SHM, Waves, Thermo, E&M Practice Problem Workbook

ACTIVITY 

BASED 

PHYSICS 

SHM, WAVES, 

THERMODYNAMICS AND 

E & M PRACTICE 

PROBLEM SETS 

W 

SOUTHINGTON HIGH SCHOOL 

CCP PHYSICS

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 .................................................................................................................................. 31 

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 

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 10 6 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 10 7 rad/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 (v o ) 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 force 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 by 

¼ Answer: 1.23 sec 

Gamzon & Gregorian-Michaelsen 6/13/12


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/s 2 . Find the value of: 

a. The spring constant. Answer: 4.2 x 10 2 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 10 3 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 


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 


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 10 3 kg/m 3 , what is the elastic 

modulus of copper Answer: E= 1.2 x 10 11 N/m 2 

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. 


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 10 9 

N/m 2 . 

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: f b = 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: v s = 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: f b = 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 10 3 m/s 

b. Granite Answer: 4.1 x 10 3 m/s 

c. Steel Answer: 5.1 x 10 3 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: 2.1 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 10 2 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 10 2 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 


Substances 


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. 


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 10 2 m/s, 44 N 

b. What is the frequency of the first overtone Answer: 880 Hz 

Material Elastic 

Modulus 

Iron, cast 100 x 10 9 N/m 2 

Steel 200 x 10 9 N/m 2 

Brass 100 x 10 9 N/m 2 

Aluminum 70 x 10 9 N/m 2 

Concrete 20 x 10 9 N/m 2 

Brick 14 x 10 9 N/m 2 

Marble 50 x 10 9 N/m 2 

Granite 45 x 10 9 N/m 2 

Wood (pine) 

Parallel to Grain 10 x 10 9 N/m 2 

Perpendicular to 1 x 10 9 N/m 2 

Grain 

Nylon 5 x 10 9 N/m 2 

Bone (limb) 15 x 10 9 N/m 2 

Material Bulk Modulus 

Water 2.0 x 10 9 N/m 2 

Mercury 2.5 x 10 9 N/m 2 

Alcohol (ethyl) 1.0 x 10 9 N/m 2 

Air 1.01 x 10 5 N/m 2 


a. Find the amplitude. 

b. Find the period. 


c. Find the angular frequency. 

Answer: ω = 4 rad/s 

7.4.2 Mass-Spring System 

d. Find the magnitude of the maximum velocity. 

1. When a family of four with a total mass of 200 kg gets into their 1200 kg car, the 

e. Find the magnitude of the maximum 

car’s springs compress 5 cm. What is the spring constant of the car’s springs 

assuming they act acceleration. 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, 

E T = .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 



L 

Answer: 


a. See notes for FBD 

7.4.3 b. Simple Pendulum 

c. E = mg(L-LcosΘ) 

1. What length of string would be necessary to make a simple pendulum with a period 

of 10.0 s 


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/s 2 

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: x m = 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, x m = 10 cm 

x(t) = .10 m cos(1.57t) 

v max = 0.16 m/s, a max = 0.25 m/s 2 



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 E T 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, x m = 0.0500 m, v max = 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 


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 along an iron rod. 


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 


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: f b = 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 


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 


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 


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

3 rd 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 


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 4 th harmonic 

Answer: 288 N 

17. The speed of sound in a certain metal block is 3.00 x 10 3 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: 24 th 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. 







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


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: d i = 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 


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 


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 10 8 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 10 8 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


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: d i = 24 cm; h i = -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: d i = 12 cm from second lens; h i = 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 10 8 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 10 6 km and it is 1.5 x 10 8 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: d i = 6.0 cm; h i = -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: d o = 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 10 8 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: θ 2 = 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: θ c = 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: d i = -12 cm 

b. How tall will the insect appear to be Answer: h i = 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: d o = 10 cm 

a. What is the height of the image Answer: h i = 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 


4.50 m 


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 n water = 1.33 and n air = 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: θ 2 = 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: d i = 11 m; h i = -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: d o = 12.2 cm 



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. 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 

3. 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 

4. 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 


5. 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 10 5 J 

6. 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 

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

4 m 2 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 

8. 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 m 2 . 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 

9. 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. Answer: 2.1 x 10 -4 m 2 



A 

B 

10. 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 rate of radiation of 

energy 

Answer: 900 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: 897 W 

C 

11. The intensity of the radiation from three objects verse wavelengths are plotted as 

shown. Use the graphs to find the temperature of each object. 

Answer: A = ~12000 K, B = ~6000 K, C = ~3000 K 



10. (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 

11. (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 

12. (G13.8) At what temperature will the Fahrenheit and Centigrade scales yield the same 

numerical value Answer: -40° 

13. (G13.30) Typical temperatures in the interior of the Earth and Sun are about 4000°C 

and 15 x 10 6 °C, respectively. What are these temperatures in Kelvin 

Answer: 4273 K, 15 x 10 6 K 

14. (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 . 


15. (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 10 6 J 

16. (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 

17. (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 

18. (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 10 3 J/kg°C 

19. (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 

20. (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 

21. (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 



a. 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 

22. (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 m 2 . 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 10 5 2.1 x 10 5 

Nitrogen 0.26 x 10 5 2.00 x 10 5 

Ethyl Alcohol 1.04 x 10 5 8.5 x 10 5 

Ammonia 0.33 x 10 5 1.37 x 10 5 

Water 3.33 x 10 5 22.6 x 10 5 

Lead 0.25 x 10 5 8.7 x 10 5 

Silver 0.88 x 10 5 23 x 10 5 

Iron 2.89 x 10 5 63.4 x 10 5 

Tungsten 1.84 x 10 5 48 x 10 5 



9.2 HUMIDITY 

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. 

Saturation Curve 

60 

Maximum Water Vapor (g/m 3 ) 

50 

40 

30 

20 

10 

0 

-40 -30 -20 -10 0 10 20 30 40 50 

Air Temperature (°C) 

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/m 3 

2. The air is currently at a temperature of 50°F and contains 4 g/m 3 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 14% 

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/m 3 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 



9.3 HEAT ENGINES 

1. (G15.7) A heat engine produces 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 10 9 W, how much exhaust heat is discharged per hour 

Answer: 1.7 x 10 13 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 10 5 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. 


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 Q cold , has a work input of |W|, and discards heat Q hot at 

a warmer place. Refrigerators are described by their coefficient of performance K, 

which is defined as: 



K = Q cold /W 

A refrigerator has a coefficient of performance of 2.10. In each cycle it absorbs 3.40x10 4 

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 -8 m 

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 -8 N 

to the left 

4. Three charges are shown 13. in the Three figure charges below. are shown Find the in the magnitude figure below. and Find direction the magnitude of an dire 

the electrostatic force at the the 5-nC electrostatic charge. force of the 5 nC charge. Answer: 1.4 x 10 -5 N 

at 257.5° 

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 10 13 N/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 

14. Three charges are shown below. Find the magnitude and direction of the 

electrostatic force on the 6 nC charge. 

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 10 4 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 10 4 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 10 6 V 

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

difference of 2.5 x 10 4 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 10 4 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 10 8 

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 


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 10 3 N 

16. (G16.11) Three particles, Q 1 = +70 µC, Q 2 = +48 µC, and Q 3 = -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 10 2 N 

+ 5.3 x 10 2 N 

-3.9 x 10 2 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 10 5 N 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 10 5 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 10 6 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/s 2 . 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 10 6 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 10 4 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 10 5 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 10 3 m/s 



10.2 EQUIVALENT RESISTANCE AND CIRCUIT ANALYSIS 

Using the formulas for series and parallel circuits, fill in the blanks in the tables 

shown 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 work 

from there.) 

I.rI 

L[' 

j 

Battery 

R, 

R2 

V 

12.0 V 

V 

V 

I 

A 

A 

A 

-- 

R 

D 

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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 10 6 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 10 8 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 10 3 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 10 6 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 


10 Ω 


120 V 

25 Ω 30 Ω 

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 15 Ω 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 40 Ω 

. Answer: 1975°C 

20 Ω 

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

following combination circuits. 

a. R eq = 27.1 Ω; I B = 4.4 A 

b. R eq = 128.8 Ω; I B = 0.93 A 



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 10 15 m/s 2 . Ignoring the effects of gravity, what is the 

electron’s speed 

Answer: 3.42 x 10 5 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 10 5 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 10 7 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 10 9 protons. 

What magnetic field do they produce 2.0 m from the beam 

Answer: 1.67 x 10 -17 T

SHM, Waves, Thermo, E&M Practice Problem Workbook

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