 EPE = ( )(10 N/m)(1 m)2 EPE = ( )(10 N/m)(1 m2) EPE = (5 N*m) EPE = 5 J

1 2 1 2 1 2

Click on the box to see the solution.

Slide 81 (Answer) / 122 Example - Calculating Elastic Potential Energy

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? EPE = kx2 EPE = ( )(10 N/m)(1 m)2 EPE = ( )(10 N/m)(1 m2) EPE = (5 N*m) EPE = 5 J

1 2 1 2 1 2

Click on the box to see the solution. Teacher Notes

[This object is a teacher notes pull tab]

Please note that there are multiple ways to model the math of this

• problem. We suggest showing your

students at least two ways and then continuing to use the model that a majority of your students prefer.

Slide 82 / 122

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

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?

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Answer

EPE= 1/2 kx2 = 1/2 (200 N/m) (0.25 m) 2 = 1/2 (200 N/m)(0.0625 m2) = 100 N/m (0.0625 m2) EPE = 6.25 J

Slide 83 / 122

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?

Slide 83 (Answer) / 122

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?

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Answer

EPE= 1/2 kx2 = 1/2 (40 N/m) (0.5 m)2 = 20 N/m (0.25 m2) EPE = 5 J

Slide 84 / 122

32 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

Slide 84 (Answer) / 122

32 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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Answer

C

Slide 85 / 122 Thinking Mathematically

EPE = kx2 1 2 1 2 KE = 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, k? What do you think is the relationship between EPE and the distance, x, the spring is stretched or compressed?

Slide 86 / 122 Thinking Mathematically

EPE = kx2

1 2

EPE is _________________________ to the spring constant. EPE is _________________________ to the square of the distance the spring is compressed or stretched. directly proportional directly proportional

Slide 87 / 122

33 If the spring constant, k, is tripled, by what factor does the EPE increase?

Slide 87 (Answer) / 122

33 If the spring constant, k, is tripled, by what factor does the EPE increase?

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Answer

3

Slide 88 / 122

34 If the spring constant, k, is halved, by what factor does the EPE decrease?

Slide 88 (Answer) / 122

34 If the spring constant, k, is halved, by what factor does the EPE decrease?

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Answer

1/2

Slide 89 / 122

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

35 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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Answer

36

Slide 90 / 122

Conservation of Energy

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• f Contents

Slide 91 / 122

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?

Conservation of Energy

Hint: think back to the roller

• coaster. What kind of

energy did it have at the top of the hill?

Slide 92 / 122

This is called the Conservation of Energy. initial Total Energy = final Total Energy TEi = TEf 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.

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.

Conservation of Energy

Click here to see conservation of energy explained in roller coasters!

Slide 94 / 122

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

Conservation of Energy

When would PE be zero? · the object is on the ground (GPE) · when a spring or other elastic material is not stretched or compressed (EPE) When would KE be zero? · the object is not moving

Slide 95 / 122 Conservation of Energy

Let's see if we can determine the total energy of a ball that is dropped 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. v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m Remember that the total mechanical energy at that position is the sum of the two individual energies: (PE + KE) TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J

Slide 96 / 122

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 J 25 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

Slide 97 / 122

At position B in the diagram below, the roller coaster car has a gravitational potential energy equal to 15 J.

40 J 15 J 25 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

Slide 98 / 122

At position C in the diagram below, the roller coaster car has a gravitational potential energy equal to 25 J.

40 J 15 J 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

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 = 0 m

Slide 99 (Answer) / 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 = 0 m

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Answer

A

Slide 100 / 122

37 At what position in the diagram below does the

• bject

have only kinetic energy? A W B X C Y D Z E None of the above

h = 0 m

Slide 100 (Answer) / 122

37 At what position in the diagram below does the

• bject

have only kinetic energy? A W B X C Y D Z E None of the above

h = 0 m

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Answer

B

Slide 101 / 122

38 At what position in the diagram below does the

• bject 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 = 0 m

Slide 101 (Answer) / 122

38 At what position in the diagram below does the

• bject 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 = 0 m

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Answer

C and D

Slide 102 / 122 Transfer of Kinetic Energy to 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 the KE? Just as potential energy can be transferred to kinetic energy, kinetic energy can be transferred into potential energy. v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J

Slide 103 / 122 Transfer of Kinetic Energy to Potential Energy

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! v= 0 m/s Height = 1 m Height = 0.5 m Height = 0 m TE = 0.5 J PE = 0.5 J KE = 0 J TE = 0.5 J PE = 0.25 J KE = 0.25 J TE = 0.5 J PE = 0 J KE = 0.5 J

Slide 104 / 122 Transfer of Kinetic Energy to Potential Energy

In reality, the ball will not bounce as high as it was dropped. Does this mean energy was lost? v= 0 m/s Height < 1 m TE = 0.5 J PE = 0 J KE = 0.5 J NME = 0.10 J NME=0.10 J TE = 0.5 J PE = 0.25 J KE = 0.15 J TE = 0.5 J PE = 0.4 J KE = 0 J Sound Energy!

• 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!

Slide 105 / 122 Transfer of Kinetic Energy to 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. Kinetic energy can also be transferred to elastic potential energy.

Slide 106 / 122 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 block-

spring system is entirely due to the KE

• f 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 107 / 122

39 In which position of the block would the system have

• nly EPE?

A B C

Slide 107 (Answer) / 122

39 In which position of the block would the system have

• nly EPE?

A B C

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Answer

C

Slide 108 / 122

40 In which position of the block would the system have both KE and EPE? A B C

Slide 108 (Answer) / 122

40 In which position of the block would the system have both KE and EPE? A B C

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Answer

B

Slide 109 / 122

41 In which position of the block would the system have

• nly KE?

A B C

Slide 109 (Answer) / 122

41 In which position of the block would the system have

• nly KE?

A B C

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Answer

A

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

v= 0 m/s Height < 1 m TE = 0.5 J PE = 0 J KE = 0.5 J NME = 0.10 J NME=0.10 J TE = 0.4 J PE = 0.25 J KE = 0.15 J TE = 0.4 J PE = 0.4 J KE = 0 J Sound Energy! TE = 0.5 J 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

• utside force acting on the system, the ball.

What if the Total Energy is not equal at the beginning and the end? Slide 112 / 122

Types of Energy Resources

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• f Contents

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.

Energy Resources Slide 114 / 122 Types of Energy Resources Slide 115 / 122 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. Solar energy is converted to electrical energy!

Slide 116 / 122 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. 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!

Slide 117 / 122 Energy Production From Water

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!

Slide 118 / 122 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 119 / 122 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.

Slide 120 / 122

42 Which of the following is not considered a renewable energy resource? A Solar B Wind C Hydroelectric (water) D Fossil Fuels

Slide 120 (Answer) / 122

42 Which of the following is not considered a renewable energy resource? A Solar B Wind C Hydroelectric (water) D Fossil Fuels

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Answer

D

Slide 121 / 122

43 The production of energy by wind, water, the sun, and fossil fuels relies on the principle of conservation of energy. True False

Slide 121 (Answer) / 122

43 The production of energy by wind, water, the sun, and fossil fuels relies on the principle of conservation of energy. True False

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Answer

TRUE

Slide 122 / 122

44 The spinning of a generator in wind turbines and hydroelectric dams converts non-mechanical energy into electrical energy. True False

Slide 122 (Answer) / 122

44 The spinning of a generator in wind turbines and hydroelectric dams converts non-mechanical energy into electrical energy. True False

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Answer

FALSE

they convert mechanical energy into electrical energy