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ACTIVITY BASED PHYSICS

SHM, WAVES, THERMODYNAMICS AND E & M PRACTICE PROBLEM SETS

SOUTHINGTON HIGH SCHOOL

CCP PHYSICS

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SHM, WAVES, THERMODYNAMICS AND E & M

PRACTICE PROBLEM SET TABLE OF CONTENTS

UNIT 7 SHM, WAVES AND SOUND ...................................................................................... 1 7.1 Simple Harmonic Motion .......................................................................................................... 1 7.2 Sound......................................................................................................................................... 4 7.3 Doppler Effect ........................................................................................................................... 5 7.4 SHM & Sound Review ............................................................................................................... 6

UNIT 8 OPTICS ................................................................................................................. 13 8.1 Reflection and Mirrors ............................................................................................................ 13 8.2 Refraction and Lenses ............................................................................................................. 19 8.3 Optics General Review ........................................................................................................... 23 8.4 Practice Ray Diagrams ........................................................................................................... 25

UNIT 9 THERMODYNAMICS ............................................................................................... 27 9.1 Temperature and Heat ............................................................................................................ 27 9.2 Humidity .................................................................................... Error! Bookmark not defined. 9.3 Heat Engines ........................................................................................................................... 32 9.4 General Thermodynamics Review .......................................................................................... 33

UNIT 10 CHARGE, FIELDS, CURRENT POTENTIAL AND DC CIRCUITS ............................. 35 10.1 Coulomb’s Law ..................................................................................................................... 35 10.2 Equivalent Resistance and Circuit Analysis ......................................................................... 38 10.3 Electricity Review ................................................................................................................. 40

UNIT 11 MAGNETISM ..................................................................................................... 42 11.1 Magnetism ............................................................................................................................. 42

MECHANICS PRACTICE PROBLEM SETS 1

Gamzon & Gregorian-Michaelsen 6/7/16

Unit 7 SHM, WAVES AND SOUND

7.1 SIMPLE HARMONIC MOTION

7.1.1 Mass-Spring Systems

1. An ultrasonic transducer used for medical diagnosis oscillates with a frequency of 6.7 x 106 Hz. How much time does each oscillation take and what is the angular frequency? Answer: T=1.5 x 10-7 s;

ω=4.21 x 107rad/s 2. A body of unknown mass is attached to an ideal spring that is mounted horizontally

with its left end held stationary. The spring constant of the spring is 120 N/m and it vibrates with a frequency of 6.00 Hz. Assuming that there is no friction, find:

a. The Period Answer: 0.17 sec b. The Angular Frequency Answer: 37.7 rad/s c. The Mass of the body Answer: 0.084 kg

3. A spring stretches 0.200 m when a 0.600 kg mass is hung from it. The spring is then

stretched 0.150 m from this equilibrium point and released. Find: a. The spring constant (k) Answer: 29.4 N/m b. The amplitude Answer: 0.150 m c. The total energy of the system. Answer: 0.33 J d. Maximum velocity (vo) Answer: 1.05 m/s e. The velocity when the mass is 0.050 m from equilibrium. Answer: .99 m/s f. The equation for the position of the mass x (t) Answer: x (t) = 0.150cos(7t)

4. A proud deep-sea fisherman hangs a 65.0 kg fish from an ideal spring with a negligible mass. The fish stretches the spring 0.120m. What is the period of oscillation of the fish if it is pulled down and released? Answer: 0.70 sec

5. A 0.150 kg toy is undergoing simple harmonic motion on the end of a horizontal

spring with a spring constant of 300 N/m. When the object is 0.12m from equilibrium, it has a speed of 0.300 m/s. Find:

a. The Total energy of the system Answer: 2.17 J b. The Velocity of the object at equilibrium Answer: 5.4 m/s c. The Amplitude of the motion. Answer: 0.120 m

7.1.2 Simple Pendulum

1. What is the period of a pendulum at sea level with a length of 1.5 m? Answer: 2.45 sec

a. What would the period of this pendulum be if the length were shortened to a ¼ of the original length? Answer: 1.23 sec



2. How long would a pendulum have to be if it has a frequency of 2 Hz? Answer: 0.062 m 3. A simple pendulum with a bob mass of 0.5 kg and a string length of 1.0 m and is

taken to the moon, which has an acceleration due to gravity that is 1/6 that of the acceleration due to gravity on Earth. If you want to maintain the same period on Moon that you have on Earth, what adjustment will you have to make to the…

a. Mass of the pendulum bob? Answer: None b. Length of the string? Answer: Shorten to 0.166 m

7.1.3 SHM Review Problems

1. (G1) When a 65-kg person climbs into a 1000-kg car, the car’s springs compress vertically by 2.8 cm. What will be the frequency of vibration when the car hits a bump? Ignore damping. Answer: 0.74 Hz

2. (G7) A balsa wood block of mass 50 g floats on a lake, bobbing up and down at a frequency of 2.5 Hz.

a. What is the value of the effective spring constant of the water? Answer: 12 N/m

b. A partially filled water bottle of mass 0.25 kg and almost the same size and shape of the balsa block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM. Answer: 1.1 Hz

3. (G9) A 0.50-kg mass at the end of a spring vibrates 3.0 times per second with an

amplitude of 0.15 m. Determine: a. The velocity when it passes the equilibrium point. Answer: 2.8 m/s b. The velocity when it is 0.10 m from equilibrium. Answer: 2.1 m/s c. The total energy of the system. Answer: 2.0 J d. The equation describing the motion of the mass. Assume φ = 0.

Answer: (0.15 m) cos [2π(3.0 Hz)t]

4. (G13) It takes a force of 80.0 N to compress the spring of a toy popgun 0.200 m to “load” a 0.150-kg ball. With what speed will the ball leave the gun? Answer: 10.3 m/s

5. (G15) A mass sitting on a horizontal, frictionless surface is attached to one end of a

spring; the other end of the spring is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 15 m/s2. Find the value of:

a. The spring constant. Answer: 4.2 x 102 N/m b. The mass. Answer: 3.3 kg

6. (G17) A 0.50-kg mass vibrates according to the equation x=0.45cos(8.40t), where x is

in meters and t is in seconds. Determine: a. The amplitude. Answer: 0.45 m



b. The frequency. Answer: 1.34 Hz c. The total energy. Answer: 3.6 J d. The kinetic energy and potential energy when x = 0.30 m.

Answer: KE=2.0 J; PE=1.6 J 7. (G21) A 25.0-g bullet strikes a 0.600-kg block attached to a fixed horizontal spring

whose spring constant is 6.70 x 103 N/m and sets it into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the two objects move together after impact? Answer: 557 m/s

8. (G29) You want to build a grandfather clock with a pendulum (a weight on the end of a light cable) that has one second between its “tick” (swinging to) and its “tock” (swinging fro). How long do you make the cable? Answer: 0.993 m

9. (G30) What is the period of a simple pendulum 50 cm long on Earth?

Answer: 0.61 m 10. (G31) The length of a simple pendulum is 0.66 m, the pendulum bob has a mass of

310 grams, and it is released at an angle of 12° to the vertical.

a. With what frequency does it vibrate? Assume SHM. Answer: 0.61 Hz b. What is the pendulum bob’s speed when it passes through the lowest point of

the swing? Answer: 0.53 m/s c. What is the total energy stored in this oscillation, assuming no loses?

Answer: 0.044 J



7.2 SOUND

Unless stated otherwise, assume that T = 20°C. 1. Find the frequency of a sound wave moving in air at a temperature of 22°C with a

wavelength of 0.667 m. Answer: f = 516 Hz 2. You hear the sound of the firing of a distant cannon 6.0 seconds after seeing the flash.

How far are you from the cannon? Answer: d = 2.1 km 3. A sound wave with a frequency of 9800 Hz travels along a copper pipe. If the

wavelength is 0.370 m and the density of copper is 8.9 x 103 kg/m3, what is the elastic modulus of copper? Answer: E= 1.2 x 1011 N/m2

4. A certain instant camera determines the distance to the subject by sending out a sound

wave and measuring the time needed for the echo to return to the camera. How long will it take the sound wave to return to the camera if the subject were 3.00 m away?

Answer: t = 0.017 s 5. If you drop a stone into a mineshaft that is 122.5 m deep, how soon after you drop the

stone do you hear it hit the bottom of the shaft? The temperature in the mineshaft is 10°C.

Answer: t = 5.36 s 6. With what tension must a rope of length 2.50 m and mass of 0.120 kg be stretched for

transverse waves of frequency of 40.0 Hz to have a wavelength of 0.750 m? Answer: T= 43.2 N 7. A ship uses a sonar system to detect underwater objects in the ocean. The system

emits underwater sound waves and measures the time interval for the reflected wave to return to the detector.

a. Determine the speed of sound in seawater if the bulk modulus is 2.2 x 109

N/m2. Answer: v= 1465 m/s b. The ship is on the continental shelf when it emits a sound wave. It takes the

echo 0.203 seconds to be picked up by the detector. What is the depth of the ocean on the continental shelf? Answer: depth = 150 m.

8. A tuning fork of frequency 262 Hz is sounded at the same time as another tuning fork

with a frequency of 257 Hz. What is the beat frequency that is heard? Answer: fb = 5 Hz 9. A tuning fork with a frequency of 432 Hz is sounded at the same time as a guitar. If 6

beats are heard in 3 seconds, what are the possible frequencies of the guitar string? Answer: f = 430 Hz or 434 Hz



7.3 DOPPLER EFFECT

1. On a cold wintry day, Bob is late for work. He drives at a speed of 15 m/s toward the factory where he works. The factory whistle is blown with a frequency of 800 Hz to indicate the start of the workday. If it is -4°C…

a. What is the frequency that Bob hears when the whistle is blown?

Answer: f’= 837 Hz

b. What is the frequency that Bob hears when he passes the building and moves away toward the parking lot behind the factory? Answer: f’= 763 Hz

2. While standing near a railroad crossing, a person hears a distant train horn. According

to the train’s engineer, the frequency of the horn is 262 Hz. If the train is traveling at 20.0 m/s toward the crossing and the speed of sound is 346 m/s…

a. What would the train horn’s wavelength be at rest? Answer: λ = 1.32 m b. By how much would the horn’s wavelength change as a result of the train’s

motion? Answer: Δλ = 0.075 m 3. An ambulance with a siren emitting a whine at 1300 Hz races by a car that was pulled

off to the side of the road. After being passed, the driver of the park car hears a frequency of 1220 Hz. How fast was the ambulance moving?

Answer: vs = 22.5 m/s 4. In 1845, French Scientist B. Ballot first tested the Doppler shift. He had a trumpet

player sound an A, 440 Hz, while riding on a flatcar pulled by a locomotive. At the same time, a stationary trumpeter played the same note. If the locomotive was moving toward Ballot at a speed of 5.0 m/s, what beat frequency would Ballot have heard?

Answer: fb = 6.5 Hz



7.4 SHM & SOUND REVIEW

7.4.1 Sound

1. (G11.35) A sound wave in air has a frequency of 262 Hz and travels at a speed of 330 m/s. How far apart are the wave crests (compressions)? Answer: 1.26 m

2. (G11.37) Calculate the speed of longitudinal waves in: a. Water Answer: 1.4 x 103 m/s b. Granite Answer: 4.1 x 103 m/s c. Steel Answer: 5.1 x 103 m/s

3. (G11.39) A cord of mass 0.55 kg is stretched between two supports 30 m apart. If the

tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other? Answer: 0.33 sec

4. (G11.41) A sailor strikes the side of his ship just below the surface of the sea. He

hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this point? Answer: 2.3 km

5. (G12.1) A hiker determines the length of a lake by listening for the echo of her shout

reflected by the cliff at the far end of the lake. She hears the echo 1.5 s after shouting. Estimate the length of the lake. Answer: 2.6 x 102 m

6. (G12.5) A person sees a heavy stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.4 sec apart. How far away did the impact occur? Answer: 5.4 x 102 m

7. (G12.6) A fishing boat is drifting just above a school of tuna on a foggy day. Without

warning, an engine backfire occurs on another boat 1.0 km away. How much time elapses between the instant when the backfire is heard…

a. by the fish? Answer: 0.69 sec b. by the fishermen? Answer: 2.9 sec

8. (G12.7) The sound from a very high burst of fireworks takes 4.5 s to arrive at your

eardrums. The burst occurred 1500 m above you and traveled vertically through two stratified layers of air, the top one at 0°C and the bottom one at 20°C. How thick is each layer of air? Answer: 1200 m, 300 m

9. (G12.43) What will be the “beat frequency” if middle C (262 Hz) and C# (277 Hz)

are played together? Answer: 15 Hz a. What if each was played two octaves lower (each frequency reduced by a

factor of 4) Answer: 3.8 Hz



10. (G12.51) The predominant frequency of a certain police car’s siren is 1800 Hz when at rest. What frequency do you detect if you move with a speed of 30.0 m/s…

a. Toward the car Answer: 1950 Hz b. Away from the car Answer: 1640 Hz

11. (G12.53) In one of the original Doppler experiments, one tuba was played on a

moving platform car at a frequency of 75 Hz, and a second identical one was played on the same tone while at rest in the railway station. What beat frequency was heard if the train approached the station at a speed of 10.0 m/s? Answer: 2 Hz

12. (G12.78) The frequency of a steam train whistle as it approaches you is 522 Hz. After

it passes you, its frequency is measured as 486 Hz. How fast was the train moving? Assume constant velocity. Answer: 12.3 m/s

13. (G12.71) A tight guitar string has a frequency of 600 Hz as its third harmonic. What

will be its fundamental frequency if it is fingered at a length of only 60% of its original length? Answer: 333 Hz

14. (G12.73) The string of a violin is 32 cm long between fixed points with a

fundamental frequency of 440 Hz and a linear density of 5.5 x 10-4 kg/m. a. What are the speed and tension in the string? Answer: 2.8 x 102 m/s, 44 N b. What is the frequency of the first overtone? Answer: 880 Hz

Material Bulk Modulus Water 2.0 x 109 N/m2 Mercury 2.5 x 109 N/m2 Alcohol (ethyl) 1.0 x 109 N/m2 Air 1.01 x 105 N/m2

Material Elastic Modulus

Iron, cast 100 x 109 N/m2

Steel 200 x 109 N/m2 Brass 100 x 109 N/m2 Aluminum 70 x 109 N/m2 Concrete 20 x 109 N/m2 Brick 14 x 109 N/m2 Marble 50 x 109 N/m2 Granite 45 x 109 N/m2 Wood (pine) Parallel to Grain 10 x 109 N/m2 Perpendicular to Grain

1 x 109 N/m2

Nylon 5 x 109 N/m2 Bone (limb) 15 x 109 N/m2

Density of Substances



7.4.2 Mass-Spring System

1. When a family of four with a total mass of 200 kg gets into their 1200 kg car, the car’s springs compress 5 cm. What is the spring constant of the car’s springs assuming they act as one single spring? Answer: 39,200 N/m

2. Imagine that you videotape the motion of a mass attached to a spring and measure the

displacement x from the equilibrium position as a function of time t. When you plot position, velocity and acceleration as a function of time you get the following graphs.

3. When a 0.50 kg-object is attached to a vertically supported spring, it stretches 0.10 m. It is then pulled another 0.10 m from its new equilibrium position. Find the period, angular frequency, total energy, and displacement equation for this mass-spring system. Answer: T = 0.63 sec,

ω = 9.9 rad/s, ET= .25 J, x(t) = 0.10 cost (9.9t)

4. An object with mass m = 0.60 kg attached to a spring with k = 10 N/m vibrates back

and forth along a horizontal frictionless surface. If the amplitude of the motion is 0.050 m, what is the velocity of the object when it is 0.010 m from the equilibrium position? Answer: 0.20 m/s

a. Find the amplitude.

b. Find the period.

c. Find the angular frequency.

Answer: ω = 4 rad/s

d. Find the magnitude of the maximum velocity.

e. Find the magnitude of the maximum

acceleration.



7.4.3 Simple Pendulum

1. What length of string would be necessary to make a simple pendulum with a period of 10.0 s? Answer: 24.8 m

2. On a planet with an unknown value of g, the period of a 0.65 m long pendulum is 2.8

s. What is g for the planet? Answer: 3.27 m/s2 3. A pendulum bob of mass m attached to a string of length L vibrates back and forth

along a circular arc. (a) Draw a free-body diagram for the bob showing all the forces acting on it. (b) What is the frequency of its motion using the symbols provided and universal constants? (c) What is the total energy of the pendulum at its highest point using the symbols provided and universal constants?

7.4.4 General Problems

1. Given x(t) = 0.01 m cos(0.02π t - π/2). Find (a) the amplitude, (b) the period, (c) the frequency, and (d) the initial phase of the motion. Answer: xm = 0.01m,

T = 100 s, f = 0.01 Hz, φ = π/2 = equilibrium

2. A particle is executing simple harmonic motion. The displacement x as a function of

time t is shown in the figure below. Find (a) the period, (b) amplitude,(c) equation of motion, (d) maximum velocity and (e) maximum acceleration.

Answer: T = 4.00 s, xm = 10 cm x(t) = .10 m cos(1.57t) vmax = 0.16 m/s, amax = 0.25 m/s2

L

Answer: a. See notes for FBD

b. c. E = mg(L-LcosΘ)



3. A mass-less spring with spring constant k = 10.0 N/m is attached to an object of mass m = 0.300 kg. One third of the spring is cut off. What is the frequency of the oscillations when the "new" spring-mass is set into motion? Answer: f = 0.92 Hz

4. Figure 6 below is a plot of the potential energy of a mass-spring system. The total

mechanical energy ET of the system = 0.200 J. Find (a) the potential energy PE and (b) the kinetic energy KE at x = 0.025 m. Find (c) the spring constant k and (d) the speed of the particle when x = 0.025 given that the mass of the object m = 0.30 kg. Find (e) the amplitude of the motion and (f) the maximum velocity of the object.

Answer: PE = 0.050 J, KE = 0.15 J, k = 160 N/m, v = 1 m/s, xm = 0.0500 m, vmax = 1.15 m/s 5. The motion of a particle is given by x(t) = 4.0 cm cos(πt - π/6). Find the particle’s

velocity when x = 2.0 cm. Answer: v = -10.9 cm/s

6. A wave travels along a stretched rope. The wavelength is 2.0 m. The wave period is 0.1 s. What is the speed of this wave? Answer: 20 m/s

7. A wave has a frequency of 58 Hz and a speed of 31 m/s. What is the wavelength of this wave? Answer: 0.53 m

8. A clothesline with a mass of 0.750 kg is 3.00 meters long. How much tension do you

have to apply to produce the observed a wave speed of 12.0 m/s? Answer: 36 N 9. Determine the wavelength of a 6000-Hz sound wave traveling in Alcohol. Answer: 0.19 m 10. A sound wave produced by a clock chime is heard 501 meters away, 1.50 sec later.

a. What is the temperature of the air through which the sound travels? Answer: T = 5°C

b. How long would it take this sound to travel 501 meters away in freshwater?

Answer: t = 0.35 s 11. If you clap your hands and hear the echo from a distant wall 0.20 seconds later, how

far away is the wall? Answer: d = 34.3 m



12. Billy Bob Joe whistles at 441 Hz and Mary Jane whistles at 462 Hz. What beat

frequency does Mary Jane hear? Answer: fb = 21 Hz 13. A railroad train is traveling at 25.0 m/s in still air. The frequency of the note emitted

by the locomotive whistle is 400 Hz. a. What is the frequency heard by a stationary observer standing in front of the

locomotive? Answer: f’ = 431 Hz

b. What is the frequency heard by a stationary observer standing behind the locomotive? Answer: f’ = 373 Hz

c. The train comes to a full stop at the nearest station so that new passengers can

get onto the train. When it has come to rest, it blows its whistle at another train coming toward the station at 10 m/s. What frequency does a passenger sitting on the moving? Answer: f’ = 412 Hz

14. A train moving at a constant speed is passing a stationary observer on a platform. On one of the train cars, a flute player is continually playing a note known as concert A, which has a frequency of 440 Hz. After the flute has passed, the observer hears the sound as a G, which has a frequency of 392 Hz. What is the speed of the train? Answer: 42 m/s

15. A guitar string has a fundamental frequency of 256 Hz. What is the frequency of the

3rd harmonic? Answer: 768 Hz a. What would the length of the guitar string have to be to produce a transverse

wave in the string with a speed of 405 m/s at the fundamental frequency? Answer: 0.79 m

16. A string that is 2.00 meters long and has a mass of .0025 kg. a. If the fundamental frequency is 120 Hz, what are the frequencies of the first

four harmonics? Answer: 120 Hz, 240 Hz, 360 Hz, 480 Hz

b. What must the tension be for the string to vibrate at the 4th harmonic? Answer: 288 N 17. The speed of sound in a certain metal block is 3.00 x 103 m/s. The graph shows the

amplitude in meters of a wave traveling through the block versus time in milliseconds. What is the wavelength of this wave? Answer: 6 m



18. A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.400 m long and has a mass of 3.00 grams.

a. What is the frequency of its fundamental mode of vibration? Answer: 408 Hz

b. What is the number of the highest harmonic that could be heard by a person

who is capable of hearing frequencies up to 10,000 Hz? Answer: 24th harmonic



Unit 8 OPTICS

8.1 REFLECTION AND MIRRORS

8.1.1 Plane Mirrors

1. Draw the reflected light ray(s) and position of the observer’s eye where it can see the reflected ray.

2. A bulb is placed in front of a plane mirror. a. Use a ruler and a protractor to construct four rays that travel from the bulb

to the mirror and reflect. Include eyes at positions that could see the reflected rays.

b. Extend the reflected rays with dotted lines behind the mirror to locate the virtual image.

c. Measure and compare the image distance to the object distance.

3. The ray diagram below shows where Observer 1 sees the virtual image of the bulb. Show where, if at all, Observer 2 sees the virtual image.



4. The ray diagram below shows where Observer 1 sees the virtual image of the

bulb. Show where, if at all, Observer 2 sees the virtual image.

5. The ray diagram below shows where Observer 1 sees the virtual image of the bulb. Show where, if at all, Observer 2 sees the virtual image.

6. A top view of a mirror and an arrow is shown below.



a. Draw a ray diagram that shows how light from both ends of the arrow reach the observer.

b. Locate and sketch the image of the arrow.

7. How does the size of the smallest mirror you would need to see your entire body at one time compare to your height? Make a ray diagram to prove it. Mr. Eye-foot represents a simplified body.

8. Would the length of the mirror needed to see your entire body change if you moved farther away from the mirror? Draw a ray diagram to support your answer.



9. One of Cinderella’s stepsisters, who is 1.60 m tall, is looking at herself in a plane mirror when she spots one of the mice helping Cinderella at the very bottom of the mirror. If the mouse is 5.0 cm away from the wall where the mirror is hung, and the mirror’s edge is 60 cm from the floor, how far away is she from the mouse? Make sure to draw a ray diagram to help solve this problem!

Answer: 3.3 cm from the mouse

8.1.2 Spherical Mirrors

1. An action figure that is 8.0 cm tall is placed 23.0 cm in front of a convergent mirror with a focal length of 10.0 cm.

a. Draw a ray diagram for the image of the action figure.

b. What are the three characteristics of the image?

Answer: Inverted, M<1, Real

c. What is the image distance? Answer: 17.7 cm

d. What is the image height? Answer: -6.15 cm

2. If the 8.0 cm tall action figure from Question 1 is now placed 6.0 cm in front of a

divergent mirror with a radius of 24.0 cm.

a. Draw a ray diagram for the image of the action figure.

b. What are the three characteristics of the image?

Answer: Upright, M<1, Virtual

c. What is the image distance? Answer: -4.0 cm

d. What is the image height? Answer: 5.3 cm

3. The focal point of a divergent mirror is 20.0 cm behind the mirror. An object is

placed 12 cm from the mirror.

a. Draw a ray diagram for the image of the object.

b. What is the image distance? Answer: -7.5 cm

c. What is the magnification of the image? Answer: M = 0.625 x

4. A magnified, inverted image is located a distance of 32.0 cm from a spherical

mirror with a focal length of 12.0 cm.

a. Is it a convergent or divergent mirror? Explain.

b. Is the image real or virtual?



c. How far was the object placed in front of the mirror? Answer: 19.2 cm

5. An inverted image has a magnification of 2 when the object is placed 22 cm from

a convergent mirror. What are the image distance and the focal length of the mirror? Answer: di = 44 cm

f = 14.7 cm

8.1.3 Reflection and Mirror Review

1. (G1) Suppose that you want to take a photograph of yourself as you look at your image in a flat mirror 1.5 m away. For what distance should the camera lens be focused? Answer: 3.0 m

2. (G4) A person whose eyes are 1.62 m above the floor stands 2.10 m in front of a

vertical plane mirror whose bottom edge is 43 cm above the floor, as shown. What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror? Answer: 76 cm

3. (G5) Two mirrors meet at a 135° angle. If light rays strike one mirror at 40° as

shown, at what angle do they leave the second mirror? Answer: 5°

4. (G9) A solar cooker, really a convergent mirror pointed at the sun, focuses the Sun’s

rays 17.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made? Answer: 34.0 cm

5. (G12) How far from a convergent mirror (radius 27.0 cm) must an object be placed if its image is to be at infinity? Answer: 13.5 cm

6. (G12) If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 cm

when your face is 30.0 cm away from it, where is your image located? Answer: -2.09 cm

a. What is the image’s magnification? Answer: +0.070 b. Is it real or virtual? Is it upright or inverted?



7. (G13) A mirror at an amusement park shows an upright image of any person who stands 1.3 m in front of it. If the image is 3x the person’s height, what is the radius of curvature? Answer: 3.9 m

8. (G15) Some rearview mirrors produce images of cars to your rear that are a bit

smaller than they would be if the mirror were flat. Is this mirror convergent or divergent?

a. What type of image is produced? b. What would the height of the image be for a car that was 1.3 m high and 15.0

m behind you, assuming the mirror’s radius of curvature is 3.2 m? Answer: 0.13 m

9. (G17) Where should an object be placed in front of a convergent mirror so that it produces an image at the same location? Answer: At C

a. Is the image real or virtual? b. Is the image inverted or upright? c. What is the magnification of the image? Answer: -1



8.2 REFRACTION AND LENSES

8.2.1 Refraction

1. Calculate the index of refraction for a clear plastic material if the velocity of light in that material is 2.5 x 108 m/s. Answer: 1.20

a. A ray of light in air is incident at an angle of 40.8° on the surface of this clear

plastic material. What is the angle of refraction in the plastic? Answer: 33°

2. A ray of light passes from kerosene to crown glass (n = 1.52) at an angle of incidence of 45.2°. If the angle of refraction in the glass is measured to be 41°, what is the index of refraction for kerosene? Answer: 1.39

3. A ray of light passes from air into a glass prism at an angle of incidence of 35°. If the

angle of refraction in the glass is 23.7°, what is the speed of light in the glass? Answer: 2.1 x 108 m/s 4. What is the critical angle for a light ray passing into air from polystyrene that has an

index of refraction of 1.60? Answer: 38.7° 5. A light source is located 2.0 m below the surface of a swimming pool and 1.5 m from

the edge. The pool is filled to the top with water. a. At what angle does the light reaching the edge of the pool leave the water? Answer: 53.0° from the normal b. Does this cause the light viewed from this angle to appear deeper or shallower

than it actually is. Explain your answer using a diagram!

6. A fiber optic cable (n=1.50) is submerged in water (n=1.33). What is the critical angle for the light to stay inside the cable? Answer: 62.4°

7. A certain kind of glass has an index of refraction of 1.65 for blue light and an index

of refraction of 1.61 for red light. If white light (containing all colors) is incident on the glass at an angle of 30°, what is the angle between the red and blue light inside the glass? Answer: 0.45°

8. A laser is incident hits a glass prism that is the shape of an equilateral triangle as

shown below. Draw a ray diagram to show what happens to the light ray when it interacts with the prism.

a. Calculate the angle at which the laser beam leaves the prism. Answer: 75°



8.2.2 Thin Lenses

1. An object 8.0 cm high is 80.0 cm in front of a converging lens that has a focal length of 25 cm.

a. Draw a ray diagram for the described situation. b. What are the three characteristics of the image?

Answer: Inverted, M<1, Real c. What is the image distance? Answer: 36 cm d. What is the image height? Answer: -3.6 cm

2. A light 10.0 cm high is placed 60.0 cm in front of a diverging lens that has a focal length of 20.0 cm.

a. Draw a ray diagram for the described situation. b. What are the three characteristics of the image?

Answer: Upright, M<1, Virtual c. What is the image distance? Answer: -15.0 cm d. What is the image height? Answer: 2.5 cm

3. An object is placed in front of a converging lens with a focal length of 10.0 cm such

that a clear image appears on a screen 5.1 m away. a. How far away from the lens was the slide placed? Answer: 10.2 cm b. If the object’s height is 12.5 mm, what is the magnification of the image on

the screen? Answer: M = -50 x

4. A lens forms an image of an object that is 16.0 cm from the lens. The image is 12.0 cm from the lens on the same side as the object.

a. What is the focal length of the lens? Answer: -48 cm b. Is it a convergent or divergent lens? Explain. c. If the object is 8.50 mm, how tall is the image? Answer: 6.38 mm d. Draw a ray diagram for the described situation.



5. A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 m to the right of the slide. The image is -80.0 times the size of the slide.

a. How far is the slide from the lens? Answer: 7.4 cm b. What is the focal length of the lens? Answer: 7.3 cm c. Is it a convergent or divergent lens? Explain.

6. An object 8.0 cm high is placed 12.0 cm to the left of a converging lens of focal

length 8.0 cm. Find the position and height of the image produced by this lens. Answer: di = 24 cm; hi = -16 cm

a. A second converging lens of focal length 6.0 cm is placed 36.0 cm to the right of the first lens. Both lenses have the same optic axis. If the image from the first lens acts as the object for the second lens, find the position and height of the image produced by the second lens.

Answer: di = 12 cm from second lens; hi = 16 cm b. What are the three characteristics of the final image compared to the original

object? Answer: upright, M>1, Real

8.2.3 Refraction and Lenses Review

1. (G27) The speed of light in ices is 2.29 x 108 m/s. What is the index of refraction of

ice? Answer: 1.31 2. (G33) Rays of the Sun are seen to make a 21.0° angle to the vertical beneath the

water. At what angle above the horizon is the Sun? Answer: 61.5° 3. (G35) In searching the bottom of a pool at night, a

watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from his foot at the edge of the pool. Where does the spot of light hit the bottom of the pool, relative to the edge, if the pool is 2.1 m deep?

Answer: 4.6 m 4. (G37) An aquarium filled with water has flat glass sides

whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular.

a. What is the angle of this light ray when it enters the glass? Answer: 26.9°

b. Then what is the angle of this light ray when it enters the water? Answer: 31.2°



c. What would be the refracted angle if the ray entered the water directly? Answer: 31.2°

5. (G41) The critical angle for a certain liquid-air surface is 44.7°. What is the index of

refraction of the liquid? Answer: 1.42 6. (G49) Sunlight is observed to focus at a point 18.5 cm behind a lens.

a. What kind of lens is it? b. What is its power in diopters? Answer: 5.41 D

7. (G50) A certain lens focuses an object 2.25 m away as an image 48.3 cm on the other

side of the lens. What type of lens is it and what is its focal length? Answer: 0.13 m a. What is the magnification of the image? Answer: 0.13 m

8. (G53) The Sun’s diameter is 1.4 x 106 km and it is 1.5 x 108 km away. How large is

the image of the Sun on the film used in a camera with… a. a 28-mm focal length lens? Answer: -0.26 mm b. a 50-mm focal length lens? Answer: -0.47 mm c. a 200-mm focal length lens? Answer: -1.9 mm

9. (G55) A -6.0 diopter is held 14.0 cm from an ant 1.0 mm high. What is the position,

type, and height of the image? Answer: -7.6 cm, 0.54 mm 10. (G57) How far from a 50.0 mm focal length lens must an object be placed if its

image is to be magnified 2.00x and be real? Answer: 75.0 mm a. What if its image is to be virtual and magnified 2.00x? Answer: 25.0 mm



8.3 OPTICS GENERAL REVIEW

1. A laser beam strikes a horizontal plane mirror at an angle of 36° to the horizontal. It then can be seen as a spot on a vertical screen that is placed 15 m away from the point of incidence. How high up along the screen is the spot located? Answer: 10.9 m

2. An object 5.0 cm tall is placed in front of a convergent mirror of focal length 4.0 cm.

If the object is 12.0 cm from the mirror, find the image position and image height. Is the image upright or inverted? Is it real or virtual? Check your results by completing a ray diagram. Answer: di = 6.0 cm; hi = -2.5 cm

3. A divergent spherical mirror forms a virtual image that is 0.8 times the size of the

object. If the image is 20 cm behind the mirror, determine: a. The position of the object. Answer: do = 25 cm b. The radius of curvature of the mirror. Answer: r = -200 cm

4. The refractive index of a certain type of glass is 1.55. What is the speed of light in this type of glass? Answer: v = 1.94 x 108 m/s

5. A narrow beam of light is incident on a diamond at an angle of 52°. What is the angle

of refraction? Answer: θ2 = 19° 6. What is the critical angle for a light ray hitting an interface with an index of refraction

of 1.49 on the incident side and an index of refraction of 1.37 on the refracted side? Answer: θc = 67°

7. A convergent lens with a focal length of 6.0 cm is held 4.0 cm from an insect that is

0.50 cm tall. a. Where is the image located? Answer: di = -12 cm b. How tall will the insect appear to be? Answer: hi = 1.5 cm c. Is the image real or virtual? d. Is the image upright or inverted?

8. A diverging lens has a focal length of 10 cm. Where should a 3.0 cm tall object be placed to produce an image 5.0 cm from the lens? Answer: do = 10 cm

a. What is the height of the image? Answer: hi = 1.5 cm b. Is it upright or inverted?

9. Two plane mirrors are inclined at an angle with each other. A ray of light is incident

on the first mirror at an angle of 25° and reflects toward the second mirror. The ray of light reflects off the second mirror at an angle of 55° with respect to the mirror itself. What is the angle between the two mirrors? Answer: 60°

10. Baldwin Young stands 68 cm from his dresser mirror, inspecting his scalp. How far is

the image of his scalp located from his actual scalp? Answer: d = 136 cm



11. A person measures the width of a swimming pool to be 4.50 meters. This same person notices that the bottom edge of the pool is just visible at an angle of 12.0° above the horizontal. Knowing that the nwater = 1.33 and nair = 1.33, calculate the depth of the pool. Answer: depth = 4.15 m

12. The critical angle of a certain piece of plastic in air is 30°. What is the critical angle if

the plastic is immersed in water? Answer: θ2 = 42° 13. In the Fall 2006, the Sky Mirror sculpture was opened in Rockefeller Center in New

York City. Standing three stories tall and weighing 23 tons, its convergent side faced the Rockefeller Center and its divergent side faced Fifth Avenue.

a. A taxi on Fifth Avenue is located 38 m from the divergent side of the

sculpture and its image is one-fifth the size of the taxi. Determine the focal length of the mirror. Answer: f = -9.5 m

b. What is the image size and image distance of the 260-m tall Rockefeller

Center if it is located an estimated distance of 95 meters from the convergent mirror surface. Assume the focal length of the two sides have the same magnitude. Answer: di = 11 m; hi = -29 m

14. The widest cinema screen in the world was reportedly constructed in New Zealand in

2007. The screen is 30.6 meters (100 feet) wide. Images from a 35-mm wide film are projected onto this screen. Suppose that the screen in the theater is located a distance of 46 m from the projector. Determine the magnification of the image and the focal length of the lens system. Answer: M = -870; f = 53 mm

15. The divergent lens has a focal point that is located 17.8 cm from the lens. A virtual

image is produced on the same side of the lens as the object at a distance of 7.23 cm from the lens. Determine the object distance. Answer: do = 12.2 cm

4.50 m



8.4 PRACTICE RAY DIAGRAMS

Provide are some examples of ray diagrams that you can copy and practice your geometric optics.



Unit 9 THERMODYNAMICS

9.1 TEMPERATURE AND HEAT

1. Find the Celsius and Kelvin temperatures corresponding to: a. A winter night in Seattle (41°F) Answer: 5°C, 278 K b. A hot summer day in Palm Springs (107.0°F) Answer: 41.67°C, 314.8 K c. A cold winter day in northern Manitoba (-18.0°F) Answer: -27.8°C, 245 K

2. (G13.3) “Room temperature” is often taken to be 68°F; what is this on the Celsius scale? Answer: 20°C

a. The temperature of the filament in a light bulb is about 1800°C; what is this on the Fahrenheit scale? Answer: 3272°F

3. (G13.5) The highest and lowest recorded temperature were 136°F (in the Libyan

desert) and -129°F (in Antarctica). What are these temperatures on the Celsius scale? Answer: 58°C, -89°C 4. (G13.8) At what temperature will the Fahrenheit and Centigrade scales yield the same

numerical value? Answer: -40° 5. (G13.30) Typical temperatures in the interior of the Earth and Sun are about 4000°C

and 15 x 106°C, respectively. What are these temperatures in Kelvin? Answer: 4273 K, 15 x 106 K 6. How much heat is generated when the brakes are used to bring a 1000-kg car from a

speed of 25 m/s to 15 m/s? Answer: 200 kJ 7. A 340-kg marble boulder rolls off the top of a cliff and falls a vertical height of 140 m

before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in the marble boulder. Answer: 0.80°C

8. A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature

of 20°C. What is its length on a hot summer day when the temperature is 35°C? Answer: 50.009 m 9. During a bout with the flu an 80-kg man ran a fever of 2.0°C above normal, that is a

body temperature of 39.0°C instead of the normal 37.0°C. If the specific heat of the human body is an average of 3470 J/kg•°C, how much heat is required to raise his temperature by that amount? Answer: 5.5 x 105 J

10. Suppose a copper rod that is 45.0 cm long and has a cross-sectional area of 1.25 x 10-

4 m2 connects two reservoirs. The hot reservoir has a temperature of 100°C and the cold reservoir is 0°C. What is the rate of heat flow by conduction through the copper rod? The thermal conductivity of copper is 385.0 W/m•K. Answer: 10.7 W

11. A hiker is wearing clothing that is 0.469-cm to keep warm. Her skin temperature is



36.1°C and her body cross-sectional area is about 1.15 m2. If the thermal conductivity of wool is 0.04 W/(m•K) and the rate of heat loss by conduction through her clothing is 314 W, what is the temperature outside? Answer: 4°C

12. The operating temperature of a tungsten filament in an incandescent light bulb is

2177°C. and its emissivity is 0.35. Find the surface area of the filament of a 150-W light bulb if all the electrical energy is radiated by the filament as electromagnetic waves into a room at 21°C. Answer: 3.4 x 10-4 m2

13. A very thin square steel plate, 10 cm on a side, is heated in a blacksmith’s forge to a

temperature of 800°C. If the emissivity is 0.60, what is the total ideal rate of radiation of energy? Answer: 450 W

a. If thin square steel plate is put into a room that is 30°C, what is the net flow of heat by radiation? Answer: 448 W

11. (G13.9) A concrete highway is built of slabs 14 m long at 20°C. How wide should

the expansion cracks between the slabs be at 20°C to prevent buckling if the range of temperatures is -30°C to +50°C? The coefficient of linear expansion for concrete is 12 x 10-6 °C-1. Answer: 0.50 cm

12. (G14.E11) A major source of heat loss from a house is through the windows.

Calculate the rate of heat flow through a glass window of 2.0 m x 1.5 m that is 3.2 mm thick, if the temperatures of the inner and outer surfaces are 15.0°C and 14.0°C, respectively. Answer: 790 W

13. (G14.33) How much power is radiated by a tungsten sphere (e = 0.35) of radius 22

cm at a temperature of 25°C? Answer: 95 W



d. If the sphere is enclosed in a room whose walls are kept at -5°C, what is

the net flow rate of energy out of the sphere? Answer: 33 W 14. (G14.56) Estimate the rate at which heat can be conducted from the interior of the

body to the surface. Assume that the thickness of tissue is about 4.0 cm, that the skin is at 34°C and the interior at 37°C, and the surface area is 1.5 m2. Answer: 22.5 W

Table 14-3 Latent Heats at 1 atm Substance Heat of Fusion (J/kg) Heat of Vaporization (J/kg)

Oxygen 0.14 x 105 2.1 x 105 Nitrogen 0.26 x 105 2.00 x 105

Ethyl Alcohol 1.04 x 105 8.5 x 105 Ammonia 0.33 x 105 1.37 x 105

Water 3.33 x 105 22.6 x 105 Lead 0.25 x 105 8.7 x 105 Silver 0.88 x 105 23 x 105 Iron 2.89 x 105 63.4 x 105

Tungsten 1.84 x 105 48 x 105



9.2 PHASE CHA NGE AND SPECIFIC HEAT

Below is the saturation curve for temperatures ranging from -30°C to 40°C. Use this information to solve the following problems. Do not write on the graph, you can use the saturation curve in your activity guide.

1. Which contains more water vapor, air at 30°C with a relative humidity of 50% or air

at 5°C that is saturated? Answer: 30°C by about 7 g/m3

2. The air is currently at a temperature of 50°F and contains 4 g/m3 of water vapor. Will

the relative humidity be higher or lower if the temperature rises to 68°F and by what percent? Answer: Lower by about 38%

3. The air temperature outside is 60°F and it has a relative humidity of 70%. What is the

dew point? Answer: 9°C 4. A parcel of air is 20°C and contains 7 g/m3 of water vapor. What is the relative

humidity of this parcel of air? Answer: 40%

a. The parcel of air rises into the atmosphere and cools at 7°C/km of altitude. At what altitude would condensation begin to occur? Answer: 2.2 km

5. A geologist working in the field drinks her morning coffee out of an aluminum cup. The cup has a mass of 0.120 kg and is initially at 20.0°C when she pours in 0.300 kg of coffee initially at 70.0°C. What is the final temperature after the coffee and the cup attain thermal equilibrium? Assume that coffee has the same specific heat capacity as water and that the only heat exchange is between the coffee and the aluminum cup. Answer: 66.0°C

6. (G14.1) How much heat is required to raise the temperature of 20.0 kg of water from 15C to 95°C? Answer: 6.7 x 106 J

Saturation Diagram

0

10

20

30

40

50

0 10 20 30 40 Temperature (C)

Wat

er V

apor

in A

ir (g

H20

vap

or/k

g Air)

Equilibrium Curve

Unsaturated Region

Super-saturated Region



7. (G14.3) To what temperature will 7700 J of work raise 3.0 kg of water initially at

10.0°C? Answer: 10.6°C

8. (G14.8) How many kilocalories of heat are generated when the brakes are used to bring a 1000-kg car to rest from a speed of 100 km/hr? Answer: 92 kilocalories

9. (G14.9) What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 5.1 kg of the metal from 20°C to 30°C? Answer: 2.6 x 103 J/kg°C

10. (G14.15) A 1.20 kg head of a hammer has a speed of 8.0 m/s just before it strikes a

nail and is brought to rest. Estimate the temperature rise of a 14-g nail generated by ten such hammer blows done in quick succession. Assume the nail absorbs all the energy. Answer: 61°C



9.3 HEAT ENGINES

1. (G15.7) A heat engine rejects 8200 J of heat while performing 3200 J of useful work. What is the efficiency of this engine? Answer: 28%

2. (G15.18) A heat engine does 7200 J of work in each cycle while absorbing 12.0 kcal

of heat from a high-temperature reservoir. What is the efficiency of this engine? Answer: 14 %

3. (G15.19) What is the maximum efficiency of a heat engine whose operating

temperatures are 580°C and 320°C? Answer: 30.5% 4. (G15.20) The exhaust temperature of a heat engine is 230°C. What must be the high

temperature if the Carnot efficiency is to be 28 percent? Answer: 426°C 5. (G15.21) A nuclear power plant operates at 75% of its maximum theoretical (Carnot)

efficiency between temperatures of 600°C and 350°C. If the plant produces electric energy at the rate of 1.3 x 109 W, how much exhaust heat is discharged per hour? Answer: 1.7 x 1013 J/h

6. (G15.25) A heat engine exhausts its heat at 350°C and has a Carnot efficiency of

39%. What exhaust temperature would enable it to achieve a Carnot efficiency of 50%? Answer: 238°C



9.4 GENERAL THERMODYNAMICS REVIEW

1. Convert -62.8°C to Fahrenheit and Kelvin: Answer: -81.0°F, 210.4 K

2. Convert 41.0°F to Celsius and Kelvin: Answer: 5°C, 278.2 K

3. One of the faces of a copper cube with a side of 7.7 cm is maintained at 100°C and the opposite face is 30°C. If the thermal conductivity of copper is 385 W/(m•K), calculate the rate of heat flow through the cube. Answer: 2075 W

4. A fluorescent light bulb contains about 0.10 grams of mercury, which needs to be

vaporized to allow the light to work. If the mercury in the light bulb starts at 20°C, and its boiling point is 357°C, how much energy is required to vaporize all of the mercury. The specific heat of mercury is 140 J/(kg•°C) and the latent heat of vaporization is 2.95 x 105 J/kg. Answer: 34 J

5. What is the relative humidity of an air parcel that has 2.4 g/kg of water vapor and has

a temperature of 50°F? Use the saturation curve in your lab manual! Answer: About 30% 6. An air parcel at 40°C has a relative humidity of 10%. What is the dew point of this air

parcel? Use the saturation curve in your lab manual! Answer: About 8°C 7. A 4 cm diameter and 6 cm long cylindrical rod at 1000 K emits a 385 kJ of radiation

in 20 minutes. What is its emissivity? Answer: 0.56 a. If the rod is in surroundings that are 293 K, what would the difference in

radiation emitted be in the same 20 minutes? Answer: 4.8 kJ less 8. A typical doughnut contains 2.0 g of protein, 17.0 g of carbohydrates, and 7.0 g of fat.

The average food-energy values of these substances are 4.0 kcal/g for protein, 4.0 kcal/g for carbohydrates, and 9.0 kcal/g for fat.

a. During heavy exercise, an average person uses energy at a rate of 510 kcal/h. How long would you have to exercise to work the doughnut off? Answer: 16.4 min

b. If the energy in the doughnut could somehow be converted into kinetic energy of your body as a whole, how fast could you move after eating the doughnut? Take your mass to be 60 kg. Answer: 139 m/s

9. A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each

cycle. a. How much heat must be supplied to the engine in each cycle? Answer: 6500 J b. What is the thermal efficiency of the engine? Answer: 34%

10. A refrigerator takes heat from Qcold, has a work input of |W|, and discards heat Qhot at

a warmer place. Refrigerators are described by their coefficient of performance K, which is defined as:

K = Qcold/W



A refrigerator has a coefficient of performance of 2.10. In each cycle it absorbs 3.40x104 J of heat from the cold reservoir.

a. How much mechanical energy is required each cycle to operate this refrigerator? Answer: 16200 J

b. During each cycle, how much heat is discarded to the high-temperature reservoir? Answer: 50,200 J

11. A Carnot engine whose high-temperature reservoir is at 620 K takes in 550 J of heat

at this temperature in each cycle and gives up 335 J to the low-temperature reservoir. a. How much mechanical work does the engine perform during each cycle?

Answer: 215J b. What is the thermal efficiency of the cycle? Answer: 39% c. What is the temperature of the low temperature reservoir? Answer: 378 K



Unit 10 CHARGE, FIELDS, CURRENT POTENTIAL AND DC CIRCUITS

10.1 COULOMB’S LAW

1. What is the magnitude of the force of a 10.0-µC charge on a 3.0-µC charge 2.0 m away? Answer: 0.068 N

2. How far apart must two electrons be if the force between them is 2.0 x 10-12 N?

Answer: 1.1 x 10-8m

3. A +2.2 X 10-9 C charge is on the x-axis at x= -1.5 m and a +5.4 x 10-9 C charge is on the x-axis at x= 2.0 m. Find the net force exerted on a +3.5 x 10-9 C located at the origin?

Answer: 1.2 x 10-8N to the left

4. Three charges are shown in the figure below. Find the magnitude and direction of the electrostatic force at the 5-nC charge. Answer: 1.4 x 10-5N at 257.5°

13. Three charges are shown in the figure below. Find the magnitude an direction of the electrostatic force of the 5 nC charge.

14. Three charges are shown below. Find the magnitude and direction of the electrostatic force on the 6 nC charge.

5. A fly accumulates 3.0 x 10-10 C of positive charge as it flies through the air. It

settles on a leave. What is the magnitude and direction of the electric field at a location 2.0 cm away from the fly? Answer: 6750 N/C

6. When a TV set is turned on to watch cartoons, an electron beam in the TV tube is

steered across the screen by an electric field between two charged plates. If an electron experiences a force of 3.0 x 10-6 N, how large is the field between the deflection plates? Answer: 1.9 x 1013N/C

7. A tiny ball with a mass of 0.012 kg carries a charge of -18-µC. What is the

magnitude and direction of the electric field needed to cause the ball to float above the ground? Answer: 6533 N/C downward

8. A charged particle of +12 nC is located 0.10 m to the left of another charged

particle of -12 nC. What is the net electric field at a point that is located between the two charges at a distance of 6.0 cm to the right of the positive charge? Answer: 9.8 x 104 N/C to the right

a. What is the net electric field at a point that is located 4.0 cm to the left of the positive charge? Answer: 6.2 x 104 N/C to the left

9. What is the electric potential 0.50 m away from a 4.5 x 10-4 C point charge? Answer: 8.1 x 106 V



10. How much energy is acquired by an electron in moving through a potential

difference of 2.5 x 104 V? Answer: 4.0 x 10-15 J

11. How far apart are two parallel plates if a potential difference of 600 V produces an electric field intensity of 1.2 x 104 N/C between them? Answer: 0.05 m

12. What is the speed of an electron that has been accelerated from rest through a

potential difference of 80.0 kV? The mass of an electron is 9.11 x 10-31 kg. Answer: 1.7 x 108 m/s

13. (G16.3) Two charged balls are 20.0 cm apart. They are moved, and the force on each of them is found to have been tripled. How far apart are they now? Answer: 11.5 cm

14. (G16.5) What is the magnitude of the attractive electric force between an iron nucleus (q = +26e) and its innermost electron if the distance between them is 1.5 x 10-12 m? Answer: 2.7 x 10-3 N

15. (G16.7) What is the magnitude of the force a +15-µC charge exerts on a +3.0-mC charge 40 cm away? (1-µC = 1 x 10-6 C, 1-mC = 1 x 10-3 C) Answer: 2.5 x 103 N

16. (G16.11) Three particles, Q1 = +70 µC, Q2 = +48 µC, and Q3 = -80 µC, are placed in a line as shown. The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. Answer: -1.4 x 102 N + 5.3 x 102N -3.9 x 102 N

17. (G16.13) A charge of 6.00 mC is placed at each corner of a square 1.00 m on a

side. Determine the magnitude and direction of the force on each charge. Answer: 6.20 x 105N away from the square’s center

18. (G16.23) A proton is released in a uniform electric field and it experiences an electric force of 3.2 x 10-14 N toward the south. What are the magnitude and direction of the electric field?

Answer: + 2.0 x 105 N/C south

19. (G16.25) What is the magnitude and direction of the electric field 30.0 cm directly above a 33.0 x 10-6 C charge? Answer: + 3.30 x 106 N/C up

20. (G16.27) An electron is released from rest in a uniform electric field and accelerates to the north at a rate of 125 m/s2. What is the magnitude and direction of the electric field?

Answer: 7.12 x 10-10 N/C south

21. (G16.31) Calculate the electric field at one corner of a square 1.00 m on a side if the other three corners are occupied by 2.80 x 10-6 C charges. Answer: 3.80 x 106 N/C away from the positive charge

22. (G17.1) How much work is needed to move an -8.6 µC charge from the ground to a point whose potential is +75 V? Answer: -6.5 x 10-4 J



23. (G17.3) How much kinetic energy will an electron gain (in Joules) if it falls through a potential difference of 21,000 V in a TV picture tube? Answer: 3.4 x 10-15 J

24. (G17.5) How strong is the electric field between two parallel plates 5.2 mm apart if the potential difference between them is 220 V? Answer: 4.2 x 104 V/m

25. (G17.9) The work done by an external force to move a -7.50-µC charge from point a to point b is 25.0 x 10-4 J. If the charge was started from rest and had 4.82 x 10-4 J of kinetic energy when it reached point b, what must be the potential difference between point a and point b? Answer: 269 V

26. (G17.13) What is the electric potential 15.0 cm from a 4.00-µC point charge? Answer: 2.40 x 105 V

27. (G17.21) Two identical +7.5-µC point charges are initially spaced 5.5 cm from each other. If they are released at the same instant from rest, how fast will they be moving when they are very far away from each other? Assume they have identical masses of 1.0 mg. Answer: 3.0 x 103 m/s



10.2 EQUIVALENT RESISTANCE AND CIRCUIT ANALYSIS

Using the formulas for series and parallel circuits, fill in the blanks in the tablesshown opposite each circuit. In the blanks across from Battery under

V: Write the emf of the battery.

I: Write the total current in the circuit.

R: Write the equivalent or total resistance of the entire circuit.

In the blanks across from R I under

V: Write the voltage drop across RI'

I: Write the current flowing through R ,-R: Write the resistance of RI'

In the blanks across from R2, R3, - . . , fill in the appropriate numbers under

V, I, and R. (Begin by looking for key information given in the table and workfrom there.)

I.rIL[' j

Battery

R,R2

V

12.0 V

V

V

I

A

A

A

R--D

2.00D4.00D

~Lr-~ I

h-J

T R:'

~

v I R

--' ' "'--

--------.--------.----

V I.-------.---

Battery V A

R, V A

R2 10.0 V A

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10.3 ELECTRICITY REVIEW

1. Two charges are separated by 3.0 cm. Object A has a charge of + 6.0µC while object B has a charge of +3.0µC. What is the force on object A?

Answer: 180 N away from B 2. A sphere with charge + 6.0µC is located near two other charged spheres. A -

3.0µC sphere is located 40.0cm to the right and a + 1.5µC sphere is located 30.0 cm directly underneath. Determine the net force (magnitude and direction) on the + 6.0µC charge. Answer: 1.35 N at 42°

3. A negative charge of 2.0 x 10-8 C experiences a force of 0.060 N to the right in an

electric field. What is the field magnitude and direction? Answer: 3 x 106 N/C, to the left

4. What is the magnitude and direction of the electric field at a point midway

between a - 8.0µC and a + 6.0µC that are 4.0 cm apart. Answer: 3.15 x 108 N/C toward negative

5. An electron acquires 3.45 x 10-16 J of kinetic energy when it is accelerated by an

electric field in a computer monitor from plate A to plate B. What is the potential difference between the plates and which plate has a higher potential?

Answer: 2.15 x 103 V; Plate B is higher

6. Two parallel plates are connected to a 100-V power supply and are separated by an air gap. How small can the gap be if the air is not to exceed its breakdown value of E = 3 x 106 V/m? Answer: 3.3 x 10-5 m

7. An automobile headlight with a resistance of 30 Ω is placed across a 12-V

battery. What is the current through the circuit? Answer: 0.40 A

8. A bird stands on an electric transmission line carrying 2500 A. The resistance per meter of the line is 2.5 x 10-5 Ω/m. If the bird’s feet are 4.0 cm apart, what voltage does the bird feel? Answer: 0.0025 V

9. What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.22

Ω? The resistivity of tungsten is 5.6 x 10-8 Ω•m. Answer: 5.7 x 10-4 m

10. Suppose the resistance in a copper wire with a diameter of 1.02 mm carrying 1.67 A has a resistance of 1.05 Ω at 20°C. What is the resistance at 0°C and 100°C if the temperature coefficient for copper is 0.00393°C-1? Answer: 0.97 Ω; 1.38 Ω

11. What is the maximum voltage that can be applied to a 2.7-kΩ resistor rated at 0.25 Watts? Answer: 26 V



12. A standard 100-W incandescent light bulb has a filament made out of tungsten. At room temperature (20°C), the tungsten filament has a resistance of 15 Ω. When the light bulb operating with a wall voltage of 120 V, it gets hot. What is the temperature of the filament when it is hot? The temperature coefficient of tungsten is 0.0044°C-1. Answer: 1975°C

13. Find the equivalent resistance and the current through the battery for each of the following combination circuits.

a. Req = 27.1 Ω; IB = 4.4 A

b. Req = 128.8 Ω; IB = 0.93 A

120 V

120 V

25 Ω 30 Ω

10 Ω

40 Ω

20 Ω

15 Ω



Unit 11 MAGNETISM

11.1 MAGNETISM

1. Use the right-hand rule to find the direction of the current in a wire in a magnetic field that results in the force on the wire shown for each case shown below:

2. A 50 cm long, straight wire conducts 4.0 A of current upward. The wire

experiences a force of 1.0 x 10-2 N when in a magnetic field that is perpendicular to the wire. What is the magnetic field around the wire? Answer: 0.005 T

3. A magnetic field of 1.0 x 10-4 T at 30° North of West acts on a 1.0 m wire that

carries a current of 15 A to the west. What is the magnitude and direction of the magnetic force on the wire? Answer: 7.5 x 10-4 N into the page

4. A wire with a length of 2.7 m and a mass of 0.89 kg is in a region of space with a

magnetic field of 0.72 T. What is the minimum current needed to levitate the wire? Answer: 4.5 A

5. You want to produce a magnetic field with a magnitude of 5.50 x 10-4 T at a

distance of 0.040 m from a long, straight wire. a. What current is required to produce this field? Answer: 110 A b. What is the magnitude of the field located at a distance of 0.080 m and

0.160 m? Answer: 2.75 x 10-4 T; 1.38 x 10-4

6. Two hikers are reading a compass under an overhead transmission line that is 5.50 m above the grand and carries a current of 800 A in a horizontal direction from north to south. What is the magnitude and direction of the magnetic field at a point directly under the conductor? Answer: 2.91 x 10-5 east

7. Two, straight, parallel, 1.0 m superconducting cables 4.5 mm apart carry equal

currents of 15,000 A in opposite directions. What is the force on each wire and what type of force is it? Answer: 10,000 N repulsive

8. Two long, parallel wires that are each 1.20 meters long are separated by a distance

of 2.50 cm. The force each wire exerts on the other is 4.80 x 10-5 N. The wires attract each other. The current in one wire is 0.600 A. What is the current in the



second wire and is it going in the same direction or the opposite direction as the first current? Answer: 8.33 A, same direction

9. An electron moving at right angles to a 0.10-T magnetic field experiences an

acceleration of 6.00 x 1015 m/s2. Ignoring the effects of gravity, what is the electron’s speed? Answer: 3.42 x 105 m/s

10. A particle with a charge of 6.40 x 10-19 C travels in a circular orbit with a radius

4.68 mm due to the force exerted on it by a magnetic field with magnitude of 1.65 T that is perpendicular to its orbit. What is the magnitude of the linear momentum (ρ) of the particle? Answer: 4.94 x 10-21 kg•m/s

11. A deuteron, which is the nucleus of an isotope of hydrogen, has a mass of 3.34 x

10-27 kg and a charge of +e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with a magnitude of 2.50 T.

a. What is the speed of the deuteron? Answer: 8.35 x 105 m/s b. What time is required for it to make half of a revolution? Answer: 2.62 x 10-8 s

12. An ion with a mass of m and a charge of +2e leaves a velocity selector moving at a speed of 400 km/s. It then moves in a half circle in a magnetic field of 60-mT that is perpendicular to the plane of its motion. At the end of this trip it is detected. If the radius of the circle is 13.9 cm, what is the mass of the ion? Answer: 6.67 x 10-27 m/s

The following problems are from Giancoli Chapter 20. 13. (G1) What is the force per meter on a wire carrying a 9.80-A current when

perpendicular to a 0.80 T magnetic field? Answer: 7.8 N/m a. What if the angle between the wire and field is 45.0°? Answer: 5.5 N/m

14. (G3) How much current is flowing in a wire 4.20 m long if the maximum force on

it is 0.900 N when placed in a uniform 0.0800-T field? Answer: 2.68 A

15. (G9) Alpha particles of charge q = +2e and a mass m = 6.6 x 10-27 kg are emitted from a radioactive source at a speed of 1.67 x 107 m/s. What magnetic field strength would be required to bend these into a circular path of radius r = 0.25 m? Answer: 1.3 T

16. (G13) A proton moves in a circular path perpendicular to a 1.15 T magnetic field.

The radius of its path is 8.40 mm. Calculate the energy of the proton. Answer: 7.16 x 10-16 J

17. (G19) Jumper cables used to start a stalled vehicle often carry a 15-A current.

How strong is the magnetic field 15 cm away? Answer: 2.0 x 10-5 T



18. (G21) What is the magnitude and direction of the force between two parallel wires 45 m long and 6.0 cm apart, each carrying 35 A in the same direction? Answer: 0.18 N attraction

19. (G27) A stream of protons passes a given point in space at a rate of 109 protons.

What magnetic field do they produce 2.0 m from the beam? Answer: 1.67 x 10-17 T

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