Center of Mass/Momentum
1.
An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped piece is
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
2.
The shaded area in the figure represents a uniformly thick sheet of metal. The center of mass of the sheet is closest to point
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: C
3.
The figure shows a piece of sheet metal suspended in two positions by a string. From the way the metal hangs, you can see that the center of gravity is nearest point
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
4.
The center of mass of the system of particles shown in the diagram is at point
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: B
5. The condition necessary for the conservation of momentum in a given system is that
A) energy is conserved. D) internal forces equal external forces.
B) one body is at rest. E) None of these is correct.
C) the net external force is zero.
Answer: C
6. Momentum is conserved in which of the following?
A) elastic collisions D) collisions between automobiles
B) inelastic collisions E) All of these are correct.
C) explosions
Answer: E
7. A boy and girl on ice skates face each other. The girl has a mass of 20 kg and the boy has a mass of 30 kg. The boy pushes the girl backward at a speed of 3.0 m/s. As a result of the push, the speed of the boy is
A) zero B) 2.0 m/s C) 3.0 m/s D) 4.5 m/s E) 9.0 m/s
Answer: B
8.
Two identical bodies of mass M move with equal speeds v. The direction of their velocities is illustrated in the figure. The magnitude of the linear momentum of the system is
A) 2Mv B) Mv C) 4Mv D) E)
Answer: D
9. A golfball and a Ping-Pong ball are dropped in a vacuum chamber. When they have fallen halfway to the floor, they have the same
A) speed.
B) potential energy.
C) kinetic energy.
D) momentum.
E) speed, potential energy, kinetic energy, and momentum.
Answer: A
10. In any and all collisions of short duration and for which it is true that no external forces act on the collision participants,
A) kinetic energy is conserved.
B) both momentum and kinetic energy are conserved.
C) neither momentum nor kinetic energy is conserved.
D) the relative velocities before and after impact are equal and oppositely directed.
E) momentum is conserved.
Answer: E
11. For a system consisting of two particles that undergo an elastic collision,
A) momentum is conserved but the total energy is not conserved.
B) neither the kinetic energy nor the momentum is conserved.
C) neither the total energy nor the momentum is necessarily conserved.
D) the mechanical energy is conserved but momentum is not conserved.
E) both kinetic energy and momentum are conserved.
Answer: E
12. If a body moves in such a way that its linear momentum is constant, then
A) its kinetic energy is zero.
B) the sum of all the forces acting on it must be zero.
C) its acceleration is greater than zero and is constant.
D) its center of mass remains at rest.
E) the sum of all the forces acting on the body is constant and nonzero.
Answer: B
13. If the momentum of a mass M is doubled, its kinetic energy will be multiplied by a factor of
A) B) 2 C) D) 4 E)
Answer: D
14. An object of mass M1 is moving with a speed v on a straight, level, frictionless track when it collides with another mass M2 that is at rest on the track. After the collision, M1 and M2 stick together and move with a speed of
A) v B) M1v C) (M1 + M2)v/M1 D) M1v/(M1 + M2) E) M1v/M2
Answer: D
15. A 40-kg girl, standing at rest on the ice, gives a 60-kg boy, who is also standing at rest on the ice, a shove. After the shove, the boy is moving backward at 2.0 m/s. Ignore friction. The girl's speed is
A) zero B) 1.3 m/s C) 2.0 m/s D) 3.0 m/s E) 6.0 m/s
Answer: D
16. A moving particle is stopped by a single head-on collision with a second, stationary particle, if the moving particle undergoes
A) an elastic collision with a second particle of much smaller mass.
B) an elastic collision with a second particle of much greater mass.
C) an elastic collision with a second particle of equal mass.
D) an inelastic collision with a second particle of any mass.
Answer: C
17. Two cars of equal mass travel in opposite directions at equal speeds. They collide in a perfectly inelastic collision. Just after the collision, their velocities are
A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.
Answer: A
18. Two equal masses travel in opposite directions with equal speed. If they collide in a perfectly elastic collision, then, just after the collision, their velocities will be
A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.
Answer: C
19. Two equal masses travel in opposite directions with equal speeds. They collide in a collision that is between elastic and inelastic. Just after the collision, their velocities are
A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.
Answer: E
20. In an elastic collision of two objects,
A) momentum is not conserved.
B) momentum is conserved, and the kinetic energy after the collision is less than its value before the collision.
C) momentum is conserved, and the kinetic energy after the collision is the same as the kinetic energy before the collision.
D) momentum is not conserved, and the kinetic energy of the system after the collision differs from the kinetic energy of the system before the collision.
E) the kinetic energy of the system after the collision depends on the masses of the objects.
Answer: C
21. Two balls of equal mass are thrown against a massive wall with equal velocities. The first rebounds with a speed equal to its striking speed, and the second sticks to the wall. The impulse that the first ball transmits to the wall, relative to the second, is
A) twice as great. D) four times as great.
B) half as great. E) one-fourth as great.
C) the same.
Answer: A
22. A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed –v. The impulse imparted to the ball by the wall is
A) 2mv B) mv C) zero D) –mv E) –2mv
Answer: E
23. The center of mass of a system of particles is so defined that
A) it is always at rest.
B) it is always at rest or moving with constant velocity.
C) it always moves in a straight line even if the particles are rotating about it.
D) the kinetic energy of the system is a maximum about any axis through the center of mass.
E) its location depends only on the masses of the particles and their locations.
Answer: E
Circular Motion/Gravity
24. When a particle moves in a circle with constant speed, its acceleration is
A) constantly increasing. D) constant in magnitude.
B) constant in direction. E) constant in magnitude and direction.
C) zero.
Answer: D
25. An object traveling in a circle at constant speed
A) is moving with constant velocity.
B) may be slowing down or picking up speed.
C) experiences no acceleration.
D) experiences an acceleration toward the center of the circle.
E) is described by none of the above statements.
Answer: D
26. A car going around a curve of radius R at a speed V experiences a centripetal acceleration ac. What is its acceleration if it goes around a curve of radius 3R at a speed of 2V?
A) (2/3)ac B) (4/3)ac C) (2/9)ac D) (9/2)ac E) (3/2)ac
Answer: B
27. A car experiences both a centripetal and a tangential acceleration. For which of the following would this be true?
A) It is going around a curve at a constant speed.
B) It is going around a curve and slowing down.
C) It is going along a straight road at a constant speed.
D) It is going along a straight road and increasing its speed.
E) It is going along a straight road and decreasing its speed.
Answer: B
28.
The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. The speed of the ball is constant. If the string should break at the instant shown, the path that the ball would follow is
A) 1 B) 2 C) 3 D) 4 E) impossible to tell from the given information.
Answer: B
29.
The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. Assume that air resistance is negligible. The free-body diagram that best represents the net force acting on the ball is
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
30.
The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. Assume that air resistance is negligible. The free-body diagram that best represents the acceleration of the ball is
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: D
31. If the mass of a satellite is doubled while the radius of its orbit remains constant, the speed of the satellite is
A) increased by a factor of 8. D) reduced by a factor of 8.
B) increased by a factor of 2. E) reduced by a factor of 2.
C) not changed.
Answer: C
32.
Of the satellites shown revolving around the earth, the one with the greatest speed is
A) 1 B) 2 C) 3 D) 4 E) 5
Answer: C
33. If the mass of a planet is doubled while its radius and the radius of orbit of its moon remain constant, the speed of the moon is
A) increased by a factor of . D) reduced by a factor of .
B) increased by a factor of 2. E) reduced by a factor of 2.
C) not changed.
Answer: A
34. A woman whose weight on earth is 500 N is lifted to a height of two earth radii above the surface of the earth. Her weight
A) decreases to one-half of the original amount.
B) decreases to one-quarter of the original amount.
C) decreases to one-fifth of the original amount.
D) decreases to one-third of the original amount.
E) decreases to one-ninth of the original amount.
Answer: E
35. The acceleration due to gravity at the surface of the earth is g. The radius of the earth is RE. The distance from the center of the earth to a point where the acceleration due to gravity is g/9 is
A) RE B) 9RE C) RE/3 D) 3RE E) None of these is correct.
Answer: D
36. At the surface of the moon, the acceleration due to the gravity of the moon is . At a distance from the center of the moon equal to three times the radius of the moon, the acceleration due to the gravity of the moon is
A) 9 B) /3 C) /4 D) /9 E) 27
Answer: D
37. Suppose a planet exists that has half the mass of earth and half its radius. On the surface of that planet, the acceleration due to gravity is
A) twice that on earth. D) one-fourth that on earth.
B) the same as that on earth. E) none of these.
C) half that on earth.
Answer: A
38. You need an expression for the acceleration of the moon toward the earth. If the mass of the earth is Me, the mass of the moon Mm, the separation of the earth and moon r, and the appropriate gravitational constant is G, the correct expression for the moon's acceleration is
A) GMeMm/r2 B) GMeMm2/r2 C) GMm/r2 D) GMe/r2 E) GMe/r2Mm
Answer: D
39. The acceleration due to gravity in the vicinity of the earth
A) varies directly with the distance from the center of the earth.