LOnumber=PC65010; CorrectionKey=GA-A Answers Lesson 2 ......Some energy is stored energy, or...

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Lesson

ESSENTIAL QUESTION

What are kinetic and potential energy?By the end of this lesson, you should be able to calculate kinetic and potential energy and know how these two types of energy are related.

Kinetic and Potential Energy

Climbing a hill requires a lot of energy but it makes the ride back down fun.

2

J S8P2.a Kinetic and potential energy

J S8P2.b Transformation between kinetic and potential energy

J S8P2.c Energy transformations in a system

DO NOT EDIT--Changes must be made through “File info” LOnumber=PC65010; CorrectionKey=GA-A


Answers

394 Unit 6 Work, Energy, and Machines

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3 Synthesize Many English words have their roots in other languages. Use the Greek word below to make an educated guess about the meaning of the term kinetic energy.

Greek word Meaning

kinetos moving

Example sentence: The harder the football is thrown, the more kinetic energy it has.

kinetic energy:

Active Reading

1 Predict Check T or F to show whether you think each statement is true or false.

T FObjects that are sitting still have kinetic energy.

The kinetic energy of an object depends on how much space the object takes up.

The gravitational potential energy of an object depends on its height above a surface.

2 Analyze If the baseball and the plastic ball were moving at the same speed, which ball would hit a bat harder? Why?

Engage Your Brain

4 Identify As you read, create a reference card for each vocabulary term. On one side of the card, write the term and its meaning. On the other side, draw an image that illustrates or makes a connection to the term. These cards can be used as bookmarks in the text so that you can refer to them while studying.

Vocabulary Terms• kinetic energy

• potential energy

• mechanical energy

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Quick Labs• Investigate Potential Energy • Identify Potential and Kinetic Energy

Exploration Lab• Mechanical Energy


AnswersAnswers to 1–3 should represent students’ current thoughts, even if incorrect.

1. F; F; T

2. Sample answer: The baseball would hit harder because it has more mass than the plastic ball.

3. the energy of an object that is moving

4. Students should define or sketch each vocabulary term in the lesson.

Lesson 2 Kinetic and Potential Energy 395

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Visualize It!



On the Move

What is kinetic energy?Energy is the ability to do work. There are different forms of energy. One form that you can find all around you is kinetic energy. Kinetic energy is the energy of motion. Every moving object has kinetic energy. For example, a hammer has kinetic energy as it moves toward a nail. When the hammer hits the nail, energy is transferred. Work is done when movement occurs in the direction of the force, and the nail is driven into a board.

The Energy of MotionActive Reading 5 Identify As you read, underline

two factors that affect an object’s kinetic energy.

What determines the amount of kinetic energy that an object has? The faster an object moves, the more kinetic energy it has. So kinetic energy depends, in part, on speed. Kinetic energy also depends on mass. If two objects move at the same speed, then the one that has more mass will have more kinetic energy. Imagine a bike and a car that are moving at the same speed. The car has more kinetic energy than the bike has because the car has more mass.

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The bike at the top of the hill is not moving. It does not have kinetic energy. The bike that is going down the hill has kinetic energy. As the bike moves faster, its kinetic energy increases.

6 Apply How does the rider’s ability to stop the bike change as the bike moves down a steep hill? Explain your reasoning.

Answers 5. See students’ pages for annotations.

6. Sample answer: As the bike moves down the hill, speed increases. It is much harder to stop the bike near the bottom than it is near the top of the hill.

396

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How is the kinetic energy of an object calculated?An object’s kinetic energy is related to its mass and speed. The speed of an object is the distance that it travels in a unit of time. The following equation shows how kinetic energy is calculated.

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Sample ProblemA foal has a mass of 100 kg and is moving at 8 m/s along the beach. What is its kinetic energy?

Identify

A. What do you know? The mass, m, is 100 kg. The speed, v, is 8 m/s.

B. What do you want to find? kinetic energy

Plan

C. Write the formula: KE = 1 __ 2 mv2

D. Substitute into the formula: KE = 1 __ 2 (100 kg)(8 m/s)2

Solve

E. Multiply: KE = 1 __ 2 (100 kg)(64 m2/s 2) = 3,200 kg · m2/s2 = 3,200 J

Answer: 3,200 J

Do the Math

kinetic energy = 1 _ 2 mv2

The letter m is the object’s mass, and the letter v is the object’s speed. When the mass is expressed in kilograms and the speed in meters per second, kinetic energy is expressed in joules (J).

You Try It

7 Calculate Complete the tables. Then, draw two graphs using the information from the tables. The first graph should show how kinetic energy changes as velocity changes. The second graph should show how kinetic energy changes as mass changes.

m v KE

800 kg 10 m/s

800 kg 15 m/s

800 kg 20 m/s

m v KE

800 kg 10 m/s

900 kg 10 m/s

1000 kg 10 m/s

Answers 7. For v2, from top to bottom: 100 m2/s2,

100 m2/s2, 225 m2/s2; for KE, from top to bottom: 10,000 J, 80,000 J, 180,000 J



Think Outside the Book Inquiry



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9 Identify Fill in the type of potential energy that is illustrated in each image.

Fruit can provide energy to your body.

The archer pulls back on the string and bends the bow’s limbs.

The boulder is high above the ground.

A B C

8 Classify With a partner, create a poster that shows examples of potential energy from everyday life. Label each example as gravitational, elastic, or chemical potential energy.

It Could Change

Visualize It!

What is potential energy?Some energy is stored energy, or potential energy. Potential energy is the energy an object has because of its position, condition, or chemical composition. Like kinetic energy, potential energy is the ability to do work. For example, an object has elastic potential energy when it has been stretched or compressed. Elastic potential energy is stored in a stretched spring or rubber band. An object has gravitational potential energy due to its position above the ground. An object held above the ground has the potential to fall. The higher the object is above the ground, the greater its gravitational potential energy. Potential energy that depends on an object’s position is referred to as mechanical potential energy. But there are other types of potential energy that do not depend on an object’s position. For example, a substance stores chemical potential energy as a result of its chemical bonds. Some of that energy can be released during chemical reactions.

Answers 9. A. chemical; B. gravitational; C. elastic




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How is the gravitational potential energy of an object calculated?The following equation describes an object’s gravitational potential energy.

Sample ProblemThe cat has a mass of 4 kg and is 1.5 m above the ground. What is the gravitational potential energy of the cat?

Identify

A. What do you know? mass = 4 kg, height = 1.5 m, acceleration due to gravity = 9.8 m/s2

B. What do you want to find? gravitational potential energy

Plan

C. Write the formula: GPE = mghD. Substitute the given values into the formula:

GPE = (4 kg)(9.8 m/s2)(1.5 m)

Solve

E. Multiply: PE = (4 kg)(9.8 m/s2)(1.5 m) = 58.8 kg · m2/s2 = 58.8 J

Answer: 58.8 J

Do the Math

gravitational potential energy = mgh

The letter m represents the object’s mass expressed in kilograms. The letter g represents the acceleration due to Earth’s gravity, which is 9.8 m/s2. The letter h is the object’s height from the ground in meters. The height is a measure of how far the object can fall. Like kinetic energy, potential energy is expressed in units of joules.

You Try It

10 Calculate Three books are on different shelves. Calculate the gravitational potential energy of each book based on its mass and its height above the floor.

Object m h PEpicture book 0.2 kg 2 mpicture book 0.2 kg 3 m

textbook 1.5 kg 4 m

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Answers 10. For PE, from top to bottom: 3.92 J, 5.88 J,

58.8 J





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It All Adds Up!

The mechanical energy of the ball is the sum of its kinetic energy and potential energy.

11 Identify As you read, underline the two components of mechanical energy.

Active Reading

12 Compare Circle the position of the ball when its gravitational potential energy is greatest.

13 Analyze When does the ball have zero gravitational potential energy? Explain your reasoning.

mechanical energy = KE + PE

ME = 1 _ 2 mv2 + mgh

If the object’s only potential energy is gravitational potential energy, you can use the following equation to find mechanical energy.

Visualize It!

How is the mechanical energy of an object calculated?A moving object can have both kinetic and potential energy. Mechanical energy is the energy possessed by an object due to its motion and position. For example, a thrown baseball has kinetic energy. It also has potential energy because it is above the ground. The sum of the ball’s kinetic energy and mechanical potential energy is its mechanical energy. You can use the following equation to find mechanical energy.

Answers 11. See students’ pages for annotations.

12. Students should circle the second ball from the left.

13. The ball has zero gravitational potential energy when it is touching the ground.



3m

2m

1m

0m

3m

2m

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0m

6-8-I_CNLAESE589473_227Afinal1-10-11LKell

Energy of the Basketball

Ener

gy (J

)

Height above �oor (m)


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You Try It

14 Calculate When the basketball is at its maximum height of 3 meters, it is not moving. The table below lists the KE and GPE for the basketball at heights of 3 m, 2 m, 1 m, and 0 m. Write the missing values for KE and GPE in the table. Then find the mechanical energy for each height.

Height KE GPE ME

3.0 m 18 J

2.0 m 6 J 12 J

1.0 m 12 J 6 J

0 m 18 J

Do the Math

15 Graph Use the data above to plot and label two lines representing the kinetic energy and the gravitational potential energy of the basketball.

16 Analyze What is the relationship between the kinetic energy and the gravitational potential energy of the basketball?

The rim height is 3 meters.

Answers 14. 0 J; 18 J; 18 J; 18 J; 0 J; 18 J

15. Students should draw the y-axis scale from 0 to 18 in units of 6. The x-axis scale is from 0 to 3 in units of 1. For kinetic energy, the points (0, 18), (1, 12), (2, 6), and (3, 0) are plotted and connected with a line. For GPE, the points (0, 0), (1, 6), (2, 12), and (3, 18) are plotted and connected with a line.

16. The sum of the two types of energy is always 18 J.



Visual Summary

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20 Claims • Evidence • Reasoning A skydiver jumps out of a plane. Describe how gravitational potential energy changes as the skydiver falls. State how the skydiver’s kinetic energy changes when the parachute opens. Summarize evidence to support your claim and explain your reasoning.

Answers: 17 speed; 18 chemical; 19 gravitational

To complete this summary, fill in the blanks with the correct word. Then, use the key below to check your answers. You can use this page to review the main concepts of the lesson.

Kinetic and Potential Energy

All moving objects have kinetic energy.

Potential energy is stored energy.

17 Kinetic energy depends on an object’s mass and

19 The formula ME = 1 __ 2 mv2 + mgh can be used to calculate mechanical energy if the only potential energy is potential energy. 18 Potential energy can be gravitational,

, or elastic.

kinetic energy = 1 _ 2 mv2

gravitational potential energy = mgh

Mechanical energy is kinetic energy plus potential energy due to position.

mechanical energy = KE + PE



Answers 17. speed

18. chemical

19. gravitational

20. Sample answer: The gravitational potential energy is greatest when the skydiver first jumps out of the plane. It decreases as the skydiver gets nearer to the ground. The skydiver’s speed decreases when the parachute opens. This causes his kinetic energy to decrease.


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Grav

itatio

nal p

oten

tial e

nerg

y (J

)

Time (S)

Gravitational Potential Energy over Time50

40

30

20

10

00 21 3 4 5 6 7 98 10

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LessonLesson Review©

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VocabularyIn your own words, define the following terms.

1 kinetic energy

2 potential energy

3 mechanical energy

Key Concepts4 Relate Describe the relationship between a

moving object’s mass and its kinetic energy.

5 Identify What are two factors that determine an object’s gravitational potential energy?

6 Analyze A passenger plane is flying above the ground. Describe the two components of its mechanical energy.

Critical Thinking7 Evaluate Can an object’s mechanical energy

be equal to its gravitational potential energy? Explain.

Use this graph to answer the following questions.

8 Apply The graph shows the gravitational potential energy of a radio-controlled toy helicopter. Describe the motion of the toy.

9 Calculate At 2.5 seconds, the helicopter has a kinetic energy of 20 J. What is its mechanical energy at that time?

2


Lesson Review Answers 1. Sample answer: the energy an object

has due to motion

2. Sample answer: the energy an object has due to its position or chemical composition

3. Sample answer: the sum of an object’s kinetic and potential energies

4. The greater the mass of an object moving at a given speed, the greater its kinetic energy.

5. the object’s mass and the object’s height

6. The two components of the mechan-ical energy of the plane are its kinetic energy due to mass and speed and its gravitational potential energy due to its mass and height above the ground.

7. Sample answer: Yes. If an object is not moving, it has zero kinetic energy. In this case, the sum of the kinetic energy and the potential energy would be the same as the gravitational potential energy.

8. Sample answer: The helicopter trav-els upwards at a steady rate for 5 seconds and then downwards at the same rate for 5 seconds.

9. 40 J


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My Notes

DO NOT EDIT--Changes must be made through “File info” CorrectionKey=GA-A


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LOnumber=PC65010; CorrectionKey=GA-A Answers Lesson 2 ......Some energy is stored energy, or...

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