pppcr11-15se

Chapters 11–15 Resources

Zitzewitz

■

Elliott

Nelson

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■

Haase

Nelson

■

■

Harper

Schuler

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■

Herzog

Zorn

A Glen Glencoe coe Prog Program ram

Student Edition Teacher T eacher Wraparound Wraparound Edition Teacher T eacher Chapter Resou Resources rces Mini Lab Works Worksheets heets Physics Lab Worksheets Study Guide Section Quizzes Reinforcement Enrichment Transparency Masters Masters Transparency Worksheets Worksheets Chapter Assessment Teacher T eacher Classroom Classroom Resources Resources Teaching Te aching Transparencies Laboratory Manual, Student Edition Laboratory Manual, Teacher Edition Probeware Laboratory Manual, Student Edition Probeware Laboratory Manual, Te Teacher acher Edition Forensics Laboratory Manual, Student Edition

Forensics Laboratory Manual, Te Teacher acher Edition Supplemental Problems Additional Challenge Problems Problems Pre-AP/Critical Thinking Problems Physics Test Prep: Studying for the End-of-Course Exam, Student Edition Physics Test Prep: Studying for the End-of-Course Exam, Teacher Edition Connecting Math to Physics Solutions Manual

Technology T echnology Answer Key Maker ExamView® Pro Interactive Chalkboard McGraw-Hill Learning Network StudentWorks™ CD-ROM TeacherW Te acherWorks™ orks™ CD-ROM site physicspp.com Web site

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the Physics: Principles Principles and Problems Problems program. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 ISBN 0-07-865904-3 Printed in the United States of America 1 2 3 4 5 6 7 8 9 045 05 04 03 02 01 00

A Glen Glencoe coe Prog Program ram

Student Edition Teacher T eacher Wraparound Wraparound Edition Teacher T eacher Chapter Resou Resources rces Mini Lab Works Worksheets heets Physics Lab Worksheets Study Guide Section Quizzes Reinforcement Enrichment Transparency Masters Masters Transparency Worksheets Worksheets Chapter Assessment Teacher T eacher Classroom Classroom Resources Resources Teaching Te aching Transparencies Laboratory Manual, Student Edition Laboratory Manual, Teacher Edition Probeware Laboratory Manual, Student Edition Probeware Laboratory Manual, Te Teacher acher Edition Forensics Laboratory Manual, Student Edition

Forensics Laboratory Manual, Te Teacher acher Edition Supplemental Problems Additional Challenge Problems Problems Pre-AP/Critical Thinking Problems Physics Test Prep: Studying for the End-of-Course Exam, Student Edition Physics Test Prep: Studying for the End-of-Course Exam, Teacher Edition Connecting Math to Physics Solutions Manual

Technology T echnology Answer Key Maker ExamView® Pro Interactive Chalkboard McGraw-Hill Learning Network StudentWorks™ CD-ROM TeacherW Te acherWorks™ orks™ CD-ROM site physicspp.com Web site

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the Physics: Principles Principles and Problems Problems program. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 ISBN 0-07-865904-3 Printed in the United States of America 1 2 3 4 5 6 7 8 9 045 05 04 03 02 01 00

Contents Chapters 11–15 Resources To T o the Teacher Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv . iv Chapter 11 11 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 .1 Chapter 12 Resources Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Chapter 13 Resources Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Chapter 14 Resources Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Chapter 15 Resources Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Teacher T eacher Guide and Answers Answers . . . . . . . . . . . . . . . . . . . . . . . .173 .173

. c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

iii

To the Teacher This book contains resources that support five Student Edition chapters of Physics: Principles and Problems. The worksheets and activities have been developed to help you teach these chapters more effectively. You will find in chapter order:

REPRODUCIBLE PAGES

H ANDS-ON A CTIVITIES Mini Lab and Physics Lab Worksheets: These worksheets are expanded versions of the Mini Labs and Physics Labs that appear in the five Student Edition chapters supported in this book. All materials lists, procedures, and questions are repeated so that students can complete a lab in most cases without having a textbook on the lab table. Data tables are enlarged so they can be used to easily record data, and all lab questions are reprinted with lines on which students can write their answers. For student safety, all appropriate safety symbols and caution statements have been reproduced on these pages. Answer pages for each Mini Lab and Physics Lab Worksheet are included in the Teacher Guide and Answers section at the back of this book.

EXTENSION AND INTERVENTION

Study Guide: These pages help your students learn physics vocabulary and concepts. Study Guide worksheets typically consist of six pages of questions and exercises for each of the five Student Edition chapters supported in this book. Items are presented in a variety of objective formats: matching, true/false, interpreting diagrams and data, multiple choice, short-answer questions, and so on. The first Study Guide worksheet for each chapter reviews vocabulary. Subsequent worksheets closely follow the organization of the textbook, providing review items for each textbook section and references to specific content.

iv

Students will find the Study Guide worksheets helpful for previewing or reviewing chapter material. As a preview, the worksheets help students focus on the concepts at the time you assign the reading. Students can complete each Study Guide section after reading the corresponding textbook section. Some students will have more success completing the sheets in smaller chunks. For this reason, the question sets on the Study Guide pages are referenced to specific readings in the textbook. When complete, these worksheets will prove to be an excellent review instrument. Answers to the Study Guide pages are included in the Teacher Guide and Answers section at the back of this book.

Reinforcement: These pages provide opportunities that complete your teaching cycle and benefit all your students. Reinforcement masters are especially helpful for students who require additional instruction in order to understand certain concepts. A Reinforcement master is provided for each of the five Student Edition chapters supported in this book. Answers to these pages are included in the Teacher Guide and Answers section at the back of this book.

Enrichment: These activities offer students the chance to apply physics concepts to new situations. Students explore high-interest topics in a variety of formats. Some of the masters are handson activities. An Enrichment master is provided for each of the five Student Edition chapters supported in this book. Answers to these pages are included in the Teacher Guide and Answers section at the back of this book.

C o p y r i g h t © G l e n c o e / M c G r a w -H i l ,l a d i v i s i o n o f T h e M c G r a w -H i l l C o m p a n i e s , I n c .

To the Teacher T RANSPARENCY A CTIVITIES

Teaching Transparency Masters and Activities: These transparencies relate to major concepts that will benefit from an extra visual learning aid. Most of the transparencies contain art or photos that extend the concepts put forth by those in the textbook. Others contain art or photos directly from the Student Edition. There are 120 Teaching Transparencies. The ones that support these five Student Edition chapters are provided here as black-and white masters accompanied by worksheets that review the concepts presented in the transparencies. Teaching Tips for some transparencies and answers to all worksheet questions are provided in the Teacher Guide and Answers section at the back of this book.

A SSESSMENT


continued

book. Each test consists of six pages of material, which is divided into three sections. Understanding Physics Concepts requires students to demonstrate their knowledge of vocabulary and other basic information presented in the chapter. They are assessed through a variety of question types, including matching, modified true/false, short answer/fill-in, and multiple choice.

■

■ Thinking

Critically requires students to use higher-order learning skills. Students will need to interpret data and discover relationships presented in graphs and tables. Other questions may require them to apply their understanding of concepts to solve problems, compare or contrast situations, and make inferences or predictions.

■ Applying

Physics Knowledge consists of items that assess students’ ability to extend their learning to new situations. Assessment is done qualitatively through short-answer questions, and quantitatively through problems. The questions and problems in this section are more difficult than those presented earlier and generally require more calculations as well as a deeper comprehension of chapter concepts.

Section Quiz: The Section Quiz page consists of questions or problems that focus on key content from one section of the Student Edition. Each quiz typically includes conceptual items that require a written response or explanation and items that require problem-solving skills or mathematical calculations, where applicable. The Section Quiz offers representative practice items that allow you to monitor your students’ understanding of the textbook. Answers to each Section Quiz are pro vided in the Teacher Guide and Answers section at the back of this book.

T EACHER GUIDE AND A NSWERS

Chapter Assessment: The Chapter Assessment pages provide materials to evaluate your students’ understanding of concepts and content from the five Student Edition chapters supported in this

Answers or possible answers to all worksheet questions and activities can be found in order of appearance at the back of this book. Criteria for acceptable answers are found where appropriate.

v

Date

Period

Name

CHAPTER

11

Mini Lab Worksheet

Energy Exchange 1.

Select different-sized steel balls and determine their masses.

2.

Stand a spring-loaded laboratory cart on end with the spring mechanism pointing upward.

3.

Place a ball on top of the spring mechanism and press down until the ball is touching the cart.

4.

Quickly release the ball so that the spring shoots it upward. CAUTION: Stay clear of the ball when launching.

5.

Repeat the process several times, and measure the average height.

6.

Estimate how high the other sizes of steel balls will rise.

Analyze and Conclude 7.

Classify the balls by height attained. What can you conclude?


Physics: Principles and Problems


3

Date

Period

Name

CHAPTER

11

Materials

• grooved track (two sections) • marble or steel ball • stopwatch • block of wood • electronic balance • metric ruler • graphing calculator

Physics Lab Worksheet Conservation of Energy There are many examples of situations where energy is conserved. One such example is a rock falling from a given height. If the rock starts at rest, at the moment the rock is dropped, it only has potential energy. As it falls, its potential energy decreases as its height decreases, but its kinetic energy increases. The sum of potential energy and kinetic energy remains constant if friction is neglected. When the rock is about to hit the ground, all of its potential energy has been converted to kinetic energy. In this experiment, you will model a falling object and calculate its speed as it hits the ground.

Question How does the transfer of an object’s potential energy to kinetic energy demonstrate conservation of energy?

Objectives . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

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Calculate the speed of a falling object as it hits the ground by using a model.

■

Interpret data to find the relationship between potential energy and kinetic energy of a falling object.

Figure 1

Figure 2

Figure 3



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Physics Lab Worksheet

11

continued

Data Table Release Height (m)

Distance (m)

Time (s)

Speed (m/s)

0.05 0.05 0.05 0.01 0.02 0.03

Procedure 1. Place the two sections of grooved track together, as shown in Figure 1. Raise one end of the track and place the block under it, about 5 cm from the raised end. Make sure the ball can roll smoothly across the junction of the two tracks. 2. Record the length of the level portion of the track in the data table. Place a ball on the track directly above the point supported by the block. Release the ball. Start the stopwatch when the ball reaches the level section of track. Stop timing when the ball reaches the end of the level portion of the track. Record the time required for the ball to travel that distance in the data table. 3. Move the support block so that it is under the midsection of the inclined track, as shown in Figure 2. Place the ball on the track just above the point supported by the block. Release the ball and measure the time needed for the ball to roll the length of the level portion of the track and record it in the data table. Notice that even though the incline is steeper, the ball is released from the same height as in step 2. 4. Calculate the speed of the ball on the level portion of the track in steps 2 and 3. Move the support block to a point about three-quarters down the length of the inclined track, as shown in Figure 3. 5. Predict the amount of time the ball will take to travel the length of the level portion of the track. Record your prediction. Test your prediction. 6. Place the support block at the midpoint of the inclined track (Figure 2). Measure a point on the inclined portion of the track that is 1.0 cm above the level portion of the track. Be sure to measure 1.0 cm above the level portion, and not 1.0 cm above the table. 7. Release the ball from this point and measure the time required for the ball to travel on the level portion of the track and record it in the data table. 8. Use a ruler to measure a point that is 2.0 cm above the level track. Release the ball from this point and measure the time required for the ball to travel on the level portion of the track. Record the time in the data table. 9. Repeat step 8 for 3.0 cm, 4.0 cm, 5.0 cm, 6.0 cm, 7.0 cm, and 8.0 cm. Record the times. 6




Name continued


11

Analyze 1. Infer What effect did changing the slope of the inclined plane in steps 2–6 have on the speed of the ball on the level portion of the track?

2. Analyze Perform a power regression for this graph using your graphing calculator. Record the equation of this function. Graph this by inputting the equation into Y . Draw a sketch of the graph. 

3. Using the data from step 9 for the release point of 8.0 cm, find the potential energy of the ball before it was released. Use an electronic balance to find the mass of the ball. Note that height must be in m, and mass in kg.


4. Using the speed data from step 9 for the release point of 8.0 cm calculate the kinetic energy of the ball on the level portion of the track. Remember, speed must be in m/s and mass in kg.

Conclude and Apply 1. Solve for speed, y, in terms of height, x. Begin by setting PE



KE.

2. How does the equation found in the previous question relate to the power regression calculated earlier?

3. Suppose you want the ball to roll twice as fast on the level portion of the track as it did when you released it from the 2-cm mark. Using the power regression performed earlier, calculate the height from which you should release the ball.



7

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11


continued

4. Explain how this experiment only models dropping a ball and finding its kinetic energy just as it hits the ground.

5. Compare and Contrast Compare the potential energy of the ball before it is released (step 8) to the kinetic energy of the ball on the level track (step 9). Explain why they are the same or why they are different.

6. Draw Conclusions Does this experiment demonstrate conservation of energy? Explain.

Going Further How can this experiment be improved to help reduce friction?

Real-World Physics How does your favorite roller coaster demonstrate the conservation of energy by the transfer of potential energy to kinetic energy?

To find out more about energy, visit the Web site: physicspp.com

8




Date

Period

Name

CHAPTER

11

Study Guide

Conservation of Energy Vocabulary Review Write the term that correctly completes the statement. Use each term once.


elastic collision

law of conservation of energy

elastic potential energy

mechanical energy

gravitational potential energy

reference level

inelastic collision

rotational kinetic energy

kinetic energy

thermal energy

1.

Within a closed, isolated system, energy can change form, but the total amount of energy is constant. This is a statement of the .

2.

The position at which the potential energy is defined to be zero is a(n) .

3.

The sum of the kinetic and gravitational potential energy of a system is the of the system.

4.

5.

6.

is the energy of motion, measured in joules. Energy stored in an Earth-object system as a result of gravitational attraction between the object and Earth is . A collision in which the kinetic energy decreases is a(n)

.

7.

Energy that depends on an object’s moment of inertia and its angular velocity is .

8.

Energy that usually makes the temperature of colliding objects rise slightly is .

9.

10.


A collision in which the kinetic energy doesn’t change is a(n) . The energy in a compressed spring or a stretched rubber band is .


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Study Guide

11

Section 11.1

continued

The Many Forms of Energy

In your textbook, read about modeling the work-energy theorem on pages 286–287. The diagram shows changes to your money during a week. Circle the choice that best completes the statement or answers the question. How much money did you have on Monday?

1.

a.

$35

c.

$20

b.

$25

d.

$0

50

30 starting

a. b.

$25

c.

$35

d.

$55 $60

How much money did you have by the end of the day on Friday?

3.

pay for lawn work

20

How much money did you have by the end of the day on Wednesday?

2.

wage

40

a.

$25

c.

$45

b.

$35

d.

$60

10 0 

10



20



30

lunch cost of CD cost of movies/dinner

cost of clothes Mon

Tue

Wed

Thu

Fri

Sat

Sun

How does the amount of money you had at the end of the week compare with the amount you had at the beginning of the week?

4.

It increased.

a.

b.

It decreased.

c.

It remained unchanged.

Read the following situations and draw before-and-after energy diagrams in the space provided. A loaded wheelbarrow has a kinetic energy of 50 J. You do 30 J of work on the wheelbarrow.

5.

Before

10

80 60 40 20

0 20

A loaded wheelbarrow has a kinetic energy of 70 J. You do 60 J of energy on the wheelbarrow. Before

After

100

) J ( k r o W d n a y g r e n E

6.

100


80 60 40 20

0 20

100


80 60 40 20

0 20

After 100


80 60 40 20

0 20

40

40

40

40

60

60

60

60




Name

Study Guide

11

continued

In your textbook, read about kinetic energy on page 287. Circle the letter of the choice that best completes the statement or answers the question. 7.

8.

9.

10.


11.

12.

13.

Which of the following would produce the greatest increase in the kinetic energy of a moving object? a.

doubling its mass

c.

halving its mass

b.

doubling its velocity

d.

halving its velocity

A baseball and a ping pong ball are both shot from a slingshot with equal velocity. Which object has the greater kinetic energy? a.

the baseball

c.

The answer depends on the launch angle.

b.

the ping pong ball

d.

The kinetic energies are equal.

A diver doing a somersault has a greater angular velocity in the a.

tuck position

c.

The answer depends on the height of the diver.

b.

fully extended position

d.

The velocities are equal.

How does the kinetic energy of a car traveling at 16 m/s compare with the kinetic energy of the same car traveling at 8 m/s? a.

It is 2 times greater.

c.


b.


d.


How much work would have to be done on a truck with a kinetic energy of 2104 J to reduce its kinetic energy by half? a.

1102 J

c.

1104 J

b.

4104 J

d.

2102 J

A car has a kinetic energy of x J. 7.5 s later it moves in the opposite direction with the same speed. What kinetic energy does it have? 

c.

0J

b.

x J

d.

2 x J

A car has a kinetic energy of x J. 7.5 s later it moves in the opposite direction with 3 times its initial speed. What kinetic energy does it have?

b.

15.

x J

a.

a.

14.

.

x J 3 x J

c.

9 x J

d.



x J

A 6 kg ball is traveling at 5 m/s. What is its kinetic energy? a.

37.5 J

c.

150 J

b.

75 J

d.

300 J

If the velocity of the ball in question 16 doubles, its kinetic energy will be a.

37.5 J

c.

150 J

b.

75 J

d.

300 J


.


11

Name

Study Guide

11

16.

17.

continued

A ball of mass 0.5 kg has 100 J of kinetic energy. What is the velocity of the ball? a.

20 m/s

c.

100 m/s

b.

40 m/s

d.

400 m/s

A ball traveling at 30 m/s has 900 J of kinetic energy. What is the mass of the ball? a.

1 kg

c.

9 kg

b.

2 kg

d.

30 kg

In your textbook, read about stored energy and gravitational potential energy on pages 288–292. For each statement below, write true or rewrite the italicized part to make the statement true. If a baseball is considered a system, work is done on it by the pitcher’s hand, gravity, and the bat .

18.

After being hit by the bat, the work done by gravity on a ball that is rising is mgh.

19.

20.

On the way down, the work done by gravity on the ball decreases the ball’s kinetic energy.

21.

If the height of the bat is considered the reference point, when the ball hits the ground, its gravitational potential energy is less than 0 J.

22.

If the Moon and Earth are considered a system, energy is stored in the system as rotational energy .

23.

The work that an archer does when pulling back on a bowstring is stored in the string as gravitational potential energy.

Use the diagram at right to answer questions 24–26. 24.

The point at which the block has both kinetic and potential energy is . a.

25.

12

b.

B

c.

C

A

The block has the maximum amount of kinetic energy at point . a.

26.

A

A

b.

B

At point A, the block has

c.

.

a.

no energy

b.

both kinetic and potential energy

c.

only kinetic energy

d.

only potential energy


C B

C



Name

Study Guide

11

Section 11.2

continued

Conservation of Energy

In your textbook, read about conservation of mechanical energy on pages 293–295. 1.


You are designing a skateboard park. The starting ramp is supposed to be 0.61 m high. a.

What would be the potential energy of a 63.5-kg skateboarder at the top of the starting ramp?

b.

How could you change the ramp design so that a 63.5-kg skateboarder moves twice as fast at the bottom? For now, ignore air resistance and friction between the skateboard and ramp. Explain why this design change would work in terms of the conservation of mechanical Energy.

c.

Assume that the same 63.5-kg skateboarder in part b falls off the side of the ramp. What is the kinetic energy of the skateboarder on the ground, at the bottom of the ramp.

2.

Consider the ramp in problem 1. Explain why the skateboarder has the same final kinetic energy whether she falls off the side of the ramp, plummeting downward, or whether she rolls down the ramp. Draw a diagram.

3.

What are some losses of mechanical energy? Give several examples.



13

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Study Guide

11

continued

In your textbook, read about analyzing collisions on pages 297–301. The diagrams show the motion of two identical 20-kg carts before and after they collide. Use the diagrams to answer questions 4–7. Circle the letter of the choice that best answers the question. Before A

B

4.

5.

6.

7.

14

20

20

10 m/s

0 m/s

20

C

After A

B

20

10 m/s

0 m/s

20

20

10 m/s

0 m/s

20

20

0 m/s

10 m/s

20

5.0

20

m/s

5.0 m/s

C

20

20

5.0 m/s

In which collision(s) was momentum conserved? a.

only A

c.

A and C

b.

only B

d.

A and B

In which collision(s) was energy conserved? a.

only A

c.

b.

only B

d.

only C A, B, and C

An inelastic collision occurs in which collision(s)? a.

A and B

c.

only B

b.

B and C

d.

only C

In the inelastic collision(s), what happened that reduced the total mechanical energy of the system? a.

Some kinetic energy changed to elastic potential energy.

b.

Some kinetic energy changed to gravitational potential energy.

c.

Some kinetic energy changed to sound energy and thermal energy.

d.

Some kinetic energy changed to chemcial energy.




Date

Period

Name

CHAPTER

11

Reinforcement Conservation of Energy

Materials

• three balls of different sizes (for example, tennis ball, ping pong ball, and golf ball)

Problem How does energy change from kinetic to potential?

Procedure

• meterstick

1. Secure the meterstick vertically to a wall. Place the stick so that the

1-cm mark is nearest the floor.

• pen and paper

2. Hold one of the balls so that the bottom of the ball is at the 1-m

• flat surface

mark, about 15 cm away from the wall. Ball 1

Ball 2

Ball 3

(m)

(m)

(m)

3. As one student drops the ball, the second student watches at eye

level to see how high the ball bounces. What is the highest point that the bottom of the ball reaches? Write the bounce height in the data table.

Trial 1


Trial 2

4. Repeat steps 2-3 four times.

Trial 3

5. Repeat steps 2-3 with the other two balls.

Trial 4

6. Calculate the average bounce height for each ball.

Trial 5

Results 1. At what point did each ball have the greatest potential energy?

2. Where did the balls have the greatest kinetic energy?

3. How do you account for the difference in bounce heights of the

three balls?

4. Why did the balls not bounce back to the original height from

which they were dropped?



17

Date

Period

Name

CHAPTER

11

Enrichment

Energy in a Trebuchet Trebuchets are medieval machines that make practical use of the conservation of energy. Invading armies used trebuchets to hurl rocks and knock down castle walls. The trebuchet is more powerful than its predecessors—the catapult and the ballista.

Sling with projectile Hinged and propped counterweight Short arm

Pivot

Long arm . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

The trebuchet has one long arm. The fulcrum is closer to one end than the other. A heavy counterweight is attached to the short end. A sling is attached to the other end. The projectile sits in a pouch at the end of the sling beneath the trebuchet. In the initial position, the counterweight is high and ready to drop. When the trigger is released, the counterweight begins to drop. The long end of the arm moves quickly and the projectile in the sling is dragged along underneath the machine and then begins to swing up and around the trebuchet. When the projectile reaches the top of the arc, the rope slips free from the hook and the projectile is projected forward. 1.

What reference point would you choose in calculating the potential energy of the trebuchet before b efore it is fired?

2.

What information would you need in order to calculate the mechanical energy of the trebuchet before it is fired? What equation would you use?

3.

What kinds of energy are present in the system in the t he second picture of the trebuchet tr ebuchet in the figure? Describe the location of each type of energy.



19

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11

Enrichment

continued

4.

Why is the projectile proj ectile held in a sling rather than placed in a container at the long end of the arm?

5.

Many trebuchets had wheels that allowed the machines to move back and forth as the counter weight moved through its swing. What might have happened to a trebuchet without wheels?

6.

In terms of energy, what factors would affect the choice of the projectile mass?

7.

In terms of energy, what factors would affect the choice of the counterweight mass?

8.

If the counterweight had a mass of 3.5103 kg (not an unusual mass for a trebuchet!), how much potential energy would the counterweight have stored at a height of 3.0 m above the reference point?

9.

20

A device similar to the trebuchet trebu chet is the mangonel. The mangonel was developed by the Romans. Research the design and operation of a mangonel and compare it to the trebuchet.




CHAPTER

11

Transparency 11-1

J 0 1 E K .  0 n 4 0 . e f 4 h o ) = t s r o 2 e t 1 l 2 ) o s v / b c t a u m m o f e 2 0 d a r 1 2 . y a = 0 y b p t E 2 i ( s m K ) c o o g l e s C k e a ( e 0 r . v n 0 e c n 2 i ( h 2 2 1 = W 3

s / m 0 . 0 2


y g r e n E c i t e n i K

g k 0 . 0 2

2

s / m 0 . 0 2

g k 0 . 0 4

4

E K

J 0 1  0 0 . 1 = 2 2 ) s v / m m 2 0 1 2 . = 0 E 1 ( K ) g k 0 . 0 2 ( 2 2 1 =

E K

3

s / m 0 . 0 1

g k 0 . 0 2

1

E K


J 0 1 h a )  0 t y 1 o 0 . b b o t 8 y s e i = t s e c a r 2 a o 2 ) e s l p r v / e c m m v i n m o 2 0 d 2 1 C E . ( = 0 n K . a E 2 ( s e 8 K ) s h g a t f k m e o r 0 o . n l t 0 e b c u 4 h o f a ( 2 W 1 2 d = 3

J 0 1 E  0 K ) 0 . 1 2 n e t o = h t e 2 s r 2 ) e a s l v / b m m p m 2 0 u 2 1 o o . = 0 d C ( s E 1 . ( s K ) a s g e k m l b 0 u . n e o 0 h d 4 ( 2 W 1 2 = 3

s / m 0 . 0 1 3

g k 0 . 0 4

E K


21

Date

Period

11

Name

Transparency 11-1 Worksheet

Kinetic Energy 1.

In the equation shown, what does KE stand for?

2.

In the equation shown, what does m stand for?

3.

In the equation shown, what does v stand for?

4.

Look at Figure 2. When the velocity of the object in Figure 1 doubles, by how much does the kinetic energy increase? Why?

5.

If the velocity of the object in Figure 2 increased to 30 m/s, what would be the new kinetic energy?

6.

Look at Figure 3. When the mass of the object in Figure 1 doubles, by how much does the kinetic energy increase? Why?

7.

If the mass of the object in Figure 3 increased to 60 kg, what would be the new kinetic energy?

8.

22

When the mass and velocity of the object in Figure 4 both double, by how much does the kinetic energy increase? Why?




CHAPTER

11

Transparency 11-2

Earth

g PE


s n o i t a c o L g n i y r a V t a y g r e n E l a i t n e t o P

PE







9.80 m/s 2

Earth

mgh

(20.0 kg)(9.80 m/s 2)(20.0 m) = 3920 J

g



PE 20.0 kg

PE



9.80 m/s 2

mgh



(20.0 kg)(9.80 m/s 2)(30.0 m) = 5880 J

20.0 kg

30.0 m

20.0 m

Moon

g PE

PE







1.62 m/s2

mgh

(20.0 kg)(1.62 m/s 2)(20.0 m) = 648 J

20.0 kg


Mars

g PE

PE







3.72 m/s2

mgh

(20.0 kg)(3.72 m/s 2)(20.0 m) = 1490 J

20.0 kg

20.0 m

20.0 m


23

Date

Period

11

Name


Potential Energy at Varying Locations 1.

In the equation shown, what does PE stand for?

2.

In the equation shown, what does m stand for?

3.

In the equation shown, what does g stand for?

4.

In the equation shown, what does h stand for?

5.

What is the difference between the two situations on Earth in the upper drawings? How does this difference affect the potential energy?

6.

What is the difference between the first situation on Earth and the situation on Mars? How does this difference affect the potential energy?

7.

What is the difference between the situation on the Moon and the situation on Mars? How does this affect the potential energy?

8.

If the object on the Moon were raised to a height of 30.0 m, what would be its potential energy?

9.

If the object on Mars were raised to a height of 30.0 m, what would be its potential energy?

24




CHAPTER

11

Transparency 11-3

Energy Transfer

PE


PE

PE

KE


KE

KE

PE

KE

PE

KE


25

Date

Period

11

Name


Energy Transfer 1.

2.

3.

What two types of energy exist in the situation shown?

How are these two types of energy defined?

At what points is the kinetic energy of the ball at a maximum? Why?

4.

When is gravitational potential energy at a maximum? Why?

5.

As the gravitational potential energy increases, how does the kinetic energy change? Is this an example of an open or a closed system?

6.

How does the sum of the kinetic and gravitational potential energy change? What principle does this demonstrate?

7.

How many times during one rise and fall of the ball are the gravitational potential and kinetic energy equal?

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12

Mini Lab Worksheet

Melting 1. Label two foam cups A and B. 2. Measure 75 mL of room-temperature water and pour into each cup. Wipe up any spilled liquid. 3. Add an ice cube to cup A, and add ice water to cup B until the water levels are equal. 4. Measure the temperature of the water in each cup at 1-min intervals until the ice has melted. 5. Record the temperatures in a data table and plot a graph. Time Intervals Cup

1

2

3

4

5

6

7

8

9

10

min

min

min

min

min

min

min

min

min

min

A B . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Analyze and Conclude 6. Do the samples reach the same final temperature? Why?



35

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Materials

■

Take care when using a hot plate. It can burn the skin.

• hot plate (or Bunsen burner) • 250-mL ovenproof glass beaker • 50–200 g of water • two thermometers (non-mercury) • stopwatch (or timer)

Physics Lab Worksheet Heating and Cooling When a beaker of water is set on a hot plate and the hot plate is turned on, heat is transferred. It first is transferred to the beaker and then to the water at the bottom of the beaker by conduction. The water then transfers heat from the bottom to the top through convection. Once the heat source is removed or shut off, the water radiates any surplus heat until it reaches room temperature. How quickly the water heats up is a function of the amount of heat added, the mass of the water, and the specific heat of water.

Question How does the constant supply of thermal energy affect the temperature of water?

Objectives ■ Measure,

in SI, temperature and mass.

and use graphs to help describe the change in temperature of water as it heats up and cools down.

■ Make


■ Explain

any similarities and differences in these two changes.

Procedure 1. Set the hot plate to the highest setting, or as recommended by your teacher. Allow a few minutes for the plate to heat up. 2. Measure the mass of the empty beaker. 3. Pour 150 mL of water into the beaker and measure the combined mass of the water and the beaker. 4. Calculate and record the mass of the water in the data table on the next page.



37

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12

continued

Data Table Mass of water Initial air temperature Final air temperature Change in air temperature

Time (min)

Temperature (°C)

Heating or Cooling

5. Record the initial temperature of the water and the air in the classroom. Note that the bulb end of the thermometers must not touch the bottom or sides of the beaker, nor should it touch a table or your hands. 6. Place the beaker on the hot plate and record the temperature every minute for 5 min. 7. Carefully remove the beaker from the hot plate and record the temperature every minute for the next 10 min. 8. At the end of 10 min, record the temperature of the air. 9. Turn off the hot plate. o f the water as instructed by your teacher. 10. When finished, allow the equipment to cool and dispose of

Analyze 1. Calculate the change in air temperature to determine if air temperature may be an extraneous variable.

2. Make a scatter-plot graph of temperature (vertical axis) versus time (horizontal axis). Use a computer or a calculator to construct the graph, if possible.

38




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12

tempera ture as the water heated up? 3. Calculate What is the change in water temperature

4. Calculate What is the drop in water temperature when the heat source was removed?

5. Calculate the average slope for the temperature increase by dividing change in temperature by the amount of time the water was heating up.

6. Calculate the average slope for the temperature decrease by dividing change in temperature by the amount of time the heat source was removed. . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Conclude and Apply chang e in water temperature temperat ure when a heat source was applied? 1. Summarize What was the change

chang e in water temperature temperat ure once the heat source was removed? 2. Summarize What was the change

3. What would happen to the water temperature after the next 10 min? Would it continue cooling down forever?



39

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12


continued

4. Did the water appear to heat up or cool down quicker? Why do you think this is so? Hint: Examine the slopes you calculated.

coo l down? Sup5. Hypothesize Where did the heat energy in the water go once the water began to cool port your hypothesis.

Going Further 1. Does placing your thermometer at the top of the water in your beaker result in different readings than if it is placed at the bottom of the beaker? Explain.

2. Hypothesize what the temperature changes might look like if you had the following amounts of water in the beaker: beak er: 50 mL, 250 mL.

3. Suppose you insulated the beaker you were using. How would the beaker’s ability to heat up and cool down be affected?

Real-World Physics 1. Suppose you were to use vegetable oil in the beaker instead of water. Hypothesize what the temperature changes might look like if you were to follow the same steps and perform the experiment.

2. If you were to take soup at room temperature and cook it in the microwave oven for 3 min, will the soup return to room temperature in 3 min? Explain your answer.

To find out more about thermal energy, visit the Web site: physicspp.com

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Study Guide

Thermal Energy Vocabulary Review Write the term that correctly completes the statement. Use each term once.


conduction

heat

radiation

convection

heat engine

second law of thermodynamics

entropy

heat of fusion

specific heat

first law of thermodynamics

heat of vaporization

thermal equilibrium

1.

is the state at which the rate of energy flow between two objects is equal and the objects are at the same temperature.

2.

Energy transferred between objects is called

3.

The amount of energy required to raise the temperature of one unit mass of a substance by one temperature unit is the of the substance.

4.

The amount of energy needed to melt 1 kg of a substance is the .

5.

The states that the change in thermal energy of an object equals the heat added to the object minus the work done by the object.

.

6.

is the transfer of kinetic energy when particles collide.

7.

is a measure of the disorder in a system.

8.

A device that converts thermal energy to mechanical energy is a(n) .

9.

The states that natural processes go in a direction that maintains or increases the total entropy of the universe.

10.

is the motion of a fluid caused by temperature differences.

11.

The amount of energy required to convert 1 kg of a substance from a liquid to a gas is the .

12.

The transfer of energy by electromagnetic waves is called



.

41

Name

Study Guide

12

Section 12.1

continued

Temperature and Thermal Energy

In your textbook, read about the theory of thermal energy and temperature on pages 314–315. For each statement below, write true or rewrite the italicized part to make the statement true. 1.

The temperature of an object is a measure of the total kinetic energy of the particles.

2.

The thermal energy in an object depends on the number of particles in the object and the temperature of the object .

3.

Two bodies are in rotational equilibrium if they are at the same temperature.

4.

A Kelvin is equal in magnitude to a Celsius degree.

5.

Absolute zero is equal to 0°C.

6.

The freezing point of water is 0°C or 212 K .

7.

Absolute zero is the point at which a substance has minimal thermal energy .

In your textbook, read about specific heat on pages 317–318. For each term on the left, write the letter of the corresponding item. 8. unit of specific heat

a. K

9. heat

b. S

10. degree Celsius

c.

 T

11. Kelvin

d. °C

12. entropy

e. Q

13. energy change

f.

J/kg·K

14. temperature change

g.

E

Answer the following questions. Use complete sentences. 15. Why is the Kelvin temperature scale rather than the Celsius temperature scale used in science? Use

“kinetic energy” in your answer.

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Study Guide

16. The diagram shows the construction of the inner liner of a

12

cork stopper

vacuum bottle. How does a vacuum bottle prevent the transfer of thermal energy: a. by conduction?

b. by convection?

Vacuum between mirrored glass walls hot or cold liquid

c. by radiation?

17. What is the specific heat of a metal if it takes 15,000 J of heat to raise the temperature of a 620-g

sample from 15.0°C to 85.0°C? . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

In your textbook, read about calorimetry on pages 319–320. Use the following information to answer questions 18–21. A student uses a foam cup as a calorimeter. The student places 100.0 g of water at 20°C in the cup. The student adds 100.0 g of lead shot at 120°C to the cup. The water and shot are then allowed to reach thermal equilibrium. The specific heat of lead is 130 J/kg·K. 18. Is Q for the water positive or negative?

19. Is Q for the lead shot positive or negative?

20. Assuming that no heat is lost to the surroundings, how does the total energy of the system com-

pare with the total energy of the water and lead before mixing?

21. What is the final temperature of the water at thermal equilibrium?



43

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Study Guide

12

Section 12.2

continued

Changes of State and the Laws of Thermodynamics

In your textbook, read about changes of state on pages 323–324. Circle the letter of the choice that best completes the statement or answers the question. 1. The energy needed to melt 1 kg of a substance is called the a. heat of vaporization

c. heat of fusion

b. condensation

d. freezing point

.

2. The temperature at which all added thermal energy is used to change a liquid to a gas is the

. a. boiling point

c. heat of fusion

b. melting point

d. heat of vaporization

3. How does the amount of energy absorbed by 1 g of ice as it melts compare to the amount of

energy released by 1 g of water as it freezes? a. More energy is released by the ice than is absorbed by the water. b. More energy is absorbed by the water than is released by the ice. c. The amounts of energy absorbed and released depend on the surrounding temperature. d. They are the same. 4. Which equation correctly relates heat, mass, and the heat of vaporization? a. Q  m  H v

c. Q  m /H v

b. Q  mH v

d. Q  H v /m

5. As a liquid changes to a gas, a. both its kinetic and potential

. c. only its potential energy increases

energy increase b. only its kinetic energy increases

d. neither its kinetic nor potential energy increases

6. How does the amount of energy needed to melt 1 kg of ice at 0°C compare to the amount

of energy needed to change 1 kg of water to steam at 100°C? The heat of fusion of water is 3.34105 J/kg, and the heat of vaporization of water is 2.26 106 J/kg. a. It takes about two-thirds as much energy to boil the water as to melt the ice. b. It takes the same amount of energy to boil the water and melt the ice. c. It takes about two-thirds as much energy to melt the ice as to boil the water. d. It takes more than six times as much energy to boil the water as to melt the ice.

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Study Guide

12

Answer the following questions. Show your calculations. 7. How much ice at 273 K can be melted by 5.00 103 J?

8. A 2.00 102 g sample of water at 60.0°C is heated to steam at 140.0°C. a. How much heat is absorbed?

b. How much energy would be released if the steam at 140.0°C were cooled to water at 60.0°C?


In your textbook, read about the first law of thermodynamics, the second law of thermodynamics, and entropy on pages 326–331. Answer the following questions. Use complete sentences. 9. State the first law of thermodynamics.

10. Some people think that they can cool off a hot kitchen by leaving the refrigerator door open. Why

is that not true?

11. When paint dries, does its entropy increase or decrease? Is this an instance where the second law

of thermodynamics does not apply? Explain your answer.



45

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Study Guide

continued

For each statement, circle 1 or 2 to indicate whether the statement relates more closely to the first law of thermodynamics or the second law of thermodynamics. 12. The total entropy of the universe tends to increase. (1) (2) 13. An increase in thermal energy depends on the work done and the heat added to a system. (1) (2) 14. Heat flows spontaneously from hot objects to cold objects. (1) (2) 15. The amount of useful energy tends to decrease. (1) (2) 16. A heat engine converts thermal energy to mechanical energy. (1) (2) 17. Using mechanical energy, a refrigerator removes thermal energy from warmer bodies. (1) (2) 18. The moving parts in an automobile engine generate waste heat. (1) (2)

Answer the following questions. Use complete sentences. 19. Explain why a heat engine must have a heat sink.

20. How does energy efficiency relate to the first and second laws of thermodynamics?

21. Why is it important for appliance and automobile manufacturers to make their products as energy

efficient as possible?

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12

Reinforcement Energy Loss

Materials

Problem • foam cup

How can you reduce loss of energy by conduction and convection?

• two metal cans with the lids removed

Procedure

• 250-mL beaker

1.

Place the foam cup, two metal cans, and beaker at least 15 cm apart.

2.

Measure 150 mL of hot tap water into each container and record the temperature of the water in each container. Cover one of the metal cans with the foam or cardboard.

3.

Record the temperature of the water every minute for ten minutes. Stir the water once or twice with the stirring rod before each measurement. Replace the lid on the covered can after each measurement.

4.

If you have a liquid crystal thermometer, measure the temperature of the outside of each container at the beginning and end of the ten-minute period. If you don’t, put your hand around each container and compare the sensation of warmth.

• graduated cylinder • hot tap water • foam or cardboard square to cover a can • thermometer • stirring rod • (optional) liquid crystal thermometer strip . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Apply Min.

Foam

Metal

Metal Glass (covered)

1.

Which container lost energy to the surroundings most quickly? The least quickly?

2.

Which methods of thermal transfer affected the loss of energy from the containers?

3.

Was there a difference in temperature between the two cans? Why?

0 1 2 3 4 5 6 7 8 9 10



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Enrichment

Calorimetry The principle of the calorimeter is that the total amount of energy in the system remains unchanged even if energy is transferred from one object to another. If a hot object is placed in cool water, the energy from the hot object will move to the colder water until thermal equilibrium is reached. Calorimeters are useful for many purposes. They may be used to determine the mass or specific heat of a substance, or the heat absorbed or released during chemical reactions. They may also be used to determine the energy value of food. 1.


What are the most important factors in the design of a calorimeter? Draw a diagram of a calorimeter and label the parts, explaining why they are included.

2.

How would a calorimeter that is used to determine the energy exchange during a chemical reaction differ from one used to determine the specific heat of a piece of metal?

3.

If you wanted to find the specific heat of a metal using a calorimeter, how would you heat the metal so that you would know its temperature before putting it in cool water in the calorimeter?



51

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12

4.

5.

6.

Enrichment

continued

Some heat is lost to the surroundings when a calorimeter is used. How does the high specific heat of water make it useful for minimizing this undesirable heat loss?

One calorimeter contains 100.0 g of water. A second, identical calorimeter contains 1000.0 g of water. In both calorimeters, the water absorbs 2090 J of thermal energy. Why can the first calorimeter measure the energy change more precisely?

Research how food scientists use calorimetry to determine the energy value of foods, and study the calorimeters they use. Why would calorimeters measure energy value less accurately if they used a match to ignite the food? C o p y r i g h t © G l e n c o e / M c G r a w -H i l ,l a d i v i s i o n o f T h e M c G r a w -H i l l C o m p a n i e s , I n c .

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CHAPTER

12

Transparency 12-1

Three Temperature Scales Degrees Celsius ( C) 

Kelvin (K)

Degrees Fahrenheit ( F) 

400 373.15 Water boils

250 212.00

100.00 200 350 150 50 100 300 273.15

Water freezes

250 . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

50

32.00

0.00 0

50

50 200

100

100

150 150

150

200

250 100

300 200 350 50

400 250 Lowest possible temperature (absolute zero)


0.00

273.15

450 459.67


53

Date

Period

12

Name


Three Temperature Scales 1.

In what ways are the three temperature scales the same? In what ways are they different?

2.

What is a Kelvin?

3.

What are the freezing and boiling points of water on each scale?

4.

The normal temperature of the human body is 98.6°F. What is this temperature on the Celsius scale? On the Kelvin scale?

5.

What advantage does the Kelvin scale have for scientific measurement?

6.

Why is zero considered to be a relative value on the Celsius scale and an absolute value on the Kelvin scale?

7.

The liquid in one container drops 100°F, while the same liquid in another container drops 100°C. How does the change in thermal energy in the two containers compare? Explain your answer.

8.

At approximately what temperature would Celsius and Farenheit thermometers register the same reading?

54




CHAPTER

12

Transparency 12-2

E

m a e t S 3 7 0 3

r m e a t e a  t W S


h p a r G e t a t S f o e g n a h C

7 . 3 1 8

D

r e t a W

7 . 5 9 3

C

m a r g r e p ) J ( t a e H

r e t a W 

e c I

B e c I 3 7 3

3 2 3

3 7 2

7 . 2 6 3 4 2

A

) K ( e r u t a r e p m e T Physics: Principles and Problems


55

Date

Period

12

Name


Change-of-State Graph 1.

2.

As heat is added to the ice in section A–B, the water in section C–D, and the water vapor from E to the end of the graph, what is happening to the molecules? How do you know?

Consider section B–C of the graph and answer the following questions. a.

As heat is added, what is happening to the molecules? How do you know?

b.

What would you observe happening?

c.

d.

How much energy is added to the ice in section B–C? What is this energy called?

3.

How much energy is needed to raise 1 g of water 1°C?

4.

How much energy is needed to change 1 g of water at 100°C to steam at 100°C?

5.

How much energy is needed to change 1 g of ice at 0°C to water at 0°C?

6.

Given a consistent source of heat, about how much longer would it take to boil 100 g of water at 100°C than to melt 100 g of ice at 0°C?

7.

How do the freezing point and the melting point of water compare? Explain your answer in terms of energy changes shown on the graph.

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CHAPTER

12

Transparency 12-3 t s u a h x E


e n i g n E n o i t s u b m o C l a n r e t n I

t s u a h x E

r e w o P

k r a p S n o i s s e r p m o C

g u l p k r a p S

e k a t n I e d i n n l r a o o p r s i a a A g v


n o t s i P


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12

Name


Internal Combustion Engine 1.

What is the general term for the type of engine shown?

2.

In general, what does this type of engine do?

3.

In the internal combustion engine shown, where does the thermal energy come from?

4.

Where in the engine is mechanical energy present?

5.

What happens during the intake stroke?

6.

What happens during the compression stroke?

7.

What happens in the part of the figure labeled spark?

8.

What happens during the power stroke?

9.

What happens during the exhaust stroke?


10.

Is an internal combustion engine 100 percent efficient? Explain your answer.

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CHAPTER

12

Transparency 12-4

How Your Refrigerator Works

Thermal energy is absorbed as liquid vaporizes in these pipes.

Evaporator Accumulator


Freezer compartment

Heat exchanger

Thermal energy is radiated as vapor condenses in these pipes.

Freezer coils and fins

Refrigerator compartment

Condenser Capillary tube Compressor

Drier-strainer



59

Date

Period

12

Name


How Your Refrigerator Works 1.

At what point does external energy enter the system?

2.

At what location in the refrigerator is the most thermal energy removed?

3.

What is the relationship between the evaporation of a liquid inside the circuit and the heat removed from the refrigerator?

4.

5.

6.

Is heat transferred in a refrigerator primarily by conduction, convection, or radation? Explain your answer.

What is the purpose of the condenser?

If the compressor in a refrigerator requires 300 J of energy to remove 800 J of heat, how much energy is released to the air in the room?

7.

What effect would leaving the refrigerator door open on a hot summer day have on the temperature in the room? Explain your answer.

8.

Why is it important to keep dust and grease from building up on the condensation coils at the back of a refrigerator?

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CHAPTER

13

Mini Lab Worksheet

Pressure How much pressure do you exert when standing on one foot? Have a partner trace your foot, and then use the outline to estimate its area.


1.

Determine your weight in newtons and the area of the outline in m2.

2.

Calculate the pressure.

3.

Compare and contrast the pressure you exert on the ground with the pressure exerted by various objects. For example, you could weigh a brick and determine the pressure it exerts when resting on different faces.


How do shoes with high heels affect the pressure that a person exerts on the ground?



69

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13

Materials

■

■


■

The chemicals used in this experiment are flammable and poisonous. Do not inhale the fumes from these chemicals. Do not have any open flame near these chemicals. Use in a well ventilated room or fume hood. Avoid contact with the chemicals on your skin or clothing. Notify your teacher immediately if an accident or spill occurs. Wash your hands after the lab is over.

• methanol (methyl alcohol)

Physics Lab Worksheet Evaporative Cooling If you have ever spilled a small amount of rubbing alcohol on your skin, you probably noticed how cool it felt. You have learned that this coolness is caused by evaporation. In this experiment, you will test the rates at which different types of alcohol evaporate. An alcohol is a substance that has a hydroxyl functional group (–OH) attached to a carbon or a chain of carbons. From your observations of evaporative cooling, you will infer the relative strength of the cohesive forces in the tested alcohols.

Question How do the rates of evaporation compare for different alcohols?

Objectives ■

Collect and organize data for the evaporation of alcohols.

■

Compare and contrast the rates of evaporation for various alcohols.

■ Analyze why ■

some alcohols evaporate faster than others.

Infer the relationship between cohesive forces and the rate of evaporation.

Procedure

• ethanol (ethyl alcohol) • 2-propanol (isopropyl alcohol) • masking tape (two pieces)

1. Wrap the thermometer with a square piece of filter paper fastened by a small rubber band. To do this, first slip the rubber band onto the thermometer. Then, wrap the paper around the thermometer and roll the rubber band over the wrapped paper. The paper should fit snugly over the thermometer’s end.

• thermometer (non-mercury) • filter paper (three pieces, 2.5 cm  2.5 cm) • small rubber bands



71

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continued

Data Table Liquid

T 2

(°C)

T 1

(°C)

T (°C)

Methyl alcohol Ethyl alcohol Isopropyl alcohol

2. Obtain a small beaker of methanol. Place the paper-covered end of the thermometer in the container of methanol. Do not let the container fall over. Keep the thermometer in the container for 1 min. 3. After 1 min has elapsed, record the temperature reading on the thermometer in the data table under T 1. This is the initial temperature of the methanol. 4. Remove the thermometer from the methanol. Place the thermometer over the edge of a table top so that the thermometer’s tip extends about 5 cm beyond the edge of the table. Use the masking tape to anchor the thermometer in place. 5. Observe the temperature during the experiment. After 4 min have elapsed, observe and record the temperature in the data table in the column marked T 2. 6. Roll the rubber band up the thermometer and dispose of the filter paper as directed by your teacher. 7. Repeat steps 1–6, but use ethanol as the liquid. Record your results in the data table. 8. Repeat steps 1–6, but use isopropyl alcohol as the liquid. Record your results in the data table.

Analyze 1. Interpret Data Did the thermometer show a temperature increase or decrease for your trials? Why?

2. Calculate T for each of your liquids by finding the difference between the ending temperatures and the initial temperatures of the liquids (T 2  T 1).

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continued

13

3. Using the chemical formulas for methanol (CH3OH), ethanol (C2H5OH), and isopropyl alcohol (C3H7OH), determine the molar mass of each of the liquids you tested. You will need to refer to the periodic table to determine the molar masses.

4. Infer What can the

T for

each trial tell you about the rates of evaporation of the alcohols?

5. Think Critically Why was paper used on the thermometer instead of using only the thermometer?


Conclude and Apply 1. Using the rates of evaporation of the alcohols you studied, how can you determine which alcohol had the strongest cohesive forces?

2. Which alcohol had the weakest cohesive forces?

3. What general trend did you find between the change in temperature (T ) and the molar mass of an alcohol?



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continued

4. Hypothesize Would a fan blowing in the lab room change the room’s air temperature? Would it change the T that you observed? Explain.

Going Further Predict the size of T for 1-butanol, which has the formula C 4H9OH, relative to the alcohols that you tested.

Real-World Physics The National Weather Service began using a new windchill index in 2001. The old chart was based on data derived from water-freezing experiments done in Antarctica in the 1940s. Explain how windchill relates to evaporative cooling, why this phenomenon is important in cold weather, and how the new chart improves upon the old chart. C o p y r i g h t © G l e n c o e / M c G r a w -H i l ,l a d i v i s i o n o f T h e M c G r a w -H i l l C o m p a n i e s , I n c .

To find out more about states of matter, visit the Web site: physicspp.com

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Study Guide

Static Electricity Vocabulary Review Write the term that correctly completes the statement. Use each term once. adhesive forces amorphous solid Archimedes’ principle Bernoulli’s principle buoyant force

coefficient of linear expansion

combined gas law

Pascal’s principle

crystal lattice

plasma

coefficient of volume expansion

fluid

pressure

ideal gas law

streamlines

pascal

thermal expansion

cohesive forces

1.


A

flows and has no definite shape of its own.

2.

Force divided by surface area equals

.

3.

states that the magnitude of the buoyant force on an object equals the weight of fluid displaced by the object.

4.

A is a gas-like state that contains electrons and positively charged ions.

5.

The

6.

The states that for a fixed amount of ideal gas, the pressure times the volume divided by the Kelvin temperature equals a constant.

7.

A fixed pattern of particles within a solid is a(n)

8.

The

can be expressed by the relationship PV = nRT .

9.

The

is an upward force on an object immersed in a liquid.

is the SI standard unit of pressure.

.

10.

states that as the velocity of a fluid increases, the pressure exerted by the fluid decreases.

11.

When an increase in temperature produces an increase in the volume of matter and a decrease in its density, it is called .

12.

are the electromagnetic attractions of particles within a substance for one another.

13.

The is equal to the change in length divided by the original length and the change in temperature.

14.

states that a change in pressure at any point on a confined fluid is transmitted undiminished through the fluid.



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continued

15.

Attractive forces between particles of different substances are .

16.

A(n) is a substance that has definite volume and shape but no regular crystal structure. are representations of the flow of fluids around objects.

17.

The is equal to the change in volume divided by the original volume and the change in temperature.

18.

Section 13.1

Properties of Fluids

In your textbook, read about pressure on page 342. For each statement below, write true or rewrite the italicized part to make the statement true. Fluids flow and have no definite volume.

1.

The SI unit of pressure is the pascal, Pa.

2.

Pressure is inversely proportional to force.

3.

Fluids have no definite shape of their own.

4.

5.

The forces that hold molecules of the floor together cause the floor to exert an upward pressure on your feet.

6.

As you move to higher altitudes on Earth, atmospheric pressure increases.

7.

The typical pressure at the center of the Sun is greater than the typical pressure at the center of Earth.

8.

1 Pa is equivalent to 1 N /m 3.

9.

Standard atmospheric pressure is equal to 101.3 kPa.

In your textbook, read about the gas laws on page 344. For each term on the left, write the letter of the corresponding item. 10.

Boyle’s Law

a.

PV  nRT

11.

Charles’ Law

b.

6.022  1023

12.

Combined Gas Law

c.

1 2 2 1  

d.

P 1V 1  P 2V 2

e.

P 1 P 2    T 1 T 2

13. 14.

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Ideal Gas Law Avogadro’s number


P V T 1

P V T 2



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Study Guide

continued

13

In your textbook, read about thermal expansion and plasma on pages 347–348. Answer the following questions. Use complete sentences. 15.

How does thermal expansion explain convection in a pan of water being heated?

16.

At what temperature does H2O reach its greatest density? What happens if you cool it below that point?

17.

What is one primary difference between gas and plasma?

Section 13.2


Forces Within Liquids

In your textbook, read about cohesive and adhesive forces on pages 349–350. The diagram shows two different liquids in glass graduated cylinders. Refer to the diagram to answer questions 1 and 2. 7

7

6

6 A

1.

2.

3.

4.

B

Which liquid has the greatest cohesion? How do you know?

How do the adhesive forces of each liquid compare?

A flat piece of aluminum foil is placed on the surface of a pan of water. Although the aluminum is more dense than water, the foil does not sink. Why?

It’s a very hot day at the beach. The air temperature is greater than 32°C and there’s no breeze to cool you off. Why do you feel cooler when you get out of the water?



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Section 13.3

Study Guide

continued

Fluids at Rest and in Motion

In your textbook, read about fluids at rest and swimming under pressure on page 352. Next to each situation, write Pascal’s principle or Archimedes’ principle to indicate which principle best applies to the situation. 1.

A person uses a hydraulic brake to stop a car.

2.

An ice cube floats in water.

3.

A fish uses an air bladder to move up and down in water.

4.

Squeezing one end of a balloon makes the other end larger.

5.

A person feels lighter in water than on land.

6.

A camper pumps up an air mattress with a foot pump.

7.

Rolling a toothpaste tube from the bottom squeezes toothpaste from the tube. A scientist determines the volume of an irregular object by placing it in water.

8.

Answer the following questions. Use complete sentences. 9.

You are trying to install a 1-m long bookshelf on a wall and want to make sure it’s level. You don’t have a level, but you do have 2 m of clear plastic tubing and some water. How could you use the tubing to level the shelf? What principle are you applying?

10.

When a cargo ship bound for Florida leaves a port on Lake Michigan, a paint spot on the side of the ship is just above the water line. The ship sails through the St. Lawrence Seaway and reaches the Atlantic Ocean. Assume that nothing has been added to or removed from the ship during its journey. Where is the paint spot compared with where it was when the ship left port? Explain your answer.

11.

What is the pressure, in kPa, exerted by a 23.0-m column of freshwater? How does this compare to standard air pressure in atmospheres?

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Study Guide

continued

13

In your textbook, read about swimming under pressure on page 352. Write the term that correctly completes the statement. The ( 12.)

force a body experiences when it is submerged in a fluid is called

the (13.)

force. The relationship of this force was discovered by the ancient Greek

scientist (14.)

, and the principle is named after him/her. This force is dependent

upon gravity, the (15.)

of the fluid and the (16.)

object submerged. The (17.)

of the

of the submerged object does not play a part in

determining this force. This principle also explains why (18.)

floats at the top of your drink.

Objects with an apparent weight of zero have (19.) this principle is the construction of (20.)

, which use water pumps to move water

in or out of chambers to change its ( 21.)

and either rise or sink. The same prin-

ciple is used with the (22.) . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

. One practical application of

of fish, allowing them to move up or down through

the water.

Section 13.4

Solids

In your textbook, read about solid bodies and thermal expansion of solids on pages 359–361. For each statement below, write true or false. 1.

Particles in a crystal lattice do not move at all.

2.

Butter and glass are examples of amorphous solids.

3.

When most substances freeze, their particles move closer together.

4.

Water is most dense at 0°C, its freezing point.

5.

Increasing the pressure on water increases its freezing point.

6.

Elasticity is the ability of a solid object to return to its original form.

7.

Ductility is the property of a solid that allows it to be hammered into sheets.

8.

The symbol for the coefficient of linear expansion is .

9.

The change in the length of a solid is proportional to the change in temperature.

10.

Metals used in a bimetallic strip have the same rates of thermal expansion.



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Study Guide

continued

Answer the following questions. Use complete sentences or show your calculations. 11.

In an area that experiences both hot summers and cold winters, why would the time of year that overhead power lines are installed change the way the wires are strung?

12.

In making a thermometer, why is it important that the glass have as little thermal expansion as possible?

13.

An aluminum baseball bat is 86.40 cm long at 20.0°C. On a hot day, when the the temperature reaches 32.0°C, what will be the length of the bat?

14.

Explain why a bridge in Vermont must have larger gaps in the expansion joints than the same structure built in Florida.

15.

The volume of a copper sphere is 2.44 cm3 at 12°C. What was the volume of the copper sphere after it was heated to 984°C? The coefficient of volume expansion for copper is   48106 (°C)1.

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Materials

Reinforcement Cohesion and Adhesion Problem

• three plastic medicine cups

How do cohesive and adhesive forces affect the behavior of substances?

• tap water

Procedure

• rubbing alcohol

1.

Fill three labeled medicine cups about half full, one each with water, alcohol, and salad oil. Place a dropper in each cup.

2.

Lay the wax paper on the table. With the tip of the dropper nearly touching the paper, place two separate drops of water on the left side of the paper. Observe the shape of the drops from the side.

3.

Holding a toothpick at about a 45° angle, pull one of the drops close to, but not touching, the second drop.

4.

Dip the toothpick in the water cup. Holding the toothpick upright, place the tip between the two drops. Record what happens.

5.

Repeat steps 2–4 with the oil and alcohol, using clean toothpicks for each liquid.

• salad oil • 10-cm square of waxed paper • three droppers • three toothpicks


Results 1.

Which of the liquids had the greatest cohesive force? How do you know?

2.

What was the reason for dipping the toothpick in water before putting it between the drops?

3.


Compare and contrast the adhesive and cohesive forces between the liquids and waxed paper.


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Materials

• several party balloons • tape measure • ice chest or freezer, stocked with ice

Enrichment The Gas Laws The first human flight took place near Paris in 1783 when two men took a 25-minute flight in a hot air balloon. In the early years of ballooning, people argued over the relative merits of using hydrogen or hot air to fill the balloon. This led to a scientific study of the laws of gas behavior. Both Charles and Gay-Lussac used ballooning to test their theories.

Procedure

• desk lamp


1.

Blow up several balloons (not too large) and tie off the ends.

2.

Using the tape measure, record the circumference of each balloon.

3.

Place several balloons in the ice chest and several more under a desk lamp. Be careful not to let the balloon touch the bulb. Leave a few balloons at room temperature.

4.

After 10 min, retrieve the balloons from the ice chest and quickly measure the circumference of each. If there is a delay, the balloon will warm to room temperature and will measure the same as before.

5.

After 20 min, retrieve the balloons from underneath the desk lamp and quickly measure the circumference of each.

6.

Using your recorded data and the gas laws, answer the questions below.

Results 1.

2.

3.


At room temperature, if you squeeze a balloon hard enough, it will burst. Explain this behavior in terms of the ideal gas law.

Explain what happened to the balloons from the ice chest and under the desk lamp. Which law applies to this experiment?

Assuming the balloon could withstand the temperatures, what would happen to the balloon if it were placed inside a 400°C oven? Give your explanation in terms of the behavior of the gas molecules inside the balloon.


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Enrichment

continued

4.

Suppose you could double the number of molecules in one balloon at room temperature. What would happen to the balloon?

5.

What would happen to these balloons at the bottom of the sea? On the top of a mountain? In outer space?

6.

Why are we able to use the ideal gas law for so many different gases and laboratory conditions?

Use the ideal gas law to solve these problems. Standard temperature and pressure (STP) is equal to a temperature of 273 K and a pressure of 1.00 atm or 101.3 kPa or 1.013 105 Pa. Use R as 0.08207 L·atm/mol K. 7.

8.

9.

Find the volume of 1.00 mole of any gas at STP.

A tank attached to an air compressor contains 20.0 L of air at a temperature of 30°C and a gauge pressure of 4.00105 Pa. Note: Gauge pressure is the amount in excess of normal atmospheric pressure. Air is a mixture of about 78 percent nitrogen and 21 percent oxygen with several other gases in minor amounts. The average molecular mass is 28.8 g/mol. a.

What is the mass of the air in the tank?

b.

What volume would the air occupy at STP?

R can be expressed in several combinations of units including J/mol·K, and l·atm/mol·K. What determines which value of R is used in solving the ideal gas law equation?

10.

What other gas law could have been used to solve question 4b?

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s a G


r e t t a M f o s e i t r e p o r P

d i u q i L

d i l o S


e m u s l e o v i p d u n c a c o e t i p r a e h s i n e t a h t n s o e c e m h u t s s f A o

r e d i n n a a t r n e o h t c e o h t h c f a o e s t e s d a i p s e e v h t o o m s t n e i l c p i t r m a u P b

t r a s p e e i p h t u f c o c o e t p i a r e h s i n e t a h t n s o e c e m h u t s s f A o

t s a p e d i l s / e v o m n r e a c h t s o e n l c a i t r e a n P o

e m u l o v d n a e p a h s d e x i F

l a t s y r c n i d e e r u k c t c o u l r s t s e l e c i c i t t r t a a P l

e l b i s s e r p m o C

s e l c i t r a p n e e w t e b e c a p s f o t o l A

y l i s a e s w o l F

d e s s e r p m o c y l i s a e t o N

s e l c i t r a p n e e w t e b e c a p s e l t t i L

w o l f o t y t i l i b a e t a r e d o M

y t i l i b i s s e r p m o c o n t s o m l A

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w o l f o t y t i l i b a o n t s o m l A


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Properties of Matter 1.

In terms of the kinetic-molecular theory, how do solids, liquids, and gases compare?

2.

How does the arrangement of molecules in a solid explain its properties?

3.

How does the arrangement of molecules in a liquid explain why it has no definite shape?

4.

How does the arrangement of molecules in a gas explain why it is compressible and why liquids and solids are not easily compressed?

5.

6.

7.

8.

90

Plastic foam is a solid, yet is compressible. How do you explain this?

A solid exerts pressure on the surface beneath it. How can a gas exert pressure on the bottom and sides of the container when there is so much space between the molecules?

If you mixed two solids, two liquids, or two gases, which would become randomly mixed the most quickly without further action on your part? Why?

As materials pass from solid to liquid to gas, what happens to their entropy?




CHAPTER

13

Transparency 13-2

Gas Laws

P 1V 1

101.3 kPa

P





P 2V 2

1 V

202.6 kPa 10.0 L 5.0 L


Boyles Law Describes pressure and volume with constant temperature. If the volume decreases, the pressure increases.

101.3 kPa V 1 T 1 V





V 2 T 2 T

101.3 kPa

Charles Law Describes temperature and volume with constant pressure. If the temperature increases, the volume increases.



91

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Gas Laws 1.

What factor do the plungers in the drawings represent?

2.

Is the pressure referred to in Boyle’s law the pressure on the gas or the pressure that the gas exerts on the container? Explain your answer.

3.

According to Boyle’s law, what happens to pressure when the volume of a gas is reduced without removing any of the gas?

4.

What factors must remain constant for Boyle’s law to predict relationships?

5.

6.

If you doubled the pressure on the second cylinder, how would its volume compare with the first cylinder?

What factors remain constant in Charles’s law?

7.

In the Charles’s law drawings, if the temperature in the second cylinder is three times the temperature in the first cylinder, how does its volume compare with the first cylinder?

8.

State a relationship about volume, pressure, and temperature that combines both Boyle’s law and Charles’s law.

9.

92

A container of gas has a volume of 100 cm3. What would happen to the volume if you doubled both the pressure and the temperature?




CHAPTER

13

Transparency 13-3

Pascal’s, Archimedes’, and Bernoulli’s Principles F 2 F 1

A  Surface

Area

A1

A2

Pascal’s Principle


Piston 1

h

Piston 2

h  l

F top

Archimedes’ Principle

F bottom

P 1 P 2

Bernoulli’s Principle


v 1

v 2


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Pascal’s, Archimedes’, and Bernoulli’s Principles 1.

Describe how the diagram of Pascal’s principle is related to the equation for pressure: pressure force/area.

2.

If A1

3.

How could you use Pascal’s principle to lift a heavy mass with the least effort?

4.

5.



10 cm and A2





30 cm , how much greater is F 2 than F 1?

In the diagram of Archimedes’ principle, analyze the forces acting on the cube due to the liquid. Which of the forces affects the position of the cube?

Would increasing the distance, h, increase or decrease the force acting on top of the cube? Why?

6.

How would you calculate the volume of liquid the cube displaces?

7.

How does the density of the liquid affect the upward force (buoyant force) acting on the cube?

8.

In the diagram of Bernoulli’s principle, what is the relationship between the velocity of a fluid and the pressure of the fluid?

9.

94

Why does the velocity of a fluid increase as it enters a narrower part of the tube?




CHAPTER

13


r e t t a M f o s e t a t S e e r h T n i n o i s n a p x E l a m r e h T

Transparency 13-4

s e s a G

s d i u q i L

s d i l o S


e s d t n h a a t e n a o p g b h l f x n . t o ) i r e i t s t I s u r a n t e g — e s a o c n a , l n o h o g d l g i i d o e e a l l ( n l h u a t t a b e e s o b e e h r r s h t n r i e u u a a n i d e n s s t c h e r s h o e i e t H b w a l

. d s i e u t e g r i q i u s L e s n a a h k — r a e c e m m e t r e n t o t u m o e a o i r s l e b n m i p r a s e p s m h x o e T e p t

g n d n e i o d l . t e k c s n e i n u d o s b n j a n i p m t x o I o i r e s — f n d l d a a t l a i p o s x r e o e r m e l o h a e p t m g e e n r d e e i k h h r o T b t w


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Thermal Expansion in Three States of Matter 1.

2.

3.

What would happen to a bridge on a hot day if there were no thermal expansion joints?

Mercury is a common liquid used in thermometers. What must be true about the way mercury responds to heat energy to make it useful in thermometers?

What would happen in a thermometer if glass expanded more than mercury with each degree rise in temperature?

4.

Why are propane burners used to heat the gas in a hot air balloon just before takeoff?

5.

Why are weather balloons only partially filled with air when they are released from the ground?

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Mini Lab Worksheet

Wave Interaction With a coiled-spring toy, you can create pressure waves, as well as transverse waves of various amplitudes, speeds, and orientations. 1.

Design an experiment to test what happens when waves from different directions meet.

2.

Perform your experiment and record your observations.


Does the speed of either wave change?

4.

Do the waves bounce off each other, or do they pass through each other?




105

Date

Period

Name

CHAPTER

14 Materials

Physics Lab Worksheet Pendulum Vibrations

• paper clip

A pendulum can provide a simple model for the investigation of wave properties. In this experiment, you will design a procedure to use the pendulum to examine amplitude, period, and frequency of a wave. You also will determine the acceleration due to gravity from the period and length of the pendulum.

• ring stand with ring

Question

• stopwatch

How can a pendulum demonstrate the properties of waves?

• string (1.5 m) • three sinkers

Objectives ■ Determine what ■ Investigate

variables affect a pendulum’s period.

the frequency and period amplitude of a pendulum.

■ Measure g ,

the acceleration due to gravity, using the period and length of a pendulum.

Procedure 1. Design a pendulum using a ring stand, a string with a paper clip, and a sinker attached to the paper clip. Be sure to check with your teacher and have your design approved before you proceed with the lab.


2. For this investigation, the length of the pendulum is the length of the string. The amplitude is how far the bob is pulled from its equilibrium point. The frequency is the cycles per second of the bob. The period is the time for the bob to travel back and forth (one cycle). When collecting data for the period, find the time it takes to make ten cycles, and then calculate the period in seconds/cycles. When finding frequency, count how many cycles occur in 10 s, and then convert your value to cycles per second.



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continued

Data Table 1 This data table format can be used for steps 2–5. Trial 1

Trial 2

Trial 3

Average

Period

Frequency

(s/cycle)

(cycles/s)

Length 1 Length 2 Length 3 Mass 1 Mass 2 Mass 3 Amplitude 1 Amplitude 2 Amplitude 3

Data Table 2 This data table format can be used for steps 2–5. Trial 1

Trial 2

Trial 3

Average

Period

Length of

(s/cycle)

String (m)

Length 1 Length 2 Length 3

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continued

14

3. Design a procedure that keeps the mass of the bob and the amplitude constant, but varies the length. Determine the frequency and period of the pendulum. Record your results in the data table. Use several trials at several lengths to collect your data. 4. Design a procedure that keeps length and amplitude constant, but varies the mass of the bob. Determine the frequency and period of the pendulum. Record your results in the data table. Use several trials to collect your data. 5. Design a procedure that keeps length and mass of the bob constant, but varies the amplitude of the pendulum. Determine the frequency and period of the pendulum. Record your results in the data table. Use several trials to collect your data. 6. Design a procedure using the pendulum to calculate g , the acceleration due to gravity, using the equation T 2    / g . T is the period, and  is the length of the pendulum string. Remember to use several trials to collect your data. 

Analyze 1. Summarize What is the relationship between the pendulum’s amplitude and its period?


2. Summarize What is the relationship between the pendulum’s bob mass and its period?

3. Compare and Contrast How are the period and length of a pendulum related?

4. Analyze Calculate g from your data in step 6.

5. Error Analysis What is the percent error of your experimental g value? What are some possible reasons for the difference between your experimental value of g and the accepted value of g ?



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continued

Conclude and Apply Infer What variable(s) affects aff ects a pendulum’s period? 1. Infer What

bett er to run three or more trials to obtain the frequency fr equency and period perio d of each 2. Analyze Why is it better pendulum?

3. Compare How is the motion of a pendulum like that of a wave?

4. Analyze and Conclude When does the pendulum bob have the greatest kinetic energy?

po tential energy? 5. Analyze and Conclude When does the pendulum bob have the greatest potential

Going Further Suppose you had a very long pendulum. What other observations could be made, over the period of a day, of this pendulum’s motion?

Real-World Physics Pendulums are used to drive some types of clocks. Using the observations from your experiments, what design problems are there in using your pendulum as a time-keeping instrument?

To find out more about the behavior of waves, visit the Web site: physicspp.com

110

Chapters 11–15 Resources Resource s



Date

Period

Name

CHAPTER

14

Study Guide

Vibrations and Waves Vocabulary V ocabulary Review Write the term that correctly completes the statement. Use each term once.


amplitude

longitudinal wave

transverse wave

antinode

node

trough

crest

period

wave

frequency

periodic motion

wavelength

interference

refraction

1.

The time needed for an object ob ject to complete co mplete one full cycle of simple harmonic motion is the .

2.

occurs when more than one wave moves through the same medium at the same time.

3.

When waves are superposed, any point that does not experience displacement is a(n) .

4.

A disturbance that carries energy through matter or space is a(n) .

5.

A wave in which the disturbance is parallel p arallel to the direction of travel is a(n) .

6.

The maximum distance an object in simple harmonic motion moves from equilibrium is called the .

7.

The lowest point of a transverse tr ansverse wave is the

8.

The shortest distance between two points where the wave pattern repeats is the .

9.

Any motion that repeats in a regular cycle is called

.

.

10.

When two waves interfere constructively constru ctively,, the point with the greatest great est displacement is called the .

11.

A(n)

12.

The number of o f complete oscillations oscillatio ns a wave makes each second is the of the wave wave..

13.

14.


travels in a direction directio n perpendicular to its displacement.

refers to the change in direction waves experience at the boundary between two different media. The highest point po int of a transverse wave is the

.


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Section 14.1

continued

Periodic Motion

In your textbook, read about springs and simple harmonic motion on pages 375–378. Answer the following questions. Use complete sentences. 1.

According to Hooke’s law, describe a graph g raph of force f orce versus displacement for an elastic elast ic spring.

2.

What does the slope of the graph in question qu estion 1 represent?

3.

What does the area under the curve in the graph gr aph in question 1 represent?

4.

What are the conditions necessary for simple harmonic motion?

5.

What is the relationship between the potential energy and the displacement of an elastic spring?

6.

A mass on a spring is moving in simple harmonic motion. When is the mass’s acceleration the greatest? When is it the least? Why?

7.

Some cars have bumpers that are modified springs. How does this design protect the car in the event of a crash?

8.

How does the mass of the bob on a pendulum affect the pendulum’s period?

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14

In your textbook, read about pendulums and resonance on pages 378–380. For each statement below, write true or rewrite the italicized part to make the statement true. The swing of a pendulum is an example of simple harmonic motion.

9.

10.

The restoring force on a pendulum bob is inversely proportional to the bob’s displacement.

11.

The net force on a pendulum at any given moment is opposite the pendulum’s displacement at that moment.

12.

Resonance occurs when small forces are applied at regular intervals to an oscillating or vibrating object and the amplitude of the object’s oscillation decreases.

13.

In order to create resonance, the time interval between applications of force must be proportional to the period of oscillation.

14.

Pegs arranged in a circle on the floor beneath a swinging pendulum will get knocked down because the floor is rotating as Earth rotates.

Section 14.2 . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Wave Properties

In your textbook, read about mechanical waves and measuring waves on pages 381–386. Circle the letter of the choice that best completes the statement. 1.

2.

3.

4.

5.

A wave carries

through space.

a.

matter

c.

both matter and energy

b.

energy

d.

neither matter nor energy

A mechanical wave is different from other types of waves because it requires a(n) a.

amplitude

c.

medium

b.

wave pulse

d.

disturbance

.

A wave that moves from left to right, creating an up and down displacement of the medium, is a(n) . a.

matter wave

c.

longitudinal wave

b.

mechanical wave

d.

transverse wave

Sound waves are

waves.

a.

longitudinal

c.

surface

b.

transverse

d.

electromagnetic

A surface wave is a wave that has characteristics of

.

a.

a transverse wave

c.

both transverse and longitudinal waves

b.

a longitudinal wave

d.

neither transverse nor longitudinal waves



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continued

For each statement below, write true or rewrite the italicized part to make the statement true. Fluids usually transmit only transverse waves.

6.

7.

Waves that travel down a rope are longitudinal waves.

8.

Waves deep under water are longitudinal waves.

9.

Waves on the surface of the ocean are transverse waves. A wave’s amplitude depends on its speed.

10.

Answer the following questions. Use complete sentences. 11.

How does wave speed relate to wavelength and period?

12.

Why do some waves have greater amplitudes than others?

13.

What does it mean for points on a wave to be in phase? What does it mean for points on a wave to be out of phase?

14.

What is the relationship between the amplitude of a wave and the rate of energy transfer?

15.

114

For waves with a constant velocity, what happens to the wavelength if the frequency of the wave decreases?




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continued

Section 14.3

14

Wave Behavior

In your textbook, read about wave behavior on pages 387–391. For each statement below, write true or rewrite the italicized part to make the statement true. 1.

When a wave encounters a boundary, the wave that strikes the boundary is called the incident wave.

2.

When a wave encounters a boundary, the wave that returns to the original medium is call the refracted wave.

3.

When a wave from a light, flexible spring passes into a heavier, stiffer spring, almost all of the wave’s energy is reflected back to the light spring.

4.

When a wave is sent down a spring connected to a wall, none of the energy in the wave is reflected back.

5.

When interference produces standing waves in a rope, the rope appears to be standing still.

Answer the following questions. Use complete sentences. . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

6.

What happens when a wave moves across a boundary from one medium to another? Consider two springs, one large and one small, joined end-to-end. Describe the wave pulse moving from a large spring into a smaller one. Explain what happens to the energy in the incident wave.

7.

What is the principle of superposition?

8.

Draw a diagram of wave fronts and rays that represents refraction. Label the boundary. Use arrows to show the change in direction.



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In your textbook, read about waves in two dimensions on pages 390–391. Answer the following questions. Use complete sentences. 9.

What is a wave front?

10.

When is a wave refracted?

11.

A ray diagram shows the direction of wave motion. What is the normal? What does it show?

12.

What is the angle of incidence? What is the angle of reflection?

13.

What is the law of reflection?

14.

What causes an echo?

15.

16.

116


How is refraction partly responsible for the formation of rainbows?

What happens when a wave moves from deep to shallow water? How does the frequency change?



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Materials

Reinforcement Assembling a Wave Tape Procedure

• twelve drinking straws • masking tape • ruler

Work in pairs for easier assembly of a wave tape. Have your partner hold or secure a long piece of tape to the desk top. This bottom tape should be placed sticky side up. If you find it too difficult to work with long tape strips, the wave tape can be assembled in shorter sections and then pieced together. 1.

Choose a partner. Have one person hold a long piece of tape, sticky side up, while the other person places several straws on the tape, 7 cm apart. Make sure the straws are centered on the tape and at right angles to the tape.

2.

As shown in the figure, secure the straws by pressing a second piece of tape, sticky side down, on top of the first piece of tape. Top tape, sticky side down


7 cm

Bottom tape, sticky side up

3.

4.


Tape one end of the wave tape to the edge of a desktop so that the straws are parallel to the edge. Hold the other end of the tape so that the tape is taut and level. Have your partner tap one end of the straw that is farthest from the desk. Observe what happens. Repeat this several times. Keep the tape taut and your hand steady.


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continued

Results 1.

2.

3.

Is this a mechanical wave? Why or why not?

What kind of wave did you observe?

By what medium is wave energy transmitted or reflected in this experiment?

4.

What happened when the wave encountered the desk?

5.

Tap the straw more than once to produce multiple waves in the tape. What do you see?


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Enrichment

Earthquake Wave Velocities Earthquakes produce both longitudinal waves, known as P waves, and transverse waves, known as S waves. Geologists have used properties of these waves to predict the composition of Earth’s interior. They believe that Earth consists of three main zones: the crust, the mantle, and the core. They believe the core consists of a liquid outer core and a solid inner core. P waves and S waves travel through various rock materials at different velocities. S waves cannot pass through molten (liquid) rock. If Earth’s composition were that of a uniform solid, the velocities of P and S waves would increase steadily with depth, because increasing pressure beneath the surface increases the elastic properties of the rock, which in turn increases wave velocities. However, the interior rock composition is not uniform; it changes with depth, so earthquake wave velocity does not increase smoothly, as shown in the graph below. Wave velocity (km/s) 4 6 8 10 12

Crust Mantle

1000 . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

S wave

P wave

2000 )

m 3000 k (

Outer Core

P wave

4000

h t p e D

5000 Inner Core 1.

How fast do P waves move in the crust?

2.

How fast do S waves move in the crust?

3.

6000

What happens to S waves approximately 2900 km below Earth’s surface? Why?



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continued

4.

Using only data on P waves, how could you determine the depth of the boundary between the mantle and the outer core?

5.

How does P-wave speed indicate that the inner core is composed of solid rock?

6.

S waves can travel through solid rock, and the inner core is solid. Why then are no S waves found in the inner core?

7.

124

Which is likely to be a more distinct transition—from the mantle to the outer core or from the outer core to the inner core? Why?




CHAPTER

14

Transparency 14-1

Transverse Waves

B

G D

A

C

F

H

E . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

B,G

Crests — the maximum upward displacement of a wave.

E

Trough — the maximum downward displacement of a wave.

D

E

↔

A F or B G ↔

↔

Amplitude — the distance from the midpoint to the crest (or trough) of a wave. Wavelength — the distance between any two points that are in phase on a wave.



125

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Transverse Waves 1.

2.

3.

Explain the relationship between the distance from the midline to the crests of the wave and the distance from the midline to the troughs of the wave. Assume that the midline is defined as zero, up is defined as the positive direction, and down is defined as the negative direction.

What determines the distance from D to E?

Describe the relationship between the amplitude of a wave and the rate at which the wave transfers energy to it surroundings. Be specific.

4.

Which of the values changes when the wave crosses from one medium to another?

5.

An antenna of what length would best receive this wave? State the length using points A–H.

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Transparency 14-2

Wave Properties

Crest . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Amplitude R e st p os i t i on

Transverse Wave

Trough Amplitude

W a v e l e ng t h

W a v e l e ng t h Rarefaction Longitudinal Wave

Compression Physics: Principles and Problems


127

Date

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Name


Wave Properties 1.

Which parts of a longitudinal wave correspond to the troughs and crests of a transverse wave?

2.

Assuming that the waves pictured are moving at the same speed, what is the relationship of their frequencies?

3.

What is the relationship between the direction a wavelength is measured and the direction the amplitude is measured for each wave pictured?

4.

5.

128


Give an example of a longitudinal wave and a transverse wave.

As pictured, are these waves in phase or out of phase? Why?



CHAPTER

14

Transparency 14-3

Harmonics in Guitar Strings


E B G D A E

1st harmonic

E B G D A E

2nd harmonic

E B G D A E

E B G D A E


3rd harmonic

4th harmonic


129

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Harmonics in Guitar Strings 1.

What type of wave pattern is demonstrated by the guitar strings shown?

2.

What part of the wave is the finger pointing to in each figure?

3.

What is the relationship between the number of nodes on the wave pattern and the harmonic number?

4.

What is the relationship between the number of nodes and the frequency of the wave?

5.

What is the relationship between the number of nodes and the wavelength of the wave?

6.

What is the relationship between the harmonic number and the frequency of the wave?

7.

What is the relationship between the harmonic number and the wavelength of the wave?

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Mini Lab Worksheet

Sounds Good Sometimes it can be pretty tough to tell just by looking whether an instrument will act as an open-pipe resonator or as a closed-pipe resonator. Ask a musician who plays a wind instrument to bring it to class. 1. Measure 2.

the length of the instrument.

Have the musician play the lowest possible note on the instrument.

3. Determine

the frequency of the note using a frequency generator.



Did the tested instrument behave most like a closed-pipe resonator or most like an open-pipe resonator? Was the frequency the fundamental or one of the subsequent harmonics?

Draw Conclusions

the frequencies of the notes that would form an octave, a perfect fifth, a perfect fourth, and a major third with your observed note.

5. Determine



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Materials

■

Immediately wipe up any spilled liquids.

■

Glass is fragile. Handle with care.

• three tuning forks of known frequencies • graduated cylinder (1000-mL) • water

Speed of Sound If a vibrating tuning fork is held above a closed pipe of the proper length, the air in the pipe will vibrate at the same frequency, f , as the tuning fork. By placing a glass tube in a large, water-filled graduated cylinder, the length of the glass tube can be changed by raising or lowering it in the water. The shortest column of air that will resonate occurs when the tube is one-fourth of a wavelength long. This resonance will produce the loudest sound, and the wavelength at this resonance is described by   4L, where L is the length from the water to the open end of the pipe. In this lab, you will determine L, calculate , and calculate the speed of sound.

Question

• tuning fork mallet

How can you use a closed-pipe resonator to determine the speed of sound?

• metric ruler

Objectives

• thermometer (non-mercury) . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C


• glass tube (approximately 40 cm in length and 3.5 cm in diameter)

■

Collect and organize data to obtain resonant points in a closed pipe.

■

Measure the length of a closed-pipe resonator.

■ Analyze


the data to determine the speed of sound.


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continued

Data Table 1 Trial

Temperature (°C)

Accepted Speed of Sound (m/s)

Experimental Speed of Sound (m/s)

1 2 3

Data Table 2 Trial

Tuning Fork Frequency (Hz)

Diameter (m)

Length of Tube Above Water (m)

Calculated Wavelength (m)

1 2 3

Data Table 3 Trial

Tuning Fork Frequency (Hz)

Accepted Speed of Sound (m/s)

Corrected Calculated Wavelength (m)

Corrected Experimental Speed of Sound (m/s)

1 2 3

Procedure 1. Put on your safety goggles. Fill the graduated cylinder nearly to the top with water. 2. Measure the room air temperature and record it in Data Table 1. 3. Select a tuning fork and record its frequency in Data Tables 2 and 3. 4. Measure and record the diameter of the glass tube in Data Table 2. 5. Carefully place the glass tube into the water-filled graduated cylinder. 6. Hold the tuning fork by the base. Swiftly strike it on the side with the tuning fork mallet. Do not strike the tuning fork on the laboratory table or other hard surface.

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7. Hold the vibrating fork over the open end of the glass tube and slowly raise the tube and the fork until the loudest sound is heard. Once this point is located, move the tube up and down slightly to determine the exact point of resonance. Measure the distance from the water to the top of the glass tube and record this distance in Data Table 2. 8. Repeat steps 3, 6, and 7 for two additional tuning forks and record your results as trials 2 and 3. The three tuning forks that you test should resonate at three different frequencies. 9. Empty the water from the graduated cylinder.

Analyze 1. Calculate the accepted speed of sound using the relationship v  331 m/s  0.60 T , where v is the speed of sound at temperature T , and T is the air temperature in degrees Celsius. Record this as the accepted speed of sound in Data Tables 1 and 3 for all the trials.

2. Since the first resonant point is located when the tube is one-fourth of a wavelength above the water, use the measured length of the tube to determine the calculated wavelength for each trial. Record the calculated wavelengths in Data Table 2.


3. Multiply the values in Data Table 2 of wavelength and frequency to determine the experimental speed of sound and record this in Data Table 1 for each of the trials.

4. Error Analysis For each trial in Data Table 1, determine the relative error between the experimental and accepted speed of sound.

Relative error 

| Accepted value Experimental value|  Accepted value 



100%

5. Critique To improve the accuracy of your calculations, the tube diameter must be taken into consideration. The following relationship provides a more accurate calculation of wavelength:   4(L  0.4d), where  is the wavelength, L is the length of the tube above the water, and d is the inside diameter of the tube. Using the values in Data Table 1 for length and diameter, recalculate  and record it in Data Table 3 as the corrected wavelength. Calculate the corrected experimental speed of sound by multiplying the tuning fork frequency and corrected wavelength and record the new value for the corrected experimental speed of sound in Data Table 3.

6. Error Analysis For each trial in Data Table 3, determine the relative error between the corrected experimental speed and the accepted speed of sound. Use the same formula that you used in step 4, above.



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Conclude and Apply 1. Infer In general, the first resonant point occurs when the tube length two lengths where resonance will occur?

/4. What are the next

 

2. Think Critically If you had a longer tube, would it be possible to locate another position where resonance occurs? Explain your answer.

Going Further 1. Which result produced the more accurate speed of sound?

2. How is the revised calculation consistent with the nature of science?

Real-World Physics Explain the relationship between the size of organ pipes and their resonant frequencies.

To find out more about the properties of sound waves, visit the Web site: physicspp.com

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Sound Vocabulary Review Write the term that corresponds to the description. Use each term once. beat

Doppler effect

open-pipe resonator

closed-pipe resonator

fundamental

pitch

consonance

harmonics

sound level

decibel

loudness

sound wave

dissonance


1.

the lowest resonant frequency

2.

a pressure variation transmitted through matter as a longitudinal wave

3.

the logarithmic scale that measures the amplitudes of sounds that humans can hear

4.

the unit of measurement for sound level

5.

depends on the frequency of a sound wave

6.

the change in frequency caused by a moving source or a moving detector

7.

the oscillation of wave amplitude heard when two frequencies are nearly identical

8.

a pleasant combination of pitches

9.

a factor perceived by the ear that depends primarily on the amplitude of the wave the observer hears

10.

a resonating tube with both ends open

11.

a resonating tube with one end closed to air

12.

multiples of the fundamental frequency

13.

an unpleasant combination of pitches



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Section 15.1

continued

Properties and Detection of Sound

In your textbook, read about properties and detection of sound on pages 403–410. Write the term that correctly completes the statement. You will not use every term. 334 m/s

echoes

longitudinal

solid

velocities

343 m/s

frequency

oscillation

temperature

volume

amplify

greater

pressure

transverse

wavelength

distance

interfere

slower

vacuum

Sound waves move in the same direction as the particles of the medium and are therefore (1)

waves. The waves are caused by variations in

(2)

relating to the different (3)

of the

atoms or molecules. Therefore, sound cannot travel through a(n) (4) The (5) second. The (6)

.

of a sound wave is the number of pressure oscillations per is the distance between successive regions of

high or low pressure. At 20°C, the sound moves through air at sea level at a speed of . In general, the speed of sound is (8)

(7)

in liquids and solids than in gases. Reflected sound waves are (9) reflection of sound waves can be used to find the (10)

. The between a source

and a reflecting surface. Answer the following questions. Show your calculations. 11. If a sound wave produced by a speaker is at room temperature and has a wavelength of 1.85 m,

what is the frequency of the sound that is generated?

12. How long is a wave that has a frequency of 2.70 102 Hz and is moving through copper at

3560 m/s?

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15

13. The speed of sound at room temperature (20°C) is 343 m/s. If the speed of sound in air increases

about 0.60 m/s for every 1°C increase, what is the temperature when the speed of sound is 353 m/s?

14. A car horn has a frequency of 448 Hz when the car is stationary. If the car approaches a stationary

recorder at a speed of 19.0 m/s, what frequency does the device record if the temperature is 20°C? What frequency does the device record after the car passes by?

15. If the recorder in question 15 were moving toward the stationary car at 42 m/s, what frequency

would it record?

16. How much greater is the sound pressure level of a 100-dB siren than an 80-dB alarm clock? How

much louder would most people perceive the siren to be? . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Section 15.2

The Physics of Music

In your textbook, read about the physics of music on pages 411–419. Circle the letter of the choice that best completes the statement or answers the question. 1. Sound is produced when there are

.

a. increases in pressure

c. increases in temperature

b. oscillations in pressure

d. electromagnetic waves

2. The frequencies of vibrating air set into resonance are determined by the a. radius

c. mass

b. length

d. width

3. Resonance occurs when

.

a. any constructive interference occurs

c. a standing wave is created

b. any destructive interference occurs

d. no nodes are formed

4. The pressure of a reflected wave is inverted

resonators.

a. only in closed-pipe

c. in both open- and closed-pipe

b. only in open-pipe

d. in neither open- nor closed-pipe


of the air column.


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Study Guide

continued

5. In a standing sound wave in a pipe, nodes are regions of

.

a. maximum or minimum pressure and low displacement b. maximum or minimum pressure and high displacement c. mean atmospheric pressure and low displacement d. mean atmospheric pressure and high displacement 6. In a standing sound wave in a pipe, two antinodes are separated by a. one-quarter wavelength

c. one-half wavelength

b. one wavelength

d. two wavelengths

.

For each statement below, write true or rewrite the italicized part to make the statement true. 7.

An open pipe can only have resonance if it has antinodes at both ends.

8.

In a closed pipe, a column of length  /4 is in resonance with a tuning fork.

9.

An open pipe can only have resonance if it has nodes at both ends.

10.

In an open pipe, a column of length 3  /4 is in resonance with a tuning fork.

11.

For both open and closed pipes, resonance lengths are spaced at half -wavelength intervals.

12.

A string resonates only when there are nodes at both ends of the string.

13.

The resonant frequencies of a string are whole-number multiples of the second harmonic.

14.

The standing waves in a string occur when the string length is a whole-number multiple of quarter wavelengths.

Refer to the accompanying figures to answer questions 15–17. 15. In the three open tubes below, draw standing waves that show the fundamental, second harmonic

( f 2  2 f 1), and third harmonic ( f 3  3 f 1). Under each tube, indicate the wavelength of the standing wave in terms of L.

L

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L

L



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15

16. In the three closed tubes below, draw standing waves that show the fundamental, third harmonic

( f 3  3 f 1), and fifth harmonic ( f 5  5 f 1). Under each tube, indicate the wavelength of the standing wave in terms of L.

L

L

L

17. In the pressure and displacement graphs below, fill in the types of nodes and antinodes in the

spaces provided. . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Closed Pipe

a.

c.

b.

d. Air Pressure

Displacement of Air

Open Pipe

e.

g.

f.

h. Air Pressure


Displacement of Air


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18. A particular note played on a cello has a frequency of 240 Hz. What is the frequency of the third

harmonic of that pitch?

19. While tuning her guitar, a guitarist compares the pitch one string produces to the pitch produced

by a string on another guitar. If the second guitar plays a note with a frequency of 330.0 Hz and the first guitar plays a note with a frequency of 335.0 Hz, what is the beat frequency produced?

20. The two guitars in Question 19 are playing so that the beat frequency between them is 3 Hz. If one

of them is playing a frequency of 348 Hz, what are the possible frequencies the other instrument is playing?

21. A musical instrument produces a beat frequency of 3 beats per second with another sound source

that produces a frequency of 8.80102 Hz. What are the possible wavelengths if the sounds are generated at 20°C?

22. When a tuning fork with a frequency of 440 Hz is used with a resonator, the loudest sound pro-

duced occurs when the length of the closed-pipe tube is 20.5 cm and 58.5 cm. a. Resonance occurs at intervals of one-half wavelength. What is the value of the wavelength? b. What is the speed of sound in this case? c. What is the approximate temperature, assuming the measurements are made at sea level?

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Materials

• tissue box • rubber bands • index card • tape or glue

Reinforcement Making a Guitar A guitar is a musical instrument that allows you to vary the length of the strings to produce waves of different frequencies. By pushing down on different points on the strings, you can create combinations of these frequencies that are pleasant to hear.

Procedure You can construct a simple guitar like the one shown using an empty rectangular tissue box, rubber bands, and an index card. folded index card tissue box

rubber band


1.

Fold the index card in thirds lengthwise, and fold the index card into a triangle (like a prism).

2.

Tape or glue the index card along one end of the box to make the bridge of the guitar.

3.

Stretch the rubber bands around the box so that they cross the index card perpendicularly.

Try stretching the rubber bands to different tensions or using rubber bands of different sizes to create different pitches.

Results 1.


What happens to the frequency of the pitch as you increase the tension in the rubber band? Why?


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Reinforcement

continued

2.

What happens to the frequency of the pitch if you push down on the rubber band halfway between the bridge and the other end of the box and pluck the rubber band? Why?

3.

What kind of wave is producing the sounds you hear?

4.

5.

154

How does the pitch of a rubber band with a smaller diameter compare to the pitch generated by one of a larger diameter? Experiment and see what factors change the pitch.

Try using objects other than a tissue box to make a guitar. Try using hollow and solid objects. Describe how different materials change the sounds that the rubber bands produce.




Date

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Enrichment

Some musical instruments, such as guitars and violins, produce sound by way of vibrating strings. The vibration that produces the sound can be represented by standing waves, such as the ones shown in the figures below. Figure A represents the fundamental frequency, and Figures B through F represent harmonics of that frequency.

A

B

C

D . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

E

F

1.

How are the number of nodes and antinodes related?

2.

How does the frequency of the wave in Figure C compare to the frequency of the wave in Figure A?

3.

In each figure, how many wavelengths appear?



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Enrichment

continued

4.

Is there a simple relationship between the number of wavelengths in each figure and the number of antinodes in each figure? If so, what is it?

5.

Is there a simple relationship between the number of wavelengths in each figure and the number of nodes? If so, what is it?

6.

If the frequency in Figure A is 220 Hz, what is the frequency of the string in Figure D?

7.

If the frequency in Figure C is 344 Hz, what is the frequency of the string in Figure E?

8.

If the length of all of the strings is 4.25 m, and the frequency of Figure B is 228 Hz, then what is the velocity of the wave in Figure C?

9.

If the velocity of the string in Figure F is 675 m/s, and the length of all of the strings is 1.85 m, then what is the frequency of the string in Figure D?

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CHAPTER

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Transparency 15-1

Decibel Scale

Sound Levels

110 dB Painful 100 dB Very noisy Rock concert . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Passing siren

70 dB Noisy

50 dB Moderate Inside car

Average classroom 30 dB Quiet

10 dB Barely audible

Quiet room


Soft whisper


157

Date

Period

15

Name


Decibel Scale 1.

What is the typical sound level of a fire engine siren? State your answer in decibels.

2.

Rustling leaves have a sound level of about 20 dB. Between which two pictured items does this fall on the scale?

3.

Loud talking has a sound level of about 60 dB. Between which two items does this fall on the scale?

4.

According to the scale, which is louder: a rock concert or a passing siren?

5.

According to the scale, what is quieter than reading in a quiet room?

6.

Which item on the scale has a moderate sound level?

7.

Which item on the scale can be described as very noisy?

8.

The pain threshold for humans is about 110 dB. Which item on the scale might cause the average person discomfort?

9.

The most faintly heard sound has a pressure amplitude of 2105 N/m2, which corresponds to a sound level of 0 dB. Which item on the scale has less than ten times that pressure amplitude?

10.

158

What is the pressure amplitude of a passing siren?




CHAPTER

15

Transparency 15-2 r e v r e s A b O

A



s


t f i h S r e l p p o D

v

S

B



r e v r e s B b O Physics: Principles and Problems


159

Date

Period

15

Name


Doppler Shift 1.

What does S represent?

2.

What do the circles represent?

3.

What is moving in the diagram? In what direction is it moving? What is not moving?

4.

What is the effect of the motion on the wave velocity?

5.

What is the effect of the motion on the wavelength of the waves that reach observer A? On the wavelength of the waves that reach observer B?

6.

7.

What is the effect of the motion on the frequency of the waves that reach observer A? On the frequency of the waves that reach observer B? Explain this effect in terms of wave speed and wavelength.

How does the motion affect what observer A perceives? How does the motion affect what observer B perceives? Why does the motion affect the observers differently?

8.

What changes would observer A and observer B notice if the velocity of the source increased?

9.

What changes would observer A and observer B notice if the velocity of the source decreased?

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Transparency 15-3

Standing Waves in Pipes Closed Pipe Pressure node (average pressure region)

Displacement antinode

L


 

L

4

Pressure antinode (high- or low-pressure region)

 

4

Displacement node

Air Pressure

Displacement of Air

Open Pipe Pressure node (average pressure region)

Pressure antinode (high- or low-pressure region)


L

Pressure node (average pressure region)

Air Pressure


 

2

Displacement node

L

 

2


Displacement of Air


161

Date

Period

15

Name


Standing Waves in Pipes 1.

What is the pressure at the pressure nodes of a standing wave?

2.

What is the pressure at the pressure antinodes of a standing wave?

3.

What is the distance between two nodes in terms of wavelength?

4.

What happens when a pressure wave reaches the open end of an open pipe?

5.

6.

Compare closed-pipe and open-pipe resonators in terms of the positions of pressure nodes and pressure antinodes.

Compare closed-pipe and open-pipe resonators in terms of the positions of displacement nodes and antinodes.

7.

What are the first four resonance lengths for a closed pipe?

8.

What are the first four resonance lengths for an open pipe?

9.

10.

162

How does the spacing of the resonances compare in open- and closed-pipe resonators?

If open pipes and closed pipes with identical lengths are used as resonators, how will the wavelengths of the resonant sounds compare? How will the frequencies compare?




CHAPTER

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Transparency 15-4

Musical Instruments

Violin The violinist uses a bow to force the strings to vibrate. Placing his or her fingers at different positions on the strings changes the length of the strings. . c n I , s e i n a p m o C l l i H w a r G c M e h T f o n o i s i v i d a , l l i H w a r G c M / e o c n e l G © t h g i r y p o C

Harp Strings of different lengths produce different pitches when plucked.

French Horn The player's lips vibrate, making the air column resonate. Pressing the keys changes the length of the air column.

Clarinet The vibrating reed creates resonance in the air column. Pressing the keys changes the length of the air column.



163

Date

Period

15

Name


Musical Instruments 1.

How is sound produced in general?

2.

Why does a violinist change the length of the violin strings?

3.

What actually produces the sound in most stringed instruments?

4.

Does a harpist need to change the length of the strings to produce different pitches? Explain your answer.

5.

How are many stringed instruments tuned? Why?

6.

What happens if you blow into the mouthpiece of a clarinet or a French horn when it is removed from the instrument?

7.

What produces the musical notes in a clarinet or a French horn?

8.

What happens when the player of a clarinet or a French horn changes the length of the air column by pressing the keys?

164




CHAPTER

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Transparency 15-5

y r o t i e d v r u e A n


r a E n a m u H e h T

s e p a t S s u c n I s u e l l a M

y r o t i l d a u n a A c


a e l h c o C

e n a r b m e m ) c i n m a u r p d r m a y e T (


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