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MULTIPLE Exam CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), it's velocity with respect to the road is A) 1.5 v. B) 2v. C) v. D) The velocity depends on the radius of the tire. 2) A cylinder is observed to be rolling freely at constant speed on a horizontal surface. Which of the following statements is true? A) It is not possible for the cylinder to roll unless friction is present. B) It is possible that the cylinder is both rolling and sliding at the same time (i.e., that v, the speed of the centerpoint, is not equal to rw). C) If the cylinder is rolling without slipping, there must be a non-zero friction force exerted by the surface. D) If friction is present, it is not possible for the motion to occur without loss of energy. E) Even if the surface has friction, the cylinder cannot roll without slipping. TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 3) Two unequal weights are connected by a massless string which passes over a frictionless pulley. If the pulley has no appreciable mass, the tension in the string is the same on both sides of the pulley; but if the pulley has mass, the tension will not be the same on both sides of the pulley. 4) There must be equal amounts of mass on either side of the center of mass. 5) If two objects have the same moment of inertia, they must have the same mass. 6) If you deform an object, you do not change its mass but you may change its moment of inertia and the location of its center of mass. 7) If two forces of equal magnitude act on an object that is hinged at a pivot, the force acting farther from the pivot must produce the greater torque about the pivot. 3) 1)
2)
4) 5) 6)
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 8) A force in the +y direction applied at the point x = 2.3 m, y = 1.4 m gives rise to a torque of 71 N m about the origin. Find the magnitude of the force. A) 71 N B) 31 N C) 51 N D) 87 N 8)
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Point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform angular acceleration of 0.01 rad/s2 about the center O. 9) In the figure, the tangential acceleration of P at time t = 0 s is closest to: 9) A) zero B) 0.010 m/s2 C) 0.005 m/s2 D) 0.020 m/s2 E) 0.015 m/s2 10) In the figure, the linear speed of P, when it reaches the y-axis, is closest to: A) 0.18 m/s B) 0.24 m/s C) 0.35 m/s D) 0.71 m/s 10) E) 0.49 m/s
A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope which is wound on the wheel and attached to it. The wheel is released from rest and the block descends 1.5 m in 2.00 s. The tension in the rope during the descent of the block is 20 N. 11) In the figure the moment of inertia of the wheel is closest to: 11) A) 3.9 kg m 2 B) 4.3 kg m 2 C) 3.5 kg m 2 D) 4.1 kg m 2 E) 3.7 kg m 2 12) A potter's wheel (a solid, uniform disk) of mass 6.1 kg and radius 0.65 m spins about its central axis. A 2.1-kg lump of clay is dropped onto the wheel at a distance 0.41 m from the axis. Calculate the rotational inertia of the system. A) 1.3 kg m 2 B) 1.6 kg m 2 C) 2.2 kg m 2 D) 0.40 kg m 2 12)
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13) In the figure, two blocks, of masses 2 kg and 3 kg, are connected by a light string which passes over a pulley of moment of inertia 0.004 kg m 2 and radius 5 cms. The coefficient of friction for the table top is 0.30. The blocks are released from rest. Using energy methods, one can deduce that after the upper block has moved 0.6 m, its speed is: A) 3.19 m/s B) 5.44 m/s C) 1.95 m/s D) 1.22 m/s E) 1.40 m/s
13)
14) In the table, the masses and the coordinates x and y of a set of three point masses in the x-y plane. The masses are interconnected by light struts, forming a rigid body. The moment of inertia of the rigid body, through the center of mass and perpendicular to the x-y plane, is closest to: A) 3000 kg m 2 B) 3200 kg m 2 C) 3600 kg m 2 D) 3800 kg m 2 E) 3400 kg m 2 15) Which of the following is an accurate statement? A) A particle moving in a straight line with constant speed necessarily has zero angular momentum. B) The angular momentum of a moving particle depends on the specific origin with respect to which the angular momentum is calculated. C) Consider a planet moving in a circular orbit about a star. Even if the planet is spinning it is not possible for its total angular momentum to be zero. D) If the torque acting on a particle is zero about an arbitrary origin, then the angular momentum of the particle is also zero about that origin. E) If the speed of a particle is constant, then the angular momentum of the particle about any specific origin must also be constant. 16) A satellite is in an elliptical orbit about the Earth. At point X, it is closest to Earth. At point Y, it is furthest from Earth. Point Z is halfway between points X and Y, along the orbital path. Where is the angular momentum (relative to the Earth) of the satellite the highest? A) It is the same at all locations B) Point X C) Point Y D) Point Z
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15)
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17) In an interesting lecture demonstration a student sits in a swivel chair holding a spinning bicycle wheel oriented with its axis vertical. Initially the chair is motionless. the Now student rotates the axis of the spinning wheel by 180, so that it is again vertical, but now the wheel is spinning in the opposite sense with respect to the room. When this is done the student and chair begin to rotate also. Which of the following is an accurate statement concerning this process? A) Angular velocity is conserved in this process. B) In the final state the chair will be rotating in the opposite sense of the wheel, but at a much higher frequency. C) Assuming the swivel bearing of the chair is frictionless, angular kinetic energy is conserved in this process. D) In the final state the chair will be rotating in the same sense as the wheel, but at a much lower frequency. E) Angular momentum, but not angular kinetic energy, is conserved in this process, independent of whether or not friction is present. TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 18) If two vectors are perpendicular, then their cross product is zero. 19) When a spinning ice-skater pulls in her arms closer to her body, her angular speed will increase.
17)
18) 19)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Three vectors are given as shown.
20) In the figure, the magnitude and direction of the vector product B A are closest to: A) 26, directed out of the plane. B) 31, directed on the plane. C) 31, directed into the plane. D) 31, directed out of the plane. E) 26, directed into the plane.
20)
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21) In the figure, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip? A) 3.93 m B) 8.44 m C) 5.00 m D) 6.28 m E) 6.04 m 22) An irregularly shaped object 10 m long is placed with each end on a scale. If the scale on the right reads 74 N and the scale on the left reads 93 N, how far from the left is the center of gravity. A) 5.6 m B) 13 m C) 8.0 m D) 4.4 m
21)
22)
23) A 80-kg uniform ladder, 5.0 m long, is placed against a smooth wall at a height of 3.3 m. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40. An 80-kg block is suspended from the top rung of the ladder, close to the wall. In the figure, the force exerted on the wall by the ladder is closest to: A) 1300 N B) 1000 N C) 1900 N D) 1600 N E) 1200 N
23)
5
24) In the figure, what mass M is required to balance the mobile? A) 60 gms B) 36 gms C) 30 gms
24) D) 18 gms E) 90 gms 25)
25) Suppose that a heavy person and a light person are balanced on a teeter-totter made of a plank of wood. Each person now moves in toward the fulcrum a distance of 25 cms. What effect will this have on the balance of the teeter-totter? A) The heavy person's end will go down. B) The light person's end will go down. C) The teeter-totter will remain in balance. D) One cannot tell whether either end will rise or fall without knowing the relative mass of the plank. E) Only if the plank has significant mass will the light person's end go down. 26) A tall tree and a short tree (both having the same width and mass density) are cut at the base at the same time, and begin tipping over. Which tree hits the ground first? A) the tall tree B) They hit at the same time. C) the small tree 27) A ladder on the ground is leaning against a wall. If the ladder is in static equilibrium, where must a friction force act on the ladder? A) at both the ground and wall B) at the ground C) at the wall 28) The period of a simple pendulum in a grandfather clock on another planet is 1.66 s. What is the acceleration due to gravity on this planet? Assume that the length of the pendulum is 1.00 m. A) 14.3 m/s2 B) 15.7 m/s2 C) 13.3 m/s2 D) 17.2 m/s2 29) A 0.25 kg harmonic oscillator has a total oscillation energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency? A) 2.3 Hz B) 3.1 Hz C) 4.5 Hz D) 1.4 Hz TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 30) A mass is oscillating at the end of a spring. Neither the period of oscillation nor the maximum speed of the mass depend on the amplitude of the motion. 31) Simple harmonic motion occurs only if the restoring force is directly proportional to the first power of the displacement.
26)
27)
28)
29)
30)
31)
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32) If pendulum A is twice as long as pendulum B, the period of oscillation of A will be twice as long as the period of B, even if they have different masses. 33) A mass oscillates at the end of a spring. If you double both the mass and the spring constant, the period of oscillation is unchanged.
32)
33)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 34) If both the mass of a simple pendulum and its length are doubled, the period will A) be unchanged. B) increase by a factor of 2. C) increase by a factor of 1.4 D) increase by a factor of 0.71. E) increase by a factor of 4. 35) If the frequency of a harmonic oscillator doubles, by what factor does the maximum value of acceleration change? A) 2 B) 2 C) 2/ D) 4 34)
35)
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Answer Key Testname: UNTITLED1
1) B 2) B 3) TRUE 4) FALSE 5) FALSE 6) TRUE 7) FALSE 8) B 9) D 10) C 11) B 12) B 13) E 14) D 15) B 16) A 17) E 18) FALSE 19) TRUE 20) E 21) D 22) D 23) A 24) B 25) B 26) C 27) B 28) A 29) C 30) FALSE 31) TRUE 32) FALSE 33) TRUE 34) C 35) D
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