Physics Critical Thinking Worksheets

Pre-AP/Critical Thinking Problems

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To the Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivChapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Chapter 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Chapter 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Chapter 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Chapter 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Chapter 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Chapter 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Chapter 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Chapter 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Chapter 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Chapter 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Chapter 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Chapter 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Chapter 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Chapter 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Chapter 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Chapter 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Chapter 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Chapter 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Contents

Physics: Principles and Problems Contents iii

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iv To the Teacher Physics: Principles and Problems

To the Teacher

This book of Pre-AP/Critical Thinking Problems offers extra problems that will challenge your higher achiev-ing students. The problems in this book are more difficult than typical physics problems. The problemswill enhance your students’ critical thinking skills and offer opportunities to demonstrate a deeper under-standing of physics concepts. Two pages of Pre-AP/Critical Thinking Problems accompany each chapter ofPhysics: Principles and Problems. The problems supporting each chapter consist of several multiple-choiceproblems and at least one open-response problem. The items on these pages take on the same format asthe multiple-choice and open-response items found in AP Physics exams.

An Answer Key provides complete answers, answer rationale, and fully worked-out solutions to all prob-lems. The Answer Key is found in the back of this book.

A Physics Toolkit1 A solid wheel of mass m and radius r rotates around an axis. The moment of inertia, I, of the

wheel is given by the equation I � �12

�mr2.

(a) What is the radius of a 5.1-kg wheel with a moment of inertia of 18 kg�m2?

a. 2.7 m c. 180 m

b. 7.1 m d. 130 m

(b) Which is the correct plot of I versus r for a wheel with a mass of 10 kg?

a. c.

b. d.

2. Two students make a pendulum of a small ball tied onto the end of a piece of string. They set thependulum in motion and use a stopwatch to measure the time taken for one complete swing; thisis the period of the pendulum. To determine how the length of the string affects the period, thestudents change the length, L, of the string, and measure the period, T, of the pendulum for eachstring length. Their measurements are given in the table on the following page.

0

2000

4000

6000

8000

10,000

Mo

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Radius (m)10 20 30 40 50

Moment of Inertia of a 10-kg Object

12,000

0

500

1000

1500

2000

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Date Period Name

Physics: Principles and Problems Pre-AP/Critical Thinking 1

1 Pre-AP/Critical ThinkingCHAPTER

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continuedPre-AP/Critical Thinking1Name

2 Pre-AP/Critical Thinking Physics: Principles and Problems

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a. Plot the values given in the table, draw the curve that best fits all points, and describe the curve.

One of the students decides to investigate the relationship between the string length and thesquare of the period. She uses their previous measurements to prepare the following table.

b. Plot the values given in this new table, draw the best-fit curve, and describe the curve.

c. According to the graph, what is the relationship between the square of the period of the pen-dulum and the length of the string?

d. Use the graph to write an equation relating period squared to string length.

String Length L (m) Period T (s) String Length L (m) Period T (s)

0.07 0.53 0.55 1.49

0.10 0.63 0.70 1.68

0.20 0.90 0.90 1.90

0.40 1.27

String Length L (m) Period Squared T 2 (s2) String Length L (m) Period Squared T 2 (s2)

0.07 0.28 0.55 2.22

0.10 0.40 0.70 2.82

0.20 0.81 0.90 3.61

0.40 1.61

Representing MotionJohn goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h.He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs southat a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walksthe rest of the way home.

1. How many kilometers does John jog in total?

a. 3.4 km c. 13.1 km

b. 12.5 km d. 785 km

2. How far will John have to walk to get home after he finishes jogging?

a. 0.0 km c. 5.58 km

b. 0.25 km d. 15.0 km

3. Which is the correct plot of total distance as a function of time for John’s jog?

a. c.

b. d.

0

2

4

6

8

10

12

Dis

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km)

Time (min)

10 20 30 40 50 60

Distance v. Time Graph of John’s Jog

700

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70

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4. Two drivers (driver A and driver B) are traveling in opposite directions on a long, straight road atdifferent constant velocities. Their motions are represented by the position-time graphs of each,shown below.

a. How long had driver A already been driving when driver B started to drive?

b. How long had driver A been driving when she was 30 km away from her starting point?

c. Which driver is faster?

d. What happens at point P?

�80

�40

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Posi

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Time (h)

0 1

Position-Time Graph for Two Drivers

2�100

�60

�20

20

60B

A

P



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Accelerated Motion1. The driver of a car traveling at 110 km/h slams on the brakes so that the car undergoes a constant

acceleration, skidding to a complete stop in 4.5 s.

(a) What is the average acceleration of the car during braking?

a. �0.041 m/s2 c. �6.9 m/s2

b. �0.15 m/s2 d. �24 m/s2

(b) If the car skids in a straight line for the entire length of the stopping distance, how long are itsskid marks?

a. 7.0�101 m c. 2.1�102 m

b. 1.4�102 m d. 2.5�102 m

(c) Which is the most accurate plot of velocity versus time for the braking car?

a. c.

b. d.

2. A person is standing on the roof of a tall building. She throws a ball from the top of the buildingin such a way that when the ball passes a window cleaner who is 2.0 m from the top, it is fallingat a speed of 7.0 m/s. It takes another 2.9 s to reach the ground.

a. How tall is the building?

b. How fast is the ball moving when it hits the ground?

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Velocity v. Time Graph for the Braking Car

3.5 4 4.50

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3.5 4 4.50

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3. A 0.250-kg cart moves on a straight horizontal track. The graph of velocity, v, versus time, t, for themotion of the cart is given below.

a. Identify every time, t, for which the cart is at rest.

b. Identify every time interval for which the speed (the magnitude of the velocity) of the cart isincreasing.

c. Determine the horizontal position, x, of the cart at t � 8.0 s if the cart is located at x � 2.0 mat t � 0 s.

d. On the axes below, sketch the graph of acceleration, a, versus time, t, for the motion of the carfrom t � 0 s to t � 25 s.

�0.8

�0.4

0.0

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Acceleration-Time Graph for Cart

20.0�1.0

�0.6

�0.2

0.2

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�0.4

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Vel

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m/s

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Time (s)

0.0 10.0

Velocity-Time Graph for Cart

20.0�1.0

�0.6

�0.2

0.2

0.6

5.0 15.0



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Forces in One Dimension1. Which graph best describes the movement of an object on which no net force is exerted?

a. c.

b. d.

2. The relationship between force and acceleration is

a. direct linear. c. direct quadratic.

b. inverse linear. d. inverse quadratic.

3. A 6.0-kg wooden block is pulled across a carpet with a force of F � 36 N. The block begins at restand accelerates to a velocity of 0.25 m/s in 0.50 s. What is the force of friction acting on the block?

a. 3.0 N c. 36 N

b. 33 N d. 39 N

4. A 1500-kg car can accelerate from rest to 72 km/h in 8.0 s. What is the net force acting on the carto cause this acceleration?

a. 3.8 kN c. 15 kN

b. 14 kN d. 240 kN

Dis

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5. A model rocket of mass 0.350 kg is launched vertically. The rocket has an engine that is ignited attime t � 0, as shown below, and the engine fires for 2.50 s, providing a thrust of 14.6 N. When therocket reaches its maximum height, a parachute is deployed, and the rocket then descendsvertically to the ground.

a. On the figures below, draw and label a free-body diagram for the rocket during each of thefollowing intervals:

t � 0 sEngine ignites Rocket descends

Maximum height;parachute deploys

t � 2.50 sEngine shuts down

Ground



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(i) while the engineis firing

b. Determine the magnitude of the average acceleration of the rocket while the engine is firing.

c. Determine the velocity of the rocket at the end of the period when the engine fires.

d. A person stands on a bathroom scale in a full-sized rocket that is being launched vertically.Consider the time interval when the rocket engine is firing. Is the scale reading during thistime interval less than, equal to, or greater than the scale reading when the rocket is at rest?Justify your answer.

(ii) after the engine shuts down, but before the parachute is deployed

(iii) the moment the parachuteis deployed

Forces in Two Dimensions1. Which graph most accurately describes the relationship between the force of kinetic friction and

the normal force?

a. c.

b. d.

2. Glaciers push rocks in front of them. Before a stationary rock starts moving as a result of the forceFglacier exerted on it, the static friction between the rock and the ground

a. decreases until it is smaller than Fglacier.

b. remains constant until it is smaller than Fglacier.

c. increases until it is equal to the product of �s and the normal force on the rock.

d. decreases until it is equal to the product of �s and the normal force on the rock.

3. You are pushing a rock along level ground and making the rock speed up. How does the size ofthe force you exert on the rock compare with the size of the force the rock exerts on you? The forceyou exert

a. is larger than the force the rock exerts on you.

b. is the same size as the force the rock exerts on you.

c. is smaller than the force the rock exerts on you.

d. could be any of the above; it depends on other factors.

F f, k

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F f, k

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F f, k

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F f, k

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FN

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4. How does the size of the friction force exerted by the ground on the rock in the previous problemcompare with the size of the force the rock exerts on you? The force of friction

a. is larger than the force the rock exerts on you.

b. is the same size as the force the rock exerts on you.

c. is smaller than the force the rock exerts on you.

d. could be any of the above; it depends on other factors.

5. As shown below, two blocks on an inclined plane are connected to each other by a light string,and the upper block also is connected to a hanging ball by a light string passing over a frictionlesspulley of negligible mass. The ball hangs over the top edge of the inclined plane. The blocks movewith a constant velocity down the inclined plane.

Block 1 has a mass of m1 � 6.00 kg and block 2 has a mass ofm2 � 3.00 kg. The inclined plane makes an angle of � � 32.0°with the horizontal. The coefficient of kinetic friction betweeneach block and the inclined plane is 0.124.

a. In the space below, draw and label a free-body diagram ofall the forces acting on block 2.

b. Determine the magnitude of the force of kinetic friction acting on block 2.

c. Determine the mass of the hanging ball, M, that enables blocks 1 and 2 to move with constant velocity down the inclined plane.

d. If the string between blocks 1 and 2 is cut, determine the acceleration of block 2 while it ismoving on the inclined plane.



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�

M

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m2

Motion in Two Dimensions1. The diagram at the right shows the trajectories of two balls. The

magnitude of the initial velocity is vi, the launch angle is �, and the horizontal and vertical components of the initial velocity are vxi and vyi.

(a) Compare the values of �i. The value for ball A

a. is greater than the value for ball B.

b. is equal to the value for ball B.

c. is less than the value for ball B.

d. cannot be compared with the value for ball B using only the information given.

(b) Compare the values of vi. The value for ball A





(c) Compare the values of vxi. The value for ball A





(d) Compare the values of vyi. The value for ball A





2. Two balls are thrown horizontally. Ball C is thrown with a force of 20 N, and ball D is thrownwith a force of 40 N. Assuming all other factors are equal, ball D will fall toward the ground

a. faster than ball C.

b. more slowly than ball C.

c. at the same rate as ball C.

d. at a rate that cannot be compared with that of ball C using the information given.

Date Period Name



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Ver

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(m

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Horizontal position (m)

A

B

3. A pilot wants to fly due north a distance of 125 km. The wind is blowing out of the west at aconstant 35 km/h. If the plane can travel at 175 km/h, how long will the trip take?

4. A boy ties a 58-g tennis ball to the end of a light string that is 65 cm long and whirls the ball above his head in a horizontal circle, as shown at right. The boy exerts a force of 5.2 N on the string to keep the ball moving in a circle at a height of 1.7 m above the ground.

(a) Determine the speed of the ball.

(b) Suppose that the string breaks as the ball swings in its circular path. Describe the motion ofthe ball

(i) the instant after the string breaks.

(ii) after the string breaks but before it hits the ground.

(c) How long will it take the ball to reach the ground?

(d) How far will the ball travel horizontally before it hits the ground?



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Gravitation1. According to Kepler’s second law of planetary motion,

a. planets maintain constant speed around the Sun.

b. planets maintain constant acceleration around the Sun.

c. the speed of a planet is greatest when it is closest to the Sun.

d. the area swept out by the orbit per time unit keeps changing.

2. A space probe is directly between two moons of a planet. If it is twice as far from moon A as it isfrom moon B, but the net force on the probe is zero, what can be said about the relative masses ofthe moons?

a. Moon A is twice as massive as moon B.

b. Moon A has the same mass as moon B.

c. Moon A is four times as massive as moon B.

d. Moon A is half as massive as moon B.

3. The Moon is receding from Earth by approximately 3.8 cm per year. Earth’s mass is 5.98�1024 kg,and its radius is 6.38�106 m. The Moon’s mass is 7.3�1022 kg, its radius is 1.79�106 m, and itsorbital period around Earth is 27.3 days. The current average distance between the two surfaces is3.85�108 m. Assume that neither body gains or loses mass and that the recession continues at arate of 3.8 cm per year.

a. Approximately how much will the gravitational attraction between the Moon and Earth changebetween now and 499 million years from now?

b. Approximately how long, in present Earth-days, will it take the Moon to orbit Earth 499 million years from now?

Date Period Name



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4. The mean distance of the planet Neptune from the Sun is 30.05 times the mean distance of Earthfrom the Sun.

a. Determine how many Earth-years it takes Neptune to orbit the Sun.

b. The mass of the Sun is 1.99�1030 kg, and the closest distance of Neptune from the Sun is4.44�109 km. What is the orbital speed of Neptune in km/s at this point?

c. Without doing any numerical calculations, answer the following. Is the orbital speed of Earthless than, equal to, or greater than the orbital speed of Neptune? Explain your reasoning.

d. The radius of Neptune is 3.883 times that of Earth, and the mass of Neptune is 17.147 timesthat of Earth. From the surface of which planet (Earth or Neptune) would it be easier to launcha satellite? Explain your reasoning.



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Rotational Motion1. The London Eye is a Ferris wheel with a circumference of 424 m and a total mass of 2,100,000 kg.

It has 25 cars, holds 800 passengers, and each ride lasts 30 min. The London Eye’s moment ofinertia is best estimated at between

a. 2�109 and 3�109 kg�m2 c. 5�109 and 10�109 kg�m2

b. 4�109 and 5�109 kg�m2 d. 2�1011 and 4�1011 kg�m2

2. In 7.0 s, a car accelerates uniformly from rest to a velocity at which its wheels are turning at 6.0 rev/s.

(a) What was the angular acceleration of the car’s wheels?

a. 0.14 rad/s2 c. 5.4 rad/s2

b. 0.86 rad/s2 d. 42 rad/s2

(b) If the tires of the car have a diameter of 42 cm, and they rolled on the ground withoutslipping, how far did the car go in those 7.0 s?

a. 4.4 m c. 110 m

b. 28 m d. 130 m

3. Consider two wheels with fixed hubs. The hub cannot move, but the wheel can rotate about it. Thehubs are fixed to a stationary object. The hubs and spokes are massless, so that the moment ofinertia of each wheel is given by I � mr2, where r is the radius of the wheel. Each wheel starts fromrest and has a force applied tangentially at its rim. Wheel A has a mass of 1.0 kg, a diameter of 1.0 m, and an applied force of 1.0 N. Wheel B has a mass of 1.0 kg and a diameter of 2.0 m. Thetwo wheels undergo identical angular accelerations. What is the magnitude of the force applied towheel B?

a. 0.13 N c. 4.0 N

b. 2.0 N d. 8.0 N

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4. A system consists of a steal beam of mass M � 68.4 kg and length L � 1.84 m, with a 39.0-kgbrass sphere attached at the right end of the rod, as shown below.

a. Determine the moment of inertia of the system for rotation about an axis through the center ofthe steel beam (axis A).

b. Determine the moment of inertia of the system for rotation about an axis through one end ofthe beam (axis B).

c. Determine the constant horizontal force, F, that must be exerted on the brass sphere in orderto produce an angular acceleration of the system such that � � 2� rads. F is exerted perpendic-ular to the steel beam, and the system rotates around axis B.

d. Consider part c. If the system started from rest, determine the linear velocity of the brasssphere after the force has been applied for 4.0 s.

AB



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Momentum and Its Conservation1. A freight car with a mass of 10 metric tons is rolling at 108 km/h along a level track when it

collides with another freight car, which is initially at rest. If the speed of the cars after they coupletogether is 36 km/h, what is the mass of the second car?

a. 40 metric tons c. 10 metric tons

b. 20 metric tons d. 5 metric tons

2. A rod of length r and mass m is pivoted at its center, and given an angular velocity, �1. Whatwould be the angular velocity of a second rod, which has the same angular momentum as the first,but whose length is 3r and whose mass is 2m?

a. c.

b. d.

3. A 5.0-g bullet with an initial velocity of 95.0 m/s lodges in a block of wood and comes to rest at adistance of 6.0 cm. Assume the bullet undergoes a constant negative acceleration; it slows at aconstant rate.

a. How much time does it take for the bullet to stop?

b. What is the impulse on the wood block?

c. What is the average force experienced by the block?

�1�18

�1�6

�1�12

�1�5

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4. The following collisions take place on a flat, horizontal tabletop with negligible friction.

a.

A 2.1-kg cart, A, with frictionless wheels is moving at a constant speed of 3.4 m/s to the righton the tabletop, as shown above, when it collides with a second cart, B, that is initially at rest.The force acting on cart A during the collision is shown as a function of time in the graphbelow, where t � 0 is the instant of initial contact. Assume that friction is negligible. Calculatethe magnitude and direction of the velocity of cart A after the collision.

b. In another experiment on the same table, an incident ball, C, of mass 0.15 kg is rolling at 1.3 m/s to the right on the tabletop. It makes a head-on collision with a target ball, D, of mass0.50 kg at rest on the table. As a result of the collision, the incident ball rebounds, rollingbackward at 0.80 m/s immediately after the collision. Calculate the velocity of ball D immedi-ately after the collision. (Ignore friction in your calculations.)

c. In a third experiment on the same table, an incident ball, E, of mass 0.250 kg rolls at 5.00 m/stoward a target ball, F, of mass 0.250 kg. The incident ball rolls to the right along the x-axis,and makes a glancing collision with a target ball, F, that is at rest on the table. The velocity ofincident ball E immediately after the collision is 4.33 m/s at an angle of 30.0º above the x-axis.Calculate the magnitude and direction of target ball F’s velocity immediately after the collision.(Ignore friction.)

0.0

�4.0

�2.0

Forc

e (k

N)

Time (ms)

0.5 1.0 1.5 2.0 2.5 3.0

BA



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Energy, Work, and Simple Machines1. Power can be described as

a. the rate of energy transfer.

b. the change in kinetic energy.

c. the force exerted over a given distance.

d. the ratio of work output to work input.

2. What is the magnitude of the force required to accelerate an electron of mass 9.1�10�31 kg fromrest to a speed of 2.0�107 m/s for a distance of 0.50 cm?

a. 1.8�10�21 N

b. 9.0�10�19 N

c. 1.8�10�16 N

d. 3.6�10�14 N

3. A lever is used to lift a 225-kg crate 3.2 m up to the bed of a truck. The lever is 82 percent efficient.How much work needs to be done on the lever in order to lift the crate?

a. 8600 J

b. 7100 J

c. 5800 J

d. 1300 J

4. In a purely electric vehicle, energy usually is stored in batteries. The stored energy is used to powerthe vehicle until the energy is depleted, and then energy has to be stored once more by rechargingthe batteries. An electric wheelchair has a mass of 32 kg and is custom–designed for a person witha mass of 80.0 kg. The stored energy available in its batteries is 2.1�106 J. The wheelchair motorrequires a power of 310.0 W for driving under typical conditions. This is sufficient to propel theperson in the wheelchair along at a speed of 17 km/h.

a. Determine the work done by the motor when the wheelchair starts at rest and speeds up to itsnormal speed.

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b. Determine the maximum distance that the wheelchair can travel on a horizontal surface at itsnormal speed, using its stored energy. (Ignore the energy needed for it to speed up when itstarts.)

c. Suppose that 0.023 percent of the power required for driving is expended against drag due tothe flexing of the wheelchair’s soft rubber tires. Calculate the magnitude of the drag force.

5. In the simplified elevator system shown in the figure at right, a motor rotates a shaft wrapping or unwrapping a chain that raises or lowers the elevator car. The car’s mass is 1.20�103 kg and is designed to carry a maximum load of 9.5�102 kg. While in motion, a constant frictional force of 3.5�104 N acts on the car.

a. What power must the motor deliver to raise the fully loaded car at a speed of 2.5 m/s?

b. The above elevator system is modified by connecting a free-hanging 5.0�102-kg counterweightto the chain that passes over the shaft of the motor, as shown below. What power must themotor now deliver to raise the fully loaded car at a speed of 2.5 m/s?



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Conservation of Energy1. An astronaut is standing on the surface of a planet that has a mass of 6.42�1023 kg and a radius

of 3397 km. The astronaut fires a 2.6-g bullet straight up into the air with an initial velocity of 406m/s. What is the greatest height the bullet will reach? The planet has no atmosphere.

a. 22 m

b. 210 m

c. 8200 m

d. 22,000 m

2. A diver stands on a diving platform 10.0 m above the surface of a pool and leaps upward with aninitial speed of 2.5 m/s. How fast is the diver moving while falling past a diving board that is 3.0 m above the surface of the pool?

a. 12 m/s

b. 14 m/s

c. 137 m/s

d. 140 m/s

3. A circus performer juggles four identical balls. The performer throws each ball upward with thesame initial velocity and releases each ball at the same height. The ball with the greatest kineticenergy will be the ball that the juggler

a. throws upward, just after it leaves her hand.

b. is watching, just as it reaches its highest point.

c. is about to catch, just before it lands in her hand.

d. does not catch, just before it lands on the floor.

4. A 3.0-kg block starts at rest at the top of a 37° incline, which is 5.0 m long. Its speed when itreaches the bottom is 2.0 m/s. What is the average friction force opposing its motion?

a. 16 N

b. 18 N

c. 19 N

d. 28 N

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5. A stuntwoman, working on the set of an action movie, performs the following stunt. She steps outof the window of a building and lands on a giant inflated pillow directly beneath the window. Thewoman’s mass is m. When she reaches the pillow, her speed is v. Air resistance can be neglected.Use work and energy methods to solve the following.

a. Find an expression for the height of the window above the pillow.

b. The stuntwoman comes to rest in the inflated pillow after falling a distance, s, into it. Find anexpression for the average force exerted by the pillow on her body.

c. For her next stunt, the woman slides down a rubber chute of length, l. She starts by climbingup a ladder, then sits on the chute and starts sliding down at a height H. Along the chute, aconstant frictional force of Ff is exerted on the woman. Find an expression for the stunt-woman’s speed when she reaches the bottom of the chute.

d. Draw two energy diagrams to compare the work done, the initial and final potential energiesof the stuntwoman, and the initial and final kinetic energies of the stuntwoman for the situations in 5. b. and 5. c.



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Thermal Energy1. A student heats 200 g of an unknown powder, measures its temperature, and then adds the

powder to an insulated beaker holding 200 g of water at a known temperature. The student thenmeasures the temperature of the mixture and calculates the temperature change for each substance.

The ratio of the temperature changes for the substances is � �6.

Assuming that no heat is exchanged between the water and its surroundings, which of these is thepowder most likely to be? (Cwater � 4180 J/kg�K)

a. lead (Clead � 130 J/kg�K)

b. brass (Cbrass � 376 J/kg�K)

c. carbon (Ccarbon � 710 J/kg�K)

d. aluminum (Caluminum � 897 J/kg�K)

2. A metal calorimeter of mass 300.0 g contains 500.0 g of water at a temperature of 15.0°C. A 560.0-g block of metal at a temperature of 100.0°C is dropped into the calorimeter and thetemperature of the water is observed to increase to 22.5°C. If the block and the calorimeter aremade of the same metal, what is the specific heat of the metal?

a. 240 J/kg�K c. 580 J/kg�K

b. 380 J/kg�K d. 610 J/kg�K

3. A total of 100.0 g of metal filings are heated to 100.0°C and added to a beaker holding 200 g of aliquid at 20.0°C. The liquid temperature increases to 24.0°C. The liquid has a specific heat ofCliquid. Assuming that no heat is exchanged between the liquid and its surroundings, which ofthese is the best estimate for the specific heat of the metal filings?

a. 0.03Cliquid c. 0.1Cliquid

b. 0.05Cliquid d. 0.5Cliquid

4. Initially, a container holds 200.0 cm3 of water at a temperature of 25.0°C. A total of 0.500 g ofwater evaporates. Assuming that no heat is exchanged between the water and its surroundings,what is the temperature of the remaining water?

a. 11.4°C c. 23.6°C

b. 13.6°C d. 26.4°C

�Tpowder��Twater

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5. You perform the following calorimetry experiment in the physics laboratory. The objective is todetermine the specific heat of copper. You use a calorimeter containing water, and do theexperiment in three parts. Before the specific heat of copper can be determined, it is necessary toknow the specific heat of the calorimeter. This value can be found by performing an experimentwith a metal of known specific heat. Iron will be used for this purpose. The specific heats of ironand water are Ciron � 450.0 J/kg�K and Cwater � 4180 J/kg�K. The calorimeter is well insulated, sono heat is gained from or lost to the surroundings.

a. First, you heat up an iron ball of mass 50.0 g from 23.0°C to 100.0°C. Determine the amountof energy required.

b. Next, you drop the hot iron ball into a 35.0-g calorimeter containing 85.0 g of water. Thecalorimeter and water start at a temperature of 20.0°C. You measure the final temperature ofthe system to be 24.4°C. Determine the specific heat of the calorimeter.

c. Now that the heat capacity of the calorimeter has been determined, it is possible to experimen-tally determine the specific heat of copper. You use the same calorimeter, again containing 85.0 g of water at 20.0°C. Now, you heat a copper ball of mass 45.0 g to 100.0°C and drop itinto the calorimeter, and then you measure the final temperature of the system to be 23.4°C.Determine the specific heat of copper.

d. You remove the copper ball and empty out the water. The empty calorimeter is now at 23.4°C.You add 25.0 g of water at 7.5°C. What is the final temperature of the system?



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States of Matter1. Geologists believe that convection currents within Earth’s mantle drive the movement of the

tectonic plates over Earth’s surface. Which diagram best illustrates mantle convection?

a. c.

b. d.

2. A geologist hypothesizes that pressure has an effect on the morphology of volcanoes. He decidesto compare volcanoes that form on the surface of Venus with volcanoes that form on Earth’s oceanfloor. The atmospheric pressure on Venus is about 9000 kPa. The density of saltwater is 1.03 g/cm3. Which ocean depth would be most appropriate to use for this comparison?

a. 9�10�1 m c. 9�105 m

b. 9�102 m d. 9�107 m

3. A spherical meteorite that is 4.00 m in diameter has a velocity of 11.0 km/s when it strikes Earth.The meteorite has a density of 8.00 g/cm3 and it takes 10.0 ms to come to rest.

a. What pressure does the meteorite exert on the ground it strikes?

b. If the same meteorite hits the ocean, what is the pressure that will be transmitted through theocean water if the ocean has a depth of 1200 m?

Cool rock Warm rock

North pole

South pole

Surface

CoreWarm rock Cool rock

North pole

South pole

Surface

Core

Cool rock Warm rock

Earth’s surface

Earth’s core

Warm rock Cool rock

Earth’s surface

Earth’s core

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4. A car’s gasoline tank has a capacity of 50.0 L. When the gasoline level reaches exactly 5.00 L, a buzzer goes off inside the car to warn the driver that the gasoline level is low.

a. The gasoline tank is filled completely when the temperature of the gasoline is 20.0°C. Thetank is equipped with an overflow valve. How much gasoline will overflow from the tank whenthe temperature of the gasoline is 30.0°C? (Assume that the tank itself does not expand.)

b. On a particularly hot day, the car goes exactly 73.5 km after the buzzer has gone off. At its usu-al temperature of 20.0°C, the car gets exactly 15.0 km/L. If there are no other factors affectingits fuel efficiency, what is the temperature of the gas in the tank that day? (Assume that thetank itself does not expand.)

5. In the laboratory, you are given a cylindrical beaker containing an unknown fluid and you are asked to determine the density, �, of the fluid. You are to use a string of negligible mass, tied to a spring scale attached to a stand. An irregularly shaped object of known mass m and unknown density D hangs from the string (D �� ).

a. The system is arranged so that the object is immersed in the unknown fluid, as shown at right. Describe the change you would see in the reading on the spring scale, and explain why it occurs.

b. Explain how you could experimentally determine the density of the unknown fluid. For eachstep, show how you would use your measurement(s) to calculate the fluid’s density.



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Vibrations and Waves1. The work done to move a spring away from its equilibrium position is equal to

a. the ratio of force to mass.

b. the kinetic energy of the spring.

c. the ratio of force to displacement.

d. the potential energy of the spring.

2. The graph below is a plot of displacement versus time of a mass oscillating on a spring.

(a) At which point on the graph is the acceleration of the mass zero?

a. A c. C

b. B d. D

(b) At which point on the graph is the net force on the mass at a maximum?

a. A c. C

b. B d. D

(c) At which point on the graph is the velocity of the mass zero?

a. A c. C

b. B d. D

3. Consider a 20.0-kg pendulum clock that keeps good time. If the clock is moved to a locationwhere it weighs 74 N, how many minutes will the minute hand move in 1 h?

a. 98 c. 38

b. 60 d. 23

A

D

C

B

Time

Dis

pla

cem

ent

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4. A 150-g object subject to a restoring force F � �kx is undergoing simple harmonic motion. Shownbelow is a plot of the potential energy, PE, of the object as a function of distance, x, from itsequilibrium position. The object has a total mechanical energy of 0.3 J.

a. What is the farthest the object moves along the x-axis in the positive direction? Explain yourreasoning.

b. What is the object’s potential energy when its displacement is 4.0 cm from its equilibriumposition?

c. Determine the object’s kinetic energy when its position is x � �8.0 cm.

d. What is the object’s speed at x � 0.0 cm?

Pote

nti

al e

ner

gy

(J)

Position (cm)

0.0

Potential Energy v. Position

�12.0 �4.0�8.0 0.0 8.04.0 12.0

0.3

0.1

0.2

0.6

0.4

0.5



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Sound1. Seismic waves, produced by earthquakes, move through or over the surface of the Earth. The four

types of seismic waves are shown in the illustration below.

The strong, back-and-forth shaking of powerful earthquakes commonly is preceded by a lowrumbling noise. This noise occurs when certain seismic waves are transmitted from the rock intothe air. Which seismic waves are most likely to cause the rumbling noise?

a. P waves c. Love waves

b. S waves d. Rayleigh waves

2. Dolphins use a method called echolocation to detect things such as obstacles and prey in the water.If a dolphin swimming in seawater at 25°C sends a 220-dB click with a frequency of 120.0 Hz, andthen detects the reflection of the click exactly one-twentieth of a second later, approximately howfar away is the object?

a. 6.00 m c. 76.65 m

b. 38.32 m d. 240.0 m

P wave

S wave

Love wave

Rayleigh wave

Dilations

Wave direction

Wavelength

Wave direction

Compressions

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3. The image below shows the frequency of a blue whale’s call over time, as detected by a stationaryhydrophone. The black regions are the loudest parts of the call.

Another hydrophone is being dragged behind a boat traveling away from the whale at 20.0 km/h.The highest frequency of the whale call that this hydrophone detects will be about

a. 24 Hz c. 15.5 Hz

b. 18.5 Hz d. 13 Hz

4. The four strings on a violin all have free lengths of 0.325 m. If standard tuning is desired, theirfundamental frequencies of vibration are those shown in the table below.

The strings are made of steel wire with a density of 7.8�103 kg/m3 and can be stretched with amaximum force per unit of cross-sectional area of Pmax � 2.2�109 Pa. To get a good sound fromsteel strings, you have to stretch them with fairly high tension, but not so high as to break thestrings.

a. If a steel E string has standard tuning, does the force per unit of cross-sectional area on thisstring exceed 0.75 Pmax? Does the force per unit of cross-sectional area on any of the otherstrings exceed this value?

b. If the E string in part a is 0.25 mm in diameter, what must be the diameters of the steel stringsA, D, and G so that all four strings have standard tuning and are under the same tension?

c. To produce notes of varying frequency, you hold down a string with your finger to reduce thestring’s free length. On which string and in what position on that string should you hold downyour finger in order to produce the fundamental tone of the note A at a frequency of 220 Hz?

Freq

uen

cy (

Hz)

Time (s)

19

18

17

16

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String Fundamental Frequency

E 660 Hz

A 440 Hz

D 294 Hz

G 196 Hz

Fundamentals of Light1. The yellow color of a canary shown on a conventional computer monitor is produced by

a. refraction of white sunlight.

b. addition of red and green light.

c. absorption of blue and red light.

d. polarization of green and yellow light.

2. Which of these best explains how chlorophyll causes the leaves of a tree to appear green?

a. Chlorophyll bends blue and red light without affecting green light.

b. Chlorophyll absorbs blue and red light while reflecting green light.

c. Chlorophyll destroys white and red light while storing green light to use.

d. Chlorophyll combines sunlight with blue light from the sky to form green light.

3. Earth is about 150,000,000 km from the Sun. Its input of solar energy per square meter is I. Marsis about 228,000,000 km from the Sun. Which of these most likely represents the input of solarenergy per square meter on Mars?

a. 0.28I

b. 0.43I

c. 0.65I

d. 0.99I

4. When magenta is taken out of white light, the color that remains is

a. yellow.

b. cyan.

c. blue.

d. green.

5. A driver is stopped for running a red light. Trying to avoid a ticket, the driver tells the police officerthat because of the Doppler shift, the red light (650 nm) was blueshifted to a green light (470 nm).What would the driver’s speed need to be for this to be true?

a. 1.1�108 m/s

b. 8.3�107 m/s

c. 1.1�109 m/s

d. 70 mph

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6. An observer on Earth locates a space probe along the axis shown in the figure below. The observerrecords that the 486-nm band of hydrogen emitted by the space probe as 485 nm. Whatconclusion can be reached about the velocity of the space probe along the axis, vP, axis, and thevelocity of the observer along the axis, vO, axis?

a. The velocities are in the same directions and vP, axis is less than vO, axis.

b. The velocities are in the same directions and vP, axis is greater than vO, axis.

c. The velocities are equal in magnitude but opposite in direction.

d. Both b and c.

7. Two polarizing filters are 15 cm apart. There is an angle of 20° between the polarizing axes of thefilters. Light from a laser passes through filter 1 and then through filter 2. In this set up, the onlychange you are allowed to make is either to the distance or to the angle between the filters, inwhich case you may halve or double the given measurement.

a. How do you change the set up to increase the intensity of laser light passing through filter 2?Explain.

b. If the light emerging from a second polarizing filter is reduced to two-thirds its intensity coming out of a first polarizing filter. What is the angle between the polarizing axes of the twofilters?

Earth

Space probe

vO



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Reflection and Mirrors1. Which of these images could be inverted?

a. image of a customer in a store’s convex security mirror

b. image of an object placed between the focal point and the surface of a concave mirror

c. image of a tree in the lens of a person’s convex sunglasses

d. image of a strawberry in the concave bowl of a shiny spoon

2. A shiny silver bowl acts as a mirrored surface with a radius of curvature of 6 cm. A strawberry isheld 4 cm above the bottom of the bowl and then dropped. Which change occurs as thestrawberry falls to a height of 2 cm?

a. The image goes from being smaller to being larger than the object.

b. The image goes from right side up to upside down.

c. The image goes from being larger to being smaller than the object.

d. The image goes from upside down to right side up.

3. A concave mirror has a focal length, f. A nickel placed before the mirror has a real image that isthree times larger than the actual nickel. Which of these represents the object distance of thenickel?

a. f

b. f

c. f

d. f

4. A concave spherical mirror forms an image of the Sun at a distance of 8.0 cm from the mirror.What is the radius of curvature of the mirror? (Use 1.50�1013 cm as the distance to the Sun.)

2�3

3�4

3�2

4�3

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5. Wide-angle, aspherical convex mirrors sometimes are used as side-mounted mirrors on passengerautomobiles. These mirrors actually consist of two different types of mirrors formed together. Theinner part is a spherical convex mirror with a fairly large radius of curvature. The outer part is aspecial convex portion that has a variable radius of curvature. The radius of curvature at the edge ofthe mirror may be a factor of ten less than that of the inner portion.

a. Consider a vehicle with such an aspherical mirror on its passenger side. The inner sphericalportion of this mirror has a radius of curvature of r � 2.50 m. When the driver views a truck ofheight h � 2.90 m that is 125 m distant to the rear of the center portion of the mirror, what isthe magnification of this part of the mirror, and what image height is seen?

b. If the radius of curvature were reduced to 0.250 m at the edge of the mirror, what would be thenew image height of the truck from part a?

c. Consider the passenger-side mirror described above. What advantages does a driver have whenviewing both nearby (closer than 10.0 m) and more distant objects through such a mirrorcompared to using either a plane mirror or a simple spherical mirror?



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Refraction and Lenses1. When a light wave travels from one medium into another, which property or properties of the

wave change?

a. its speed only c. its speed and wavelength only

b. its speed and frequency only d. its speed, wavelength, and frequency

2. When a light wave not perpendicular to the surface travels from a mineral crystal into the air,

a. v increases and � increases c. v decreases and � decreases

b. v increases and f decreases d. v decreases and f increases

3. Unlike a convex lens, a concave lens causes all rays to

a. refract c. diverge

b. reflect d. converge

4. When light passes through a lens, chromatic aberration occurs when

a. the shape of the lens causes rays to diverge.

b. different wavelengths focus at different points.

c. parallel rays do not all focus into a single point.

d. the incident angle is greater than the critical angle.

5. The figure shows the path of a ray of light passing through three layers. Use information in thetable to answer the question.

Which of these list, from 1 to 3, the materials that could make up each layer?

a. air, ethanol, air c. ethanol, water, diamond

b. diamond, air, crown glass d. water, crown glass, ethanol

Indices of Refraction

Material

Air

Diamond

Index ofRefraction

Crown glass

Ethanol

Water

1.0003

2.42

1.52

1.36

1.33

1

2

3

a

bb

c

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6. A submerged fish looks up and sees a fisherman seated at the edge of the water on the distantshore of the pond. At which of the following angles to the vertical must the fish be looking?

a. 36.9° c. 48.8°

b. 41.2° d. 90.0°

7. A ray of light from a region containing air (index of refraction n1 � 1.00) enters one end of anoptical fiber at angle of incidence �i, as shown in the figure below. The index of refraction of theoptical fiber is n2 � 1.48.

a. If the angle of incidence at the end of the fiber is �i � 48.5°, what is the angle of reflection, �,from the sidewall of the fiber?

b. Optical fibers are surrounded by a shield known as cladding. The cladding has a slightly lowerindex of refraction and is fused to the optical fiber making a completely reflective interface.Using the index of refraction of the cladding (n � 1.42), show that at the sidewall of the fiber,internal reflection is total.

c. Is there an angle of incidence, �i 90°, for which internal reflection from the sidewall is nottotal?

�

�i



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Interference and Diffraction1. Sunlight is shining on a 5.00�10�8-m-thick film of oil. (The material behind the oil has a lower

refractive index than the oil.) If the speed of light in the oil is 1.85�108 m/s, what color does theoil appear to be?

a. red c. white

b. blue d. black

2. The figure below shows the setup for an experiment on the behavior of light.

Which of these best explains the purpose of the single thin slit found in the first screen?

a. to allow only some wavelengths of light to pass through to the second screen

b. to send high and low wavelengths of light to separate slits on the second screen

c. to cause light waves to reach the slits in the second screen in an interference pattern

d. to ensure that light waves passing through the slits in the second screen are coherent

3. Rainbows that form in the sky during or after a rainstorm form primarily because of the ability ofwaves to

a. bounce off surfaces.

b. combine to increase their amplitude.

c. change direction when confronted with obstacles.

d. change velocity when moving from one medium to another.

4. Consider a double-slit experiment where the distance between slits is 2.40�10�5 m. What is thewavelength of light used if the difference between a third-order band and a first-order band is 12.4 mm, and the screen is 0.5 m away from the slits?

a. 600 nm c. 200 nm

b. 300 nm d. 100 nm

Light source

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5. A yellow sodium arc lamp actually is composed of two closely spaced wavelengths, 588.995 nmand 589.592 nm. What is the angular separation between these two first-order lines for a gratingwith exactly 5000 slits/cm?

a. 17.13° c. 0°

a. 0.0002° d. 0.0179°

6. A grating spectroscope is a device used to perform wavelength measurements on a beam of light.The instrument is composed of a diffraction grating that spreads the light into its componentcolors and a scope that allows careful measurement of the position of the spectral lines.

An instrument consisting of a combination of a telescope and grating spectroscope allowsastronomers to analyze light emitted by distant objects. One purpose of such analysis is todetermine the red shift and recessional velocity of very distant objects, such as quasars.

Suppose that a telescope-spectroscope combination includes a diffraction grating with a lineseparation of 4.000�10�6 m. When the instrument measures light wavelengths from the nearbystar Vega, the angle at which the principal maximum of the strong H� spectral line from hydrogenis observed at �1 � 9.444°. However, the observed angle for the same H� spectral line from a verydistant quasar is �2 � 10.88°.

a. Compute the wavelengths in nanometers observed from Earth of the H� spectral lines for Vegaand for the distant quasar.

b. Vega has a small nonzero velocity with respect to Earth, but it may be considered to be at restfor practical purposes. Compute the radial velocity, as a fraction of the speed of light, withwhich the distant quasar is receding from Earth.



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Static Electricity1. The relationship between the electrostatic force between two charged particles and the distance

between them is most similar to the relationship between the

a. period of a planet and its distance from the Sun.

b. moment of inertia of a planet and its mean radius.

c. gravitational force on a planet and its distance from the Sun.

d. kinetic energy of a planet and its velocity around the Sun.

2. Students are preparing a demonstration of electrostatic phenomena. They are selecting objects thatthey can rub and then hold near bits of cloth, paper, or tape to see if these materials are attractedor repelled. When selecting objects to rub, students should choose those that are made ofmaterials that are

a. chemically reactive. c. negatively charged.

b. poor conductors. d. magnetic metals.

3. In a television set, a beam of electrons is shot horizontally from the rear of the TV tube toward thescreen with a speed about 1.0�107 m/s. If the distance from the rear of the TV set to the front is0.5 m, approximately how far do the electrons drop because of gravity as they move across thetube?

a. 1.2 mm c. 1.2�10�13 m

b. 1.2�10�4 m d. 1.2�10�14 m

4. A sodium atom with a mass of 3.39�10�25 kg and a charge of 1 is hovering 3.00 m above theground. A second particle with a mass of 9.71�10�10 kg is fixed in space exactly 3.00 m rightabove it. Assuming this is happening in a vacuum and that the ground has no net charge, what isthe difference between the number of protons and the number of electrons in the second particle?

Date Period Name



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5. Look at the two sets of parallel plates illustrated below. The constant potential difference, V, is thesame between each set. Each set of plates is held at the same constant potential difference, V. Theleft-side plates are positive with respect to the right-side plates. Between each set of plates, smallplastic beads, each with the same mass, m, are suspended by threads of negligible mass and fixedto points between the plates at the top. The beads carry charges q1 and q2 respectively. The beadsdeflect as shown so that �1 � 15.1° and �2 � 22.4°.

a. If E is the magnitude of the electric field between the plates, T is the tension in the thread, andg is the acceleration of gravity, sketch a diagram showing the forces acting on the bead carryingcharge q1.

b. What is the ratio of the magnitudes of the charges, ?

c. If the magnitude of the electric field between each set of plates is E � 2250 V/m and the massof each bead is m � 0.0152 kg, what are the signs, and magnitudes in micro-coulombs, ofcharges q1 and q2?

�q2��q1�

�1

q1

��

��

��

��

��

��

��

��

��

��

��

��

�2

q2

��

��

��

��

��

��

��

��

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��

��

��



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Electric Fields1. When a test charge is used to measure the electric field around a charged object, the test charge

must be very small, primarily so that it

a. is not significantly affected by the electric field of Earth.

b. is not significantly affected by the gravitational pull of Earth.

c. does not exert an electric force strong enough to move the charged object.

d. does not exert a gravitational force strong enough to move the charged object.

2. A voltmeter measures

a. potential energy. c. electric field intensity at a charge.

b. change in charge magnitude. d. work needed to move a unit charge.

Use the diagram below to answer problems 3 and 4.

3. The diagram above illustrates the electric field lines between three equally spaced objects. Whatcould be the charges on those objects?

a. A, B�, C� c. A�, B�, C

b. A, B, C d. A, B�, C

4. Position A and position B are said to be at equipotential if

a. no work is done in moving a charge from A to B.

b. no outside force is needed to move a charge from A to B.

c. A and B are located in electric fields equal in strength but opposite in direction.

d. A and B are located in electric fields that are equal in both strength and direction.

5. Approximately how many electrons must be placed on each of two small spheres placed 3.00 cmapart if the force of repulsion between the spheres is to be 1.00�10�19 N?

a. 2 c. 62,500

b. 625 d. 390,625

A

B

C

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Use the diagram below to answer problems 6a–d.

6. The diagram above depicts an electron (mass, me � 9.11�10�31 kg) entering a parallel-platecapacitor that is contained in a vacuum and maintained at a constant potential difference of 40.0 V. Upon entry, the initial velocity of the electron is v � 5.06�106 m/s parallel to the plates.After traveling a distance x = 2.38 cm across the plates, the electron exits the capacitor havingdeflected a distance of z � 0.725 cm toward the positively charged plate.

a. What is the magnitude of the electric field inside the capacitor?

b. What is the velocity of the electron when it leaves the capacitor?

c. By how much does the kinetic energy of the electron change while it is inside the capacitor?

d. How much distance separates the plates of the capacitor?

�

��

� � ��

0.725 cm

v

E

2.38 cm



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Current Electricity1. In a simple circuit a voltage of 5.0 V is applied across a resistance of 10.0 �. What is the power

dissipated in the resistor?

a. 0.50 W

b. 2.5 W

c. 5.0 W

d. 5.0�101 W

2. When power companies send electricity to consumers, they

a. increase the voltage in order to send energy faster.

b. increase the current in order to send energy at a lower voltage.

c. decrease the current in order to reduce the amount of energy lost.

d. decrease the voltage in order to reduce the amount of power in the lines.

3. A series circuit consists of a switch, a 6-V battery, a lightbulb, and some copper wire. Whenever thecircuit is turned on, each of these elements has the same

a. current through it.

b. potential difference across it.

c. resistance in it.

d. temperature.

4. A 1.5-A current runs a heater that has a resistance of 130 �. How much thermal energy isproduced when the heater is on for 15 min?

a. 2.9�102 J

b. 7.8�104 J

c. 1.8�195 J

d. 2.6�105 J

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5. An electronic device that runs on a configuration of rechargeable cells draws a DC current of 390 mA and requires a supply voltage of 3.6 V. The device must operate for a minimum of 10 hbetween full charges. When fully charged, one of the cells specified for this device produces anEMF of 1.2 V and current-time of 2200 mA-h.

a. What is the minimum number of rechargeable cells required to fulfill the power supply specifi-cations described above? Sketch the configuration of this minimum number of rechargeablecells in order to fulfill the requirements specified.

b. How much energy in joules does the device dissipate in 10.0 h?

c. How much total charge flows from the source cells through the device in 10.0 h?



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Series and Parallel Circuits1. A student lacks the 4-k� resistor needed to finish building a circuit. The student does have a

3.0-k�, a 6.2-k�, and a 9.1-k� resistor. Which of the following choices shows how these resistorscan be arranged so that the equivalent resistance is closest to 4 k�?

a. c.

b. d.

2. The circuit shown below is plugged into a 240-V DC outlet. How many electrons flow through thewire at point A in 1 min?

a. 6.0�1021 c. 1.1�1022

b. 9.0�1021 d. 1.2�1022

3. Seven resistors are connected as shown in the diagram below. Find the equivalent resistancebetween the points A and B.

a. 34.2 k� c. 13.2 k�

b. 7.45 k� d. 9.0 k�

A

6.2 k�

3.0 k� 1.0 k�

B

2.0 k� 5.0 k�

14 k�

3.0 k�

A

5.0 �5.0 �

5.0 �

�

3.0 k�

6.2 k�

9.1 k�3.0 k�

9.1 k�

6.2 k�

6.2 k�

3.0 k�

9.1 k�3.0 k� 9.1 k�6.2 k�

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4. A lightbulb designed to dissipate 75 W when it is connected to a 125-V source is connected in acircuit with an 1850-W, 125-V hot plate and an 875-W, 125-V coffee maker. The circuit is designedso that if the lightbulb burns out, the other appliances continue to operate as intended.

a. Draw a schematic diagram that shows the components in a complete circuit. Include ammetersand voltmeters.

b. Could the three appliances be operated simultaneously on a circuit protected by a 20-A circuitbreaker?

c. What is the resistance of each device? Use this result to determine the equivalent resistance forthe appliances in this circuit.

d. If the lightbulb were to burn out, what would happen to the amount of current through theother appliances?



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Magnetic Fields1. If the bar magnet shown to the right is broken in

half, at which point will the magnetic flux havethe lowest magnitude?

a. A c. C

b. B d. D

2. Which diagram best illustrates the orientation of the magnetic domains in the object shown below?Assume the darker shading on the needles is the north pole.

a. c.

b. d.

3. A straight 0.20-m-long piece of wire carrying 8.0�1019 electrons/s is oriented horizontally atEarth’s south magnetic pole. Assuming Earth’s magnetic field is 1.0�10�4 T, what is the force ofEarth’s magnetic field on the wire?

a. 0 N c. 2.6�104 N

b. 2.6�10�4 N d. 1.6�1015 N

4. What is the absolute value of the maximum ratio of the magnetic force to the gravitational forceon a proton traveling near Earth’s surface at one-half the speed of light in Earth’s magnetic field?(Earth’s magnetic field is 1.0�10�4 T and a proton’s mass is 1.67�10�27 kg.)

a. 1.0 c. 2.4�10�15

b. 1.6�10�26 d. 1.5�1011

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N S N S N S

N S N S N S

N S N S

S N S N S N

S N S N S N

S N S N

N

S

N

S

N

S

N

S

N

S

N

S

S

N

S

N

S

N

S

N

S

N

S

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N S

A B

C

D

5. Isotopes are atoms of the same element that have slightly different masses. Sometimes it is desiredthat isotopes be separated. Scientists may use an instrument called a mass spectrometer for thispurpose. For example, geologists separate isotopes of the element rubidium, 85

37Rb with atomic mass84.912 u (u � 1.4105�10�25 kg) and 87

37Rb with atomic mass 86.909 u (u � 1.4437�10�25 kg), insamples prepared from certain rock materials in one process used to date the rocks.

Part of a mass spectrometer is illustrated above. Processed samples become a stream of singlyionized atoms that enter a region of constant magnetic field, B, after being accelerated to avelocity, v, in the direction shown. Isotopes follow circular paths of different radii.

a. Write a general equation giving path radius, r, in terms of ion mass, m, ion charge q, magneticfield strength, B, and speed, v. Hint: The magnetic force creates the centripetal acceleration.

b. Let the speed of the rubidium atoms entering the instrument be v = 1.25�105 m/s and themagnetic field strength be B � 0.750 T. What is the distance, d, between atoms of the rubidi-um isotopes Rb87

37 and Rb8537 following paths of radii r85 and r87?

Rb85

2r85

2r87

Rb87

d

B

v



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Electromagnetic Induction1. EMF is best described as a(n)

a. electric force.

b. energy measure.

c. charge flow rate.

d. potential difference.

2. Which graph best describes the electromotive force generated by rotating a wire loop in a uniformmagnetic field? Assume the wire is part of a closed circuit and its direction changes from 0° to180° relative to the field’s direction.

a. c.

b. d.

0� 180�90�

Angle (�)

EMF

0� 180�90�

Angle (�)

EMF

0� 180�90�

Angle (�)

EMF

0� 180�90�

Angle (�)

EMF

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3. What is the minimum velocity that a 30.0-cm-long loop of wire must be rotated through Earth’smagnetic field in order to induce an electromotive force of 1.8 �V? Assume a field strength of5.0�10�5 T.

a. 0.0 m/s c. 1.2�10�3 m/s

b. 1.2�10�5 m/s d. 1.2�10�1 m/s

4. An 18-kV neon sign is connected to a transformer and plugged into a conventional outlet (U.S.). Ifthe primary coil in the transformer has 300 turns, how many coils does the secondary coil have?

a. 2 c. 450

b. 150 d. 45,000

5. You need to build a step-down transformer capable of reducing the input voltage, where EMF � 480 kV, to an output voltage of 240 V.

a. You supply the output voltage to an appliance that dissipates 1.5 kW. If the transformer is 95 percent efficient, what power is delivered at 480 kV?

b. Find the currents flowing through the primary and secondary circuits of the transformer.

c. Which coil must have the most turns, the primary or the secondary? Prove this using the trans-former equation.



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Electromagnetism1. An electron is moving with a velocity, v, out of the page. For which arrangement of magnets and

charged plates would it be possible to exert two equal but opposite forces on the electron?

a. c. d.

b.

2. A particle with a charge-to-mass ratio of 4.8�1011 C/kg starts at rest and is accelerated by 2.6�108 m/s2 over a distance of 1.0 km, after which it maintains constant velocity. The particlethen encounters a magnetic field with a strength of 0.12 mT. Assuming no other forces are acting on the particle, what is the radius of its path?

a. 4.5�103 m c. 1.3�10�2 m

b. 4.5�101 m d. 1.3�10�3 m

3. Protons move through a mass spectrometer utilizing a magnetic field of 0.60 T, following a pathwhose radius of curvature is 3.0 cm. What is the potential difference through which the protonsare accelerated?

a. 2.6�10�15 V c. 1.7�106 V

b. 1.6�104 V d. 2.9�107 V

4. Which statement or statements below can accurately complete this sentence: “Unlike sound waves,electromagnetic waves

a. transfer energy.”

b. can be generated by vibrations.”

c. do not require a medium to travel through.”

d. do not change velocity when they move from one medium to another.”

�

�

SNSN

�

�

S

N

S

N

�

�

N

S

N

S

�

�

NSNS

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5. A jeweler has been presented with a large piece of amber for appraisal. Lately, a great deal of fakeamber has been in circulation. People are passing off acrylic resin and colored glass beads asamber. The jeweler has invented a device that measures the refraction of light when it passesthrough an unknown material.

a. How can the jeweler use the known dielectric constant of each material to determine whetheror not the appraised piece is actually amber?

b. When light travels through the piece presented for appraisal, it has a refractive index of 1.9.Determine the identity of the material.

c. What is the velocity of light through the piece that the jeweler appraises?



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Material Dielectric Constant (K)

Amber 2.85

Acrylic resin 3.60

Glass beads 3.10

Quantum Theory1. Whether or not electrons are ejected from a metal exposed to electromagnetic radiation depends

on the radiation’s .

a. speed c. wavelength

b. intensity d. incidence angle

2. When light strikes the surface of a solid, it causes an increase in the vibrational energy of thesolid’s atoms. Which graph most accurately describes this increase in vibrational energy of an atomover time?

a. c.

b. d.

3. According to Einstein’s theory of relativity, a particle’s rest energy (or the potential energy of themass, the energy it has when at rest) is given by E � mc2, where m is the particle’s mass and c is thespeed of light. What is the energy, in eV, of an electron?

a. 5.1 eV c. 8.2�10�14 eV

b. 5.1�105 eV d. 9.1�10�31 eV

4. When yellow light from a sodium lamp (wavelength 589 nm) shines on a certain material, anegative potential of 0.300 V is needed to stop all the electrons from reaching the collector. Whatpotential will be needed to stop the electrons if light with a wavelength of 438 nm is used instead?

a. �0.700 V c. 1.09 V

b. 0.303 V d. 1.03 V

Vib

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Time

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Time

Vib

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Time

Vib

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on

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Time

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5. A laser shines on a metal plate with the photoelectric properties described in the graph above.

a. What is the threshold frequency of the metal plate?

b. If the measured kinetic energy of the photoelectrons emitted from the plate is 3.30 eV, what isthe wavelength of the laser light?

c. What is the frequency of the laser?

d. What kind of radiation is emitted from the laser?

5.00 6.00 7.00 8.00 9.00 10.00 11.000.00

1.00

2.00

Max

imu

m k

inet

ic e

ner

gy

(eV

)

Frequency (�1014 Hz)

Maximum Kinetic Energy ofPhotoelectrons v. Frequency



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The Atom1. Rutherford’s planetary model of the atom is least consistent with which of the following

observations?

a. Most of an atom’s mass is in its nucleus.

b. A photon can impart momentum to an electron.

c. Atoms emit radiation of only certain wavelengths.

d. Electrons and protons have equal and opposite charges.

2. The emission spectrum of an atom provides information primarily regarding

a. the mass of the nucleus.

b. the energy levels of the atom.

c. the wavelike behavior of protons.

d. the magnitude of an electric charge.

3. Which of the following most likely describes the image shown below?

a. emission spectrum of a neon sign

b. absorption spectrum of an outer planet

c. emission spectrum of an incandescent solid

d. absorption spectrum of the upper atmosphere

4. Which of the following statements is (are) true?

I. An excited atom can return to its ground state by absorbing electromagnetic radiation.

II. The energy of an atom is increased when electromagnetic radiation is emitted from it.

III. The energy of electromagnetic radiation increases as its frequency increases.

IV. An electron in the n � 4 state in the hydrogen atom can go to the n � 2 state by emittingelectromagnetic radiation at the appropriate frequency.

V. The frequency and wavelength of electromagnetic radiation are inversely proportional to each other.

a. II, III, IV c. I, II, III

b. III, V d. III, IV, V

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5. Derive an expression to describe the frequency of rotation of the lowest energy electron (n � 1) inBohr’s model of the atom.

6. At what percentage of the speed of light does an electron in the third orbit of the Bohr atommove?

7. The thermal energy of a particle of an ideal gas at Kelvin temperature T is given by the equation

E � �32

� kT, where k has a value of 1.38�10�23 J/K.

a. At what minimum temperature would the thermal energy of a particle of an ideal gas be suffi-cient to excite a hydrogen atom from the n � 1 to the n � 2 state?

b. At what minimum temperature will the thermal energy of a particle of an ideal gas be sufficient to ionize a hydrogen atom?



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Solid-State Electronics1. Copper has 1 free electron per atom, or 8.49�1022 free electrons per cm3. How many free

electrons exist in 1 kg of copper?

a. 8.49�1022

b. 6.02�1023

c. 9.51�1024

d. 7.61�1026

2. If a fixed potential difference applied across a material creates a current that increases as thematerial heats up, the material is most likely

a. silicon.

b. rubber.

c. copper.

d. aluminum.

3. One difference between a diode and a transistor is that

a. transistors use two dopants.

b. diodes are used in microchips.

c. they use different types of dopants.

d. they use different types of junctions.

4. If a material contains overlapping conduction and valence bands, both of which are partiallyfilled, then

a. no potential difference is required to induce a current in the material.

b. the acceleration of electrons will require a relatively large input of radiation.

c. the conductance of the material will be directly related to its temperature.

d. a small electric field will make electrons move from one atom to another.

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5. Diodes conduct charges in one direction only, and can be considered a type of electronic valve. If abattery is connected such that its positive terminal is to the p side of the diode, the diode isforward-biased. If the negative terminal is to the p side, the diode is reverse-biased.

a. Is an LED forward-biased or reverse-biased when it emits light? Explain.

b. An LED produces light with a wavelength of 650 nm when an electron moves from the con-duction band to the valence band. What color light is emitted. How do you know?

c. What must be the width of the forbidden gap, in eV, in this diode?



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The Nucleus1. The strong nuclear force overcomes

a. the repulsive electromagnetic force between two atomic nuclei.

b. the repulsive electromagnetic force between protons in a nucleus.

c. the attractive electromagnetic force between a nucleus and the electrons that surround it.

d. the attractive electromagnetic force between a nucleus and the electrons surrounding another atom.

2. The energy released during nuclear fission is equal to the

a. strong nuclear force between the two fission products.

b. repulsive electric force between the splitting protons.

c. energy equivalent of the mass lost in the reaction.

d. binding energy in the fission products.

3. An atom emits an electron from the nucleus when

a. a high-energy photon is emitted.

b. a proton is formed from a neutron.

c. there is enough energy to cross the forbidden gap between energy bands.

d. the frequency of incident radiation exceeds the threshold frequency of the atom.

4. When two quarks are forced apart, the force that is carried by gluons behaves most similarly to a(n)

a. dipole magnetic force.

b. gravitational force.

c. electric force.

d. spring force.

5. Plutonium-236 (23694Pu) has a half-life of 2.85 years due to alpha decay. This means that, after

8.55 years, 100 g of plutonium-236

a. will have decayed to 12.5 g by emitting helium atoms.

b. will have decayed to 12.5 g by emitting helium nuclei.

c. will have decayed to 12.5 g by transforming neutrons into protons.

d. will still be 100 g of plutonium-236 because it emitted photons only.

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6. When Rutherford scattered � particles off the thin gold foil, he discovered that the atomic radiuswas over 18,000 times the size of its nucleus. The radius, r, of a nucleus is roughly equal to a

constant, R0, multiplied by its mass number to the �13

� power, A�13�, where r0 � 1.2�10�15 m.

Assuming a nucleus is spherical, what is the volume as a function of mass number?

7. The number of nuclei remaining in a sample of a radioactive isotope after time t is given by the equation, N � N0e��t. In this equation, N represents the number of nuclei remaining, N0 represents the original number of nuclei present in the sample, e has the value 2.718, � is the activity constant, and t is the time that has passed.

a. If � and t are positive values, describe what happens to the magnitude of N as time passes.

b. Show that, if t � , N � N0.

c. The activity constant of radon-219 (Rn85218) is 0.177 s�1. (You can interpret the constant as

meaning 17.7% of the remaining nuclei in a sample of radon-219 will decay in 1 s.) What isthe half-life of Rn85

218?

1�2

0.693�

�



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