3) When a rigid body rotates about a fixed axis all the points in the body have the same centripetal acceleration. FALSE

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1 PHYSICS 1401 Exam 3 Review Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body rotates about a fixed axis all the points in the body have the same tangential speed. FALSE 2) A wave pulse on a string whose end is fixed is reflected without inversion. FALSE 2) 1) 3) When a rigid body rotates about a fixed axis all the points in the body have the same centripetal acceleration. FALSE 3) 4) Sound waves in air are transverse waves. FALSE 4) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement? A) Child AXXX B) Child B C) They have the same zero linear displacement. D) They have the same non-zero linear displacement. E) There is not enough information given to answer the question. 6) Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential acceleration? A) Child AXXX B) Child B C) They have the same non-zero centripetal acceleration. D) They have the same zero centripetal acceleration. E) There is not enough information given to answer the question. 5) 6) 7) A solid cylinder is rolling without slipping. What fraction of its kinetic energy is rotational? 7) A) 2/3 B) 3/4 C) 1/4 D) 1/3XXX E) 1/2 8) Two balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down an incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first? A) Both reach the bottom together.xxx B) The large sphere C) The small sphere D) It depends on the height of the incline. E) It depends on the length of the inclined surface. 8) 1

2 9) A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? A) hoop, sphere, disk B) sphere, disk, hoopxxx C) hoop, sphere, disk D) disk, hoop, sphere E) hoop, disk, sphere 10) A solid disk is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes an angle of 25.0 with the horizontal. What is the speed of the disk after it has rolled 3.00 m up the ramp? A) 8.02 m/s B) 1.92 m/sxxx C) 2.06 m/s D) 6.79 m/s E) 4.01 m/s 11) A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts down a ramp that makes an angle of 25.0 with the horizontal. What is the rotational kinetic energy of the hoop after it has rolled 3.00 m down the ramp? A) 44.9 JXXX B) 62.0 J C) 22.4 J D) 34.2 J E) This question cannot be answered without knowing the radius of the hoop. 12) A Ferris wheel with a radius of 14.0 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the bottom of the wheel? A) 562 N B) 432 N C) 852 N D) 625 NXXX E) 589 N 13) An Atwood machine has a mass of 3.50 kg connected by a light string to a mass of 6.00 kg over a pulley with a moment of inertia of kg m2 and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m? A) 4.95 m/s B) 2.00 m/s C) 2.28 m/sxxx D) 4.00 m/s E) 6.00 m/s 14) A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy? A) JXXX B) 0.96 J C) 0.18 J D) 1.05 J E) 0.53 J 9) 10) 11) 12) 13) 14) 2

3 15) A potter's wheel is rotating at 1.00 rpm. What centripetal force is required to hold a 1.00 g lump of clay in place, 10.0 cm from the axis of rotation? A) N B) NXXX C) N D) N E) N 16) A string is wound tightly around a fixed pulley whose radius is 5.0 cm. As the string is pulled, the pulley rotates without slipping. What is the angular speed of the pulley when the string has a linear speed of 5.0 m/s? A) 25 rad/s B) 20 rad/s C) 50 rad/s D) 100 rad/sxxx E) 10 rad/s 15) 16) 17) Earth's radius is m, and it completes one revolution every day. What is the tangential speed of a person standing on the equator? A) 148 m/s B) 21.5 m/s C) 232 m/s D) 73.8 m/s E) 464 m/sxxx 17) 18) A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s2. Through what angle has the wheel turned when its angular speed reaches 72.0 rad/s? A) 66.8 rad B) 316 rad C) 83.2 rad D) 697 rad E) 948 radxxx 19) An object is moving in a circular path with an angular speed of 1.52 rad/s. How long does it take the object to complete one revolution? A) 2.07 s B) 8.26 s C) 118 s D) 4.77 s E) 4.13 s 20) Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is A) 1/2. B) 2. C) 4.XXX D) 8/5. E) 4/5. 21) A man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of m from his shoulder. What is the torque on the shoulder joint if the arm is horizontal? A) 43.2 Nm B) 14.5 Nm C) 4.40 NmXXX D) Nm E) 0 Nm 18) 19) 20) 21) 3

4 22) Angular momentum cannot be conserved if 22) A) the moment of inertia changes. B) the net torque is not zero.xxx C) the angular acceleration changes. D) the angular velocity changes. E) there is a net force on the system. FIGURE ) A store's sign, with a mass of 20.0 kg and 3.00 m long, has its center of gravity at the center of the sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end, as shown in Figure The wire makes an angle of 25.0 with the horizontal. What is the tension in the wire? A) 464 N B) 196 N C) 116 N D) 232 NXXX E) 297 N 24) A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick? A) 178 g B) 73.4 g C) 32.6 g D) 89.7 g E) 127 gxxx 25) A uniform meter stick with a mass of 135 g rotates about an axis perpendicular to the stick passing through the center of the stick with an angular speed of 3.50 rad/s2. What is the magnitude of the angular momentum of the stick? A) kg m2/sxxx B) kg m2/s C) kg m2/s D) kg m2/s E) kg m2/s 23) 24) 25) 4

5 FIGURE ) The L-shaped object shown in Figure 11-9 consists of the masses connected by light rods. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the x-axis? A) 47.4 J B) 62.3 J C) 34.2 JXXX D) 23.7 J E) 17.6 J 26) FIGURE ) An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two pillars 1.60 m apart, as shown in Figure Find the force exerted by pillar A. A) 1.71 kn upwards B) 2.51 kn downwards C) 3.44 kn upwards D) 2.51 kn upwards E) 1.71 kn downwardsxxx 28) A horizontal, 2.00 m long, 3.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam? A) zero B) 400 N m south C) 800 N m north D) 400 N m northxxx E) 800 N m south 27) 28) 29) When you ride a bicycle, in what direction is the angular velocity of the wheels? 29) A) to your right B) forwards C) up D) backwards E) to your leftxxx 5

6 30) A person sits on a freely spinning lab stool (no friction). When this person extends her arms, 30) A) her moment of inertia decreases and her angular velocity increases. B) her moment of inertia increases and her angular velocity decreases.xxx C) her moment of inertia increases and her angular velocity increases. D) her moment of inertia increases and her angular velocity remains the same. E) her moment of inertia decreases and her angular velocity decreases. 31) Two equal forces are applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque? A) both exert equal non-zero torques B) the second at the doorknobxxx C) the first at the midpoint D) both exert zero torques E) Additional information is needed. 31) 32) The time for one cycle of a periodic process is called the 32) A) period.xxx B) energy. C) wavelength. D) amplitude. E) frequency. 33) For periodic motion, the maximum displacement from the equilibrium point is called the 33) A) amplitude.xxx B) energy. C) period. D) wavelength. E) frequency. 34) A mass is attached to a spring and oscillates with a period T. If the mass is doubled, what is the new period? A) T 2XXX B) 2T C) T/ 2 D) T/2 E) T 35) If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 4 B) 1/4 C) 1/2 D) 1 E) 2XXX 34) 35) 36) The total mechanical energy of a simple harmonic oscillator is 36) A) zero as it passes the equilibrium point. B) constant.xxx C) a maximum when it passes through the equilibrium point. D) a minimum when it passes through the equilibrium point. E) zero when it reaches the maximum displacement. 6

7 37) A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum? A) midway between A and BXXX B) one-third of the way between A and B C) one-fourth of the way between A and B D) at either A or B E) none of the above 38) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration? A) The period decreases. B) The period increases.xxx C) The period becomes zero. D) The period does not change. E) The period decreases if the downward acceleration is more than g/2 but increases if the downward acceleration is less than g/2. 37) 38) 39) If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations? 39) A) 1450 Hz B) 4560 Hz C) 3.98 Hz D) 1.27 HzXXX E) 2.54 Hz 40) On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? A) T 6XXX B) T/6 C) T/ 6 D) 6T E) T/3 41) Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system's mechanical energy? A) increases the energy by a factor of two B) increases the energy by a factor of four C) increases the energy by a factor of square root of two D) increases the energy by a factor of three E) produces no changexxx 40) 41) 42) The position of a mass that is oscillating on a spring is given by x = (18.3 cm) cos[(2.35 s-1)t]. What is the frequency of this motion? A) 2.67 Hz B) HzXXX C) 1.34 Hz D) Hz E) Hz 42) 7

8 43) A mass is oscillating on a spring with a period of 4.60 s. At t = 0 s the mass has zero speed and is at x = 8.30 cm. What is the value of t the first time after t = 0 s that the mass is at x = 4.15 cm? A) 1.15 s B) 1.30 s C) 1.53 s D) sxxx E) s 44) A spring with a force constant of 1.50 N/m is attached to a mass of 120 g. The system has a damping constant of Ns/m. How long does it take the amplitude of the oscillations to decrease from 10.0 mm to 5.00 mm? A) 9.24 sxxx B) 10.0 s C) 4.62 s D) 12.5 s E) 6.25 s 43) 44) 45) What is the length of a simple pendulum with a period of 2.00 s? 45) A) 19.6 m B) m C) 1.62 m D) mxxx E) 1.22 m 46) A 16.2-g bullet with an initial speed of 870 m/s embeds itself in a 40.0-kg block, which is attached to a horizontal spring with a force constant of 1010 N/m. What is the maximum compression of the spring? A) 5.57 cm B) 3.42 cm C) 1.26 cm D) 7.01 cmxxx E) 6.34 cm 46) 47) How much work is required to stretch a spring 25.2 cm if its force constant is 12.3 N/m? 47) A) JXXX B) J C) 1.05 J D) J E) 3.10 J 48) A mass is oscillating on a spring with a period of 4.60 s. At t = 0 s the mass has zero speed and is at x = 8.30 cm. What is its speed at t = 2.50 s? A) 10.9 cm/s B) 0 cm/s C) 1.80 cm/s D) 3.06 cm/sxxx E) 3.32 cm/s 48) 49) The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion? A) 17.4 rad/s B) rad/s C) rad/s D) 2.34 rad/s E) 5.46 rad/sxxx 49) 8

9 FIGURE ) In Figure 14-1, the wavelength is 50) A) 1 m. B) 8 m. C) 4 m. D) 2 m. E) cannot be determined from the given informationxxx 51) Two strings are made of the same material. String 1 has radius r1 while string 2 has radius r2 = r1/2. When stretched by the same tension, the respective speed of propagation of waves v1 and v2 satisfy the condition A) v1 =v2/ 2. B) v1 = 2v2. C) v1 = v2/4. D) v1 = 2v2. E) v1 = v2/2.xxx 51) 52) Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t) II y = 0.15 sin(6x + 42t) III y = 0.13 cos(6x + 21t) IV y = sin(3x - 42t) Which of these waves travel in the +x direction? A) I and IVXXX B) I and II C) II and III D) I and III E) II and IV 53) A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave? A) 0.50 m/s B) 2.5 m/s C) 0.40 m/s D) 10 m/sxxx E) 0.10 m/s 52) 53) 9

10 54) The lowest tone to resonate in an open pipe of length L is 200 Hz. Which one of the following frequencies will not resonate in the same pipe? A) 200 Hz B) 800 Hz C) 400 Hz D) 900 Hz E) 600 Hz 55) An organ pipe, open at both ends, is 5.20 m long. What is its fundamental frequency? The speed of sound in air is 343 m/s. A) 99.0 Hz B) 132 Hz C) 33.0 HzXXX D) 16.5 Hz E) 66.0 Hz 56) A 25.0-g string is stretched with a tension of 43.0 N between two fixed points 12.0 m apart. What is the frequency of the second harmonic? A) 6.00 Hz B) 18.0 Hz C) 12.0 HzXXX D) 36.0 Hz E) 24.0 Hz 54) 55) 56) 57) The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What is the amplitude of the wave? A) 12.0 mm B) 6.00 mmxxx C) 3.00 mm D) 2.00 mm E) None of the other choices is correct. 57) 58) The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What is the speed of the wave? A) 2.22 m/sxxx B) 23.5 m/s C) 1.41 m/s D) 3.16 m/s E) m/s 59) A 15.0-m rope is pulled taut with a tension of 140 N. It takes s for a wave to propagate along the rope. What is the mass of the rope? A) 1.67 kg B) 2.10 kg C) 5.09 kg D) 3.19 kg E) 2.77 kgxxx 58) 59) 10

11 60) A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami? A) HzXXX B) 6.76 Hz C) Hz D) Hz E) 1.07 Hz 60) 11

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