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Section 1:Kinematics
1. The displacement x of an object moving along the x-axis is shown above as a function of time t. The acceleration of this object must be
A. zero
B. constant but not zero
C. increasing
D. decreasing
E. equal to g
2. A 2-kilogram block rests at the edge of a platform that is 10 meters above level ground. The block is launched horizontally from the edge of the platform with an initial speed of 3 meters per second. Air resistance is negligible. The time it will take for the block to reach the ground is most nearly
A. 0.3 s
B. 1.0 s
C. 1.4 s
D. 2.0 s
E. 3.0 s
3. A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v?
A. d
B. √2 d
C. 2d
D. 4d
E. It cannot be determined unless the height of the cliff is known.
4. Which of the following pairs of graphs shows the distance traveled versus time and the speed versus time for an object uniformly accelerated from rest at time t = 0?
A. Distance Speed
B. Distance Speed
C. Distance Speed
D. Distance Speed
E. Distance Speed
5. 
An object released from rest at time t = 0 slides down a frictionless incline a distance of 1 meter during the first second. The distance traveled by the object during the time interval from t = 1 second to t = 2 seconds is
A. 1 m
B. 2 m
C. 3 m
D. 4 m
E. 5 m
Time t1 Time t2
6. Vectors V1 and V2 shown above have equal magnitudes. The vectors represent the velocities of an object at times t1 and t2, respectively. The average acceleration of the object between time t1 and t2 was
A. zero
B. directed north
C. directed west
D. directed north of east
E. directed north of west
7. A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30° above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
A. 5 m
B. 10 m
C. 500 m
D. 1000 m
E. 2000 m
8. A particle moves along the x-axis with a non-constant acceleration described by a = 12t, where a is in meters per second squared and t is in seconds. If the particle starts from rest so that its speed v and position x are zero then t = 0, where is it located when t = 2 seconds?
A. x = 12 m
B. x = 16 m
C. x = 24 m
D. x = 32 m
E. x = 48 m
9. A rock is dropped from the top of a 45-meter tower and at the same time a ball is thrown from the top of the tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a distance of 30 meters apart. The horizontal velocity of the ball thrown was most nearly
A. 5 m/s
B. 10 m/s
C. 14.1 m/s
D. 20 m/s
E. 28.3 m/s
10. 
An object is thrown with a horizontal velocity of 20 m/s from a cliff that is 125 m above level ground. If air resistance is negligible, the time that it takes the object to fall to the ground from the cliff is most nearly
A. 3 s
B. 5 s
C. 6 s
D. 12 s
E. 25 s
11. The motion of a particle along a straight line is represented by the position versus time graph above. At which of the labeled points on the graph is the magnitude of the acceleration of the particle greatest?
A. A
B. B
C. C
D. D
E. E
Questions 12 – 13
The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation:
v = 4 + 2t3
12. What is the acceleration of the automobile at t = 2 s?
A. 12 m/s2
B. 16 m/s2
C. 20 m/s2
D. 24 m/s2
E. 28 m/s2
13. How far has the automobile traveled in the interval between t = 0 and t = 2 s?
A. 16 m
B. 20 m
C. 24 m
D. 32 m
E. 72 m
14. In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration of about 9.8 m/s2. This means that
A. speed of the object increases 9.8 m/s during each second
B. speed of the object as it falls is 9.8 m/s
C. object falls 9.8 meters during each second
D. object falls 9.8 meters during the first second only
E. derivative of the distance with respect to time for the object equals 9.8 m/s2
15. A 500-kilogram sports car accelerates uniformly from rest, reaching a speed of 30 meters per second in 6 seconds. During the 6 seconds, the car has traveled a distance of
A. 15 m
B. 30 m
C. 60 m
D. 90 m
E. 180 m
16. An object is shot vertically upward into the air with a positive initial velocity. Which of the following correctly describes the velocity and acceleration of the object at its maximum elevation?
Velocity Acceleration
A. Positive Positive
B. Zero Zero
C. Negative Negative
D. Zero Negative
E. Positive Negative
1. A system in equilibrium consists of an object of weight W that hangs from three ropes, as shown above. The tensions in the ropes are T1, T2, and T3. Which of the following are correct values of T2, and T3?
T2 T3
A. W tan 60° W/cos 60°
B. W tan 60° W/sin 60°
C. W tan 60° W sin 60°
D. W/tan 60° W/cos 60°
E. W/tan 60° W/sin 60°
2. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the Earth, then which of the following is true?
A. F1 is much greater than F2.
B. F1 is slightly greater than F2.
C. F1 is equal to F2.
D. F2 is slightly greater than F1.
3. 
A ball initially moves horizontally with velocity vi, as shown above. It is then struck by a stick. After leaving the stick, the ball moves vertically with a velocity vf, which is smaller in magnitude than vi. Which of the following vectors best represents the direction of the average force that the stick exerts on the ball?
A. B.
C. D.
E.
4. A newly discovered planet, “Cosmo,” has a mass that is 4 times the mass of the Earth. The radius of the Earth is Re. The gravitational field strength at the surface of Cosmo is equal to that at the surface of the Earth if the radius of Cosmo is equal to
A. ½ Re
B. Re
C. 2 Re
D. √Re
E. Re2
5. A block of mass 5 kilograms lies on an inclined plane, as shown above. The horizontal and vertical supports for the plane have lengths of 4 meters and 3 meters, respectively. The coefficient of friction between the plane and the block is 0.3. The magnitude of the force F necessary to pull the block up the plane with constant speed is most nearly
A. 30 N
B. 42 N
C. 49 N
D. 50 N
E. 58 N
6. A particle of mass m moves along a straight path with a speed v defined by the function v = bt2 + c, where b and c are constants and t is time. What is the magnitude F of the net force on the particle at time t = t1?
A. bt12 + c
B. 3mbt1 + 2c
C. mbt1
D. mbt1 + c
E. 2mbt1
7. The radius of the Earth is approximately 6,000 kilometers. The acceleration of an astronaut in a perfectly circular orbit 300 kilometers above Earth would be most nearly
A. 0 m/s2
B. 0.05 m/s2
C. 5 m/s2
D. 9 m/s2
E. 11 m/s2
8. 
Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2, respectively. If R2 = 2R1, the accelerations a2 and a1 of the two satellites are related by which of the following?
A. a2 = 4a1
B. a2 = 2a1
C. a2 = a1
D. a2 = a1/2
E. a2 = a1/4
9. 
A block of mass 2 kg slides along a horizontal tabletop. A horizontal applied force of 12 N and a vertical applied force of 15 N act on the block, as shown above. If the coefficient of kinetic friction between the block and the table is 0.2, the frictional force exerted on the block is most nearly
A. 1 N
B. 3 N
C. 4 N
D. 5 N
E. 7 N
10. A block of weight W is pulled along a horizontal surface at constant speed v by a force F, which acts at an angle of θ with the horizontal, as shown above. The normal force exerted on the block by the surface has magnitude
A. W - F cos θ
B. W - F sin θ
C. W
D. W + F sin θ
E. W + F cos θ
11. 
Mars has a mass one tenth that of Earth and a diameter one half that of Earth. The acceleration of a falling body near the surface of Mars is most nearly
A. 0.25 m/s2
B. 0.5 m/s2
C. 2 m/s2
D. 4 m/s2
E. 25 m/s2
12. When an object of weight W is suspended from the center of a massless string as shown above, the tension at any point in the string is
A. 2W cos θ
B. (W cos θ) / 2
C. W cos θ
D. W / (2 cos θ)
E. W / cos θ
13. An object weighing 4 newtons swings on the end of a string as a simple pendulum. At the bottom of the swing, the tension in the string is 6 newtons. What is the magnitude of the centripetal acceleration of the object at the bottom of the swing?
A. 0
B. 0.5 g
C. 1.0 g
D. 1.5 g
E. 2.5 g
14. A satellite moves in a stable circular orbit with speed vo at a distance R from the center of a planet. For this satellite to move in a stable circular orbit a distance 2R from the center of the planet, the speed of the satellite must be
A. vo / 2
B. vo / √2
C. vo
D. √(2 vo)
E. 2 vo
15. Two blocks are pushed along a horizontal frictionless surface by a force of 20 newtons to the right, as shown above. The force that the 2-kilogram block exerts on the 3-kilogram block is
A. 8 newtons to the left
B. 8 newtons to the right
C. 10 newtons to the left
D. 12 newtons to the right
E. 20 newtons to the left
16. Two 0.60-kilogram objects are connected by a thread that passes over a light, frictionless pulley, as shown above. The objects are initially held at rest. If a third object with a mass of 0.30 kilogram is added on top of one of the 0.60-kilogram objects as shown and the objects are released, the magnitude of the acceleration of the 0.30-kilogram object is most nearly
A. 10.0 m/s2
B. 6.0 m/s2
C. 3.0 m/s2
D. 2.0 m/s2
E. 1.0 m/s2
17. A mass m moves on a curved path from point X to point Y. Which of the following diagrams indicates a possible combination of the net force F on the mass, and the velocity v and acceleration a of the mass at the location shown?
A. B.
C. D.
E.
1. 
Let g be the acceleration due to gravity at the surface of a planet of radius R. Which of the following is a dimensionally correct formula for the minimum kinetic energy K that a projectile of mass m must have at the planet’s surface if the projectile is to escape from the planet’s gravitational field?
A. K = Ö(gR)
B. K = mgR
C. K = mg/R
D. K = mÖ(g/R)
E. K = gR
2. The constant force F with components Fx = 3 N and Fy = 4 N, shown above, acts on a body while that body moves from the point P (x = 2 m, y = 6 m) to the point Q (x = 14 m, y = 1 m). How much work does the force do on the body during this process?
A. 16 J
B. 30 J
C. 46 J
D. 56 J
E. 65 J
3. A ball is thrown upward. At a height of 10 meters above the ground, the ball has potential energy of 50 joules (with potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height reached by the ball is most nearly
A. 10 m
B. 20 m
C. 30 m
D. 40 m
E. 50 m
4. During a certain time interval a constant force delivers an average power of 4 watts to an object. If the object has an average speed of 2 meters per second and the force acts in the direction of motion of the object, the magnitude of the force is
A. 16 N
B. 8 N
C. 6 N
D. 4 N
E. 2 N
5. 
A weight lifter lifts a mass m at a constant speed to a height h in time t. How much work is done by the weight lifter?
A. mg
B. mh
C. mgh
D. mght
E. mgh/t
6. A conservative force has the potential energy function U(x), shown by the graph above. A particle moving in one dimension under the influence of this force has kinetic energy 1.0 joule when it is at position x1. Which of the following is a correct statement about the motion of the particle?
A. It oscillates with maximum position x2 and minimum position x0.
B. It moves to the right of x3 and does not return.
C. It moves to the left of x0 and does not return.
D. It comes to rest at either x0 or x2.
E. It cannot reach either x0 or x2.
7. When an object is moved from rest at point A to rest at point B in a gravitational field, the net work done by the field depends on the mass of the object and
A. the positions of A and B only
B. the path taken between A and B only
C. both the positions of A and B and the path taken between them
D. the velocity of the object as it moves between A and B
E. the nature of the external force moving the object from A to B
8. A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is point at an angle of 45° from the vertical, what maximum height can now be reached by the projectile?
A. h/4
B. h/(2Ö2)
C. h/2
D. h/Ö2
E. h
9. 
A small mass is released form rest at a very great distance from a larger stationary mass. Which of the following graphs best represents the gravitational potential energy U of the system of the two masses as a function of time t?
A. B.
C. D.
E.
10. A rock is lifted for a certain time by a force F that is greater in magnitude than the rock’s weight W. The change in kinetic energy of the rock during this time is equal to the
A. work done by the net force (F – W)
B. work done by F alone
C. work done by W alone
D. work done by the net force (F – W) minus the increase in the rock’s potential energy
E. difference in the potential energy of the rock before and after this time
11. A 10-kilogram body is constrained to move along the x-axis. The potential energy U of the body in joules is given as a function of its position x in meters by U(x) = 6x2 – 4x + 3. The force on the particle at x = 3 meters is
A. 32 N in + x direction
B. 32 N in – x direction
C. 45 N in + x direction
D. 45 N in – x direction
E. 98 N in + x direction
12. 
A horizontal force F is used to pull a 5-kilogram block across a floor at a constant speed of 3 meters per second. The frictional force between the block and the floor is 10 newtons. The work done by the force F in 1 minute is most nearly
A. 0 J
B. 30 J
C. 600 J
D. 1350 J
E. 1800 J
13. A pendulum consists of a ball of mass m suspended at the end of a massless cord of length L as shown above. The pendulum is drawn aside through an angle of 60° with the vertical and released. At the low point of its swing, the speed of the pendulum ball is
A. √(g L)
B. √(2g L)
C. 0.5 g L
D. g L
E. 2 g L
Section 4: Momentum and Systems of Particles
1. 
The sum of all the external forces on a system of particles is zero. Which of the following must be true of the system?
A. The total mechanical energy is constant.
B. The total potential energy is constant.
C. The total kinetic energy is constant.
D. The total linear momentum is constant.
E. It is in static equilibrium.
2. 
A toy cannon is fixed to a small cart and both move to the right with speed v along a straight track, as shown above. The cannon points in the direction of motion. When the cannon fires a projectile the cart and cannon are brought to rest. If M is the mass of the cart and cannon combined with out the projectile, and m is the mass of the projectile, what it the speed of the projectile relative to the ground immediately after it is fired?
A. Mv/m
B. (M + m)v/m
C. (M - m)v/m
D. mv/M
E. mv/(M - m)
3. A ball of mass M and speed v collides head-on with a ball of mass 2M and speed v/2, as shown above. If the two balls stick together, their speed after the collision is
A. 0
B. v/2
C. Ö2 v/2
D. Ö3 v/2
E. 3v/2
4. 
Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 m/s, 0°. It then collides elastically with identical ball Y, which is initially at rest, as shown in the diagram above (not to scale). After the collision, ball X moves at velocity 6 m/s, 53°. Which of the following best represents the speed, v, and direction f of ball Y after the collision?
A. v = 0, f = 0°
B. v = 10 m/s, f = 0°
C. v = 4 m/s, f = 37°
D. v = 8 m/s, f = 37°
E. v = 8 m/s, f = 53°
5. A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground. How does the balloon move relative to the ground?
A. Up with speed v
B. Up with a speed less than v
C. Down with speed v
D. Down with a speed less than v
E. The balloon does not move.
6. An object of mass m is moving with speed vo to the right on a horizontal frictionless surface when it explodes into two pieces. Subsequently, one piece of mass 2m/5 moves with a speed vo/2 to the left across the surface. The speed of the other piece of the object is
A. vo/2
B. vo/3
C. 7 vo/5
D. 3 vo/2
E. 2 vo
7. A rod of negligible mass is pivoted at a point that is off-center, so that length l1 is different from length l2. The figures above show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is the value of m in terms of the known masses?
A. M1 + M2
B. (M1 + M2)/2
C. M1M2
D. M1M2/2
Questions 8 – 9
A 4 kg mass has a speed of 6 m/s on a horizontal frictionless surface, as shown above. The mass collides head-on and elastically with an identical 4 kg mass initially at rest. The second 4 kg mass then collides head-on and sticks to a third 4 kg mass initially at rest.
8. The final speed of the first 4 kg mass is
A. 0 m/s
B. 2 m/s
C. 3 m/s
D. 4 m/s
E. 6 m/s
9. The final speed of the two 4 kg masses that stick together is
A. 0 m/s
B. 2 m/s
C. 3 m/s
D. 4 m/s
E. 6 m/s
10. 
A projectile of mass M1 is fired horizontally from a spring gun that is initially at rest on a frictionless surface. The combined mass of the gun and projectile is M2. If the kinetic energy of the projectile after firing is K, the gun will recoil with a kinetic energy equal to
A. K
B. (M1/M2) K
C. (M1/M2)2 K
D. (M1/(M2 -M1)) K
E. ÖM1/(M2 - M1) K
11. A piece of wire of uniform cross section is bent in the shape shown above. What are the coordinates (x, y) of the center of mass?
A. (15/14, 6/7)
B. (6/7, 6/7)
C. (15/14, 8/7)
D. (1, 1)
E. (1, 6/7)
Section 5: Rotational Motion
1. 
A disk X rotates freely with angular velocity w on frictionless bearings, as shown above. A second identical disk Y, initially not rotating, is placed on X so that both disks rotate together without slipping. When the disks are rotating together, which of the following is half what it was before?
A. Moment of inertia of X
B. Moment of inertia of Y
C. Angular velocity of X
D. Angular velocity of Y
E. Angular momentum of both disks
2. The ring and the disk shown above have identical masses, radii, and velocities, and are not attached to each other. If the ring and the disk each roll without slipping up an inclined plane, how will the distances that they move up the plane before coming to rest compare?
A. The ring will move farther than will the disk.
B. The disk will move farther than will the ring.
C. The ring and the disk will move equal distances.
D. The relative distances depend on the angle of elevation of the plane.
E. The relative distances depend on the length of the plane.
3. A figure skater is spinning on frictionless ice with her arms fully extended horizontally. She then drops her arms to her sides. Which of the following correctly describes her rotational kinetic energy and angular momentum as her arms fall?
Kinetic Energy Angular Momentum
A. Remains constant Remains constant
B. Decreases Increases
C. Decreases Decreases
D. Increases Decreases
E. Increases Remains Constant
4. 
A satellite travels around the Sun in an elliptical orbit as shown above. As the satellite travels from point X to point Y, which of the following is true about its speed and angular momentum?
Speed Angular Momentum
A. Remains constant Remains constant
B. Increases Increases
C. Decreases Decreases
D. Increases Remains constant
E. Decreases Remains constant
5. A turntable that is initially at rest is set in motion with a constant angular acceleration a. What is the angular velocity of the turntable after it has made one complete revolution?
A. Ö2a
B. Ö2pa
C. Ö4pa
D. 2a
E. 4pa
6. 
The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed w. If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?
A. 2:1
B. 1:1
C. 1:2
D. 1:4
E. 1:8
7. 
A satellite S is in an elliptical orbit around a planet P, as shown above, with r1 and r2 being its closest and farthest distances, respectively, from the center of the planet. If the satellite has a speed v1 at its closest distance, what is its speed at its farthest distance?
A. v1(r1/r2)
B. v1(r2/r1)
C. v1(r2 - r1)
D. v1(r1 + r2)/2
E. v1(r2 - r1)/(r1 + r2)
Questions 8 – 9
B C D
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above.
8. Which of the five lettered points represents the center of mass of the sphere-rod combination?
A. A
B. B
C. C
D. D
E. E
9. The sphere-rod combination can be pivoted about an axis that is perpendicular to the plane of the page and that passes through one of the five lettered points. Through which point should the axis pass for the moment of inertia of the sphere-rod combination about this axis to be greatest?
A. A
B. B
C. C
D. D
E. E
10. A bowling ball of mass M and radius R, whose moment of inertia about its center is 2/5 MR2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is
A. 1/5 v2/g
B. 2/5 v2/g
C. 1/2 v2/g
D. 7/10 v2/g
E. v2/g
11. A massless rigid rod of length 3d is pivoted at a fixed point W, and two forces each of magnitude F are applied vertically upward as shown above. A third vertical force of magnitude F may be applied, either upward or downward, at one of the labeled points. With the proper choice of direction at each point, the rod can be in equilibrium if the third force of magnitude F is applied at point
A. W only
B. Y only
C. V or X only
D. V or Y only
E. V, W, or X
12. 2F 60° O l 60° 2F O l l/2 F O 2F O l
In which of the following diagrams is the torque about point O equal in magnitude to the torque about point X in the diagram above? (All forces lie in the plane of the paper.)
A. B.
C. D.
E. None of the above
Answers
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