Name: Date: 1. For this question, assume that all velocities are horizontal and that there is no friction. Two skaters A and B are on an ice surface. A and B have the same mass M = 90.5 kg. A throws a ball with mass m = 200 g toward B with a speed v = 21.5 m/s relative to the ice. B catches the ball and throws it back to A with the same speed. After A catches the ball, his speed with respect to the ice is A) 4.3 10 3 m/s B) 4.3 m/s C) 4.8 10 2 m/s D) 9.5 10 2 m/s E) 0.34 m/s 2. 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 3. 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 4. Two bodies A and B move toward each other with speeds of 80 cm/s and 20 cm/s, respectively. The mass of A is 140 g and that of B is 60 g. After a head-on, perfectly elastic collision, the speed of B is A) 8.0 cm/s B) 20 cm/s C) 92 cm/s D) 1.2 m/s E) 1.3 m/s 5. A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s. If
they collide inelastically, the speed of the balls just after the collision is approximately A) 1.0 m/s B) 20 m/s C) 6.7 m/s D) 1.5 m/s E) zero 6. Glider A, traveling at 10 m/s on an air track, collides elastically with glider B traveling at 8.0 m/s in the same direction. The gliders are of equal mass. The final speed of glider B is A) 8.4 m/s B) 10 m/s C) 8.0 m/s D) 4.0 m/s E) 12 m/s 7. A block of wood with a mass M = 4.65 kg is resting on a horizontal surface when a bullet with a mass m = 18 g and moving with a speed v = 725 m/s strikes it. The coefficient of friction between the block and the surface is µ = 0.35. The distance the block moves across the surface is A) 1.1 m B) 3.3 m C) 0.41 m D) 11 m E) None of these is correct. 8.
The balls shown in the figure are strung on a taut wire and slide without friction. If the balls are of equal mass, the diagram that best represents an elastic collision is A) 1 B) 2 C) 3 D) 4 E) 5 9. A 40 kg boy, on a stunt, jumps from one ice sled to another sled placed next to the first one, and then quickly jumps back to the first one. The horizontal speed relative to the ice for each jump is 2 m/s and the mass of each sled is 20 kg. What is the speed of the second sled after the second jump? Assume that there is no friction between the sled and the ice. A) 1 m/s B) 2 m/s C) 3 m/s D) 4 m/s E) 8 m/s 10. An 1810-kg truck traveling eastward at 64.4 km/h collides at an intersection with a 905-kg automobile traveling northward at 96.5 km/h. The vehicles lock together and immediately after the collision are headed in which direction?
A) 30º N of E B) 37º N of E C) 45º N of E D) 53º N of E E) 67º N of E 11. A bullet, m = 0.500 kg, traveling with a velocity of 100 m/s strikes and embeds itself in the bob of a ballistic pendulum, M = 9.50 kg. The combined masses rise to a height h = 1.28 m. The speed V f of the combined masses immediately following impact is A) 5.00 m/s B) 5.26 m/s C) 9.10 m/s D) 10.0 m/s E) 22.3 m/s 12. A 7000-kg coal car of a train coasts at 7.0 m/s on a frictionless track when a 3000-kg load of coal is dropped vertically onto the car. The coal car's speed after the coal is added is A) 2.1 m/s B) 3.0 m/s C) 4.9 m/s D) 7.0 m/s E) 16 m/s 13. A particle of mass m moving at 5.0 m/s in the positive x direction makes a glancing elastic collision with a particle of mass 2m that is at rest before the collision. After the collision, m moves off at an angle of 45º to the x axis and 2m moves off at 60º to the x axis. The speed of m after the collision is A) 4.5 m/s B) 2.5 m/s C) 3.3 m/s
D) 1.8 m/s E) 1.1 m/s 14. Two identical masses are hung on strings of the same length. One mass is released from a height h above its free-hanging position and strikes the second mass; the two stick together and move off. They rise to a height H given by A) 3h/4 B) h/4 C) h/2 D) h E) None of these is correct. 15. You shoot an arrow with a mass of 0.54 kg at 45º above the horizontal. The bow exerts a force of 125 N for 0.65 s. With no air resistance, the maximum height the arrow reaches is A) 1.2 km B) 5.4 m C) 0.57 km D) 0.29 km E) 0.61 km 16. A helium atom (mass = 4m) moving with speed V collides elastically with a tritium (hydrogen 3 ) atom (mass = 3m) at rest. Calculate the speed of the tritium atom after the collision. A) 0.86 V B) 1.33 V C) 1.14 V D) 1.25 V E) 1.00 V 17. A 20-g bullet is fired into a 2.0-kg block of wood placed on a horizontal surface. The
bullet stops in the block. The impact moves the block (+ bullet) a distance of 5 m before it comes to rest. If the coefficient of kinetic friction between the block and surface is 0.25, calculate the speed of the block (+ bullet) system immediately after impact. A) 20 m/s B) 3.5 m/s C) 25 m/s D) 5.0 m/s E) 2.2 m/s 18. A bullet (mass = m 1 ) is fired at speed V into a block of mass m 2 at rest. If the bullet escapes from the block with only a third of its original speed then the recoil speed of the block is given by A) m 1 V/ 3m 2 B) 2m 1 V/ 3m 2 C) m 2 V/ 3m 1 D) 2m 2 V/ 3m 1 E) 4m 2 V/ 9m 1 19. Water is fired horizontally out of a 7-cm diameter hose directly onto a wall at a speed of 7m/s. Assuming that the water after impact falls straight down the wall, the average force on the wall is (density of water = 1000 kg/m 3 ) A) 27 N B) 190 N C) 47 N D) 60 N E) 94 N 20. A bullet is fired at 100 m/s horizontally into a 2-kg block suspended by a light string of length 1.2 m. If the block and bullet system swing up by 20 degrees to the vertical, the mass of the bullet is given by: A) 79 g B) 24 g C) 28 g D) 15 g E) 123 g 21. You are pedaling a bicycle at 9.8 m/s. The radius of the wheels of the bicycle is 51.9cm. The angular velocity of rotation of the wheels is A) 19 rad/s B) 2.5 rad/s C) 4.5 rad/s
D) 3.0 rad/s E) 6.3 rad/s 22. The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s 2 at its circumference is A) 4.4 10 2 rad/s B) 7.0 10 3 rad/s C) 0.28 rad/s D) 0.22 rad/s E) 1.3 10 3 rad/s 23. The angular acceleration of the flywheel of a generator is given by α(t) = 6bt 12ct 2 where b and c are constants and a is in rad/s 2 provided t is in seconds. If the initial angular velocity is taken to be w 0, the angular velocity at time t is given by A) ω 0 + 6bt 2 12ct 3 B) 6b 24ct C) 3bt 2 4ct 3 + ω 0 D) 3bt 2 4ct 3 E) 6b 24ct + ω 0 24. A turntable has an angular velocity of 1.4 rad/s. The coefficient of static friction between the turntable and a block placed on it is 0.20. The maximum distance from the center of the turntable that the block can be placed without sliding is approximately A) 0.50 m B) 1.0 m C) 1.4 m D) 2.0 m E) 4.4 m 25.
A 2-kg sphere attached to an axle by a spring is displaced from its rest position to a radius of 20 cm from the axle centerline by a standard mass of 20 kg, as in Figure 1. The same 2-kg sphere is also displaced 20 cm from the axle centerline, as in Figure 2, when the sphere is rotated at a speed of approximately A) 4.4 m/s B) 9.8 m/s C) 14 m/s D) 98 m/s E) 0.44 km/s 26. A 5 10 6 -kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 10 3 rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately A) 1 N B) 1 mn C) 5 mn D) 5 kn E) 5 N 27. A solid sphere (I = 0.4MR 2 ) of radius 0.06 m and mass 0.50 kg rolls without slipping 14m down a 30º inclined plane. At the bottom of the plane, the linear velocity of the center of mass of the sphere is approximately A) 3.5 m/s B) 3.9 m/s C) 8.7 m/s D) 18 m/s E) 9.9 m/s 28. A cylinder (I = mr 2 ) rolls along a level floor with a speed v. The work required to stop this cylinder is A) mv 2
B) mv 2 C) mv 2 D) mv 2 E) 1.25mv 2 29. A solid sphere of radius r = 5 cm and mass m = 0.2 kg rolls in a groove as shown. The angle, θ, between the points of contact with the groove is 120. If the sphere has a linear velocity of 10 mm/s, what is the rotational kinetic energy? A) 0.8 mj B) 1.0 mj C) 1.6 mj D) 2.0 mj E) undetermined. 30. A hoop of mass 50 kg rolls without slipping. If the center-of-mass of the hoop has a translational speed of 4.0 m/s, the total kinetic energy of the hoop is A) 0.20 kj B) 0.40 kj C) 1.1 kj D) 3.9 kj E) None of these is correct. 31. A wagon wheel consists of 8 spokes of uniform diameter, each of mass m s and length L cm. The outer ring has a mass m ring. What is the moment of inertia of the wheel? Assume that each spoke extends from the center to the other ring and the ring is of negligible thickness.
A) B) C) D) E) 32. The moment of inertia of a slim rod about a transverse axis through one end is ml 2 /3, where m is the mass of the rod and L is its length. The moment of inertia of a 0.24- kg meterstick about a transverse axis through its center is A) 0.14 kg m 2 B) 20 kg m 2 C) 0.020 kg m 2 D) 80 kg m 2 E) 4.5 kg m 2 33.
If all of the objects illustrated in the figure have equal masses, the moment of inertia about the indicated axis is largest for the A) ring B) cross C) sphere D) cube E) rod 34. A 7.00-kg mass and a 4.00-kg mass are mounted on a spindle free to turn about the x axis as shown. Assume the mass of the arms and the spindle to be negligible. The rotational inertia of this system is approximately A) 44.0 kg m 2 B) 47.0 kg m 2 C) 99.0 kg m 2 D) 148 kg m 2 E) 211 kg m 2 35. Water is drawn from a well in a bucket tied to the end of a rope whose other end
wraps around a cylinder of mass 50 kg and diameter 25 cm. As you turn this cylinder with a crank, the rope raises the bucket. If the mass of a bucket of water is 20 kg, what torque must you apply to the crank to raise the bucket of water at a constant speed? A) 24 N m B) 2.5 N m C) 80 N m D) 2.4 10 3 N m E) 49 N m 36. A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min. After the power is shut off, a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later. What is the average torque exerted by the axe on the grindstone? A) 9.6 mn m B) 0.12 N m C) 0.75 N m D) 0.60 kn m E) 0.060 N m 37. What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg m 2. A) 4.5 N m B) 9.0 N m C) 45 N m D) 30 N m E) 60 N m 38. A solid cylinder has a moment of inertia of 2 kg m 2. It is at rest at time zero when a net torque given by τ = 6t 2 + 6 (SI units) is applied. After 2 s, the angular velocity of the cylinder will be A) 3.0 rad/s B) 12 rad/s C) 14 rad/s D) 24 rad/s E) 28 rad/s 39. A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and
released. The moment of inertia of the wheel is 2.71 kg m 2. If the wheel rotates on frictionless bearings, the acceleration of the falling weight is A) 3.26 m/s 2 B) 1.04 m/s 2 C) 2.44 m/s 2 D) 1.95 m/s 2 E) 4.27 m/s 2 40. A wheel of radius R 1 has an axle of radius R 2 = R 1. If a force F 1 is applied tangent to the wheel, a force F 2, applied tangent to the axle that will keep the wheel from turning, is equal to A) F 1 /4 B) F 1 C) 4F 1 D) 16F 1 E) F 1 /16 41. The moment of inertia of the wheel in the figure is 0.50 kg m 2, and the bearing is
frictionless. The acceleration of the 15-kg mass is approximately A) 9.8 m/s 2 B) 8.7 m/s 2 C) 74 m/s 2 D) 16 m/s 2 E) 0.53 m/s 2 42. In the figure, the rotational inertia of the wheel and axle about the center is 12.0 kg m 2, the constant force F is 39.2 N, and the radius r is 0.800 m. The wheel starts from rest. When the force has acted through 2.00 m, the rotational velocity ω acquired by the wheel due to this force will be A) 1.26 rad/s B) 3.33 rad/s C) 3.61 rad/s D) 6.24 rad/s E) 10.3 rad/s 43. Two blocks m 1 (= 0.4 kg) and m 2 (= 0.6 kg) are initially positioned at x = 0.6 and x = 1.1m. One cord is used to couple the blocks together and another to attach m 1 to a vertical pole at the origin. The blocks are made to rotate in a horizontal circle on a frictionless surface. If the period of rotation is 0.4s then calculate the ratio of the tension for the inner cord divided by the tension in the outer cord. A) 0.64 B) 1.4 C) 1.6 D) 0.74 E) 1.8 44. Two solid balls (one large, the other small) and a cylinder roll down a hill. Which has the greatest speed at the bottom and which the least?
A) The large ball has the greatest; the small ball has the least. B) The small ball has the greatest; the large ball has the least. C) The cylinder has the greatest; the small ball has the least. D) The cylinder has the greatest; both balls have the same lesser speed. E) Both balls have the same greater speed; the cylinder has the least. 45. Starting from rest at the same time, a coin and a ring roll down an incline without slipping. Which reaches the bottom first? A) The ring reaches the bottom first. B) The coin reaches the bottom first. C) They arrive at the bottom simultaneously. D) The winner depends on the relative masses of the two. E) The winner depends on the relative diameters of the two. 46. A bicycle is moving at a speed v = 12.6 m/s. A small stone is stuck to one of the tires. At the instant the stone is at point A in the figure, it comes free. The velocity of the stone (magnitude and direction) relative to Earth just after release is A) 17.8 m/s at 45º above the horizontal, towards the front of the bicycle. B) 12.6 m/s at 45º above the horizontal, away from the bicycle. C) 12.6 m/s at 37º below the horizontal. D) 12.6 m/s straight up. E) 17.8 m/s at 45º above the horizontal, towards the back of the bicycle. 47. A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. In what order will they arrive at the bottom? A) solid cylinder, hollow cylinder, block B) hollow cylinder, solid cylinder, block C) block, hollow cylinder, solid cylinder D) block, solid cylinder, hollow cylinder E) all at the same instant 48. The moment of inertia of a certain wheel about its axle is mr 2. The translational
speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is A) 9.75 m/s B) 8.53 m/s C) 7.31 m/s D) 6.10 m/s E) 4.88 m/s 49. A solid disk (I cm = mr 2 ) rolls without slipping up a plane a distance s. The plane is inclined at an angle θ with the horizontal. The disk has mass m, radius R, and an initial translational speed v. The distance s the disk rolls is A) v 2 /(g sin θ) B) v 2 /(g sin θ) C) Rv/(g sin θ) D) mg(sin θ cos θ)(rv) 2 E) v 2 /(g sin θ) 50. A solid spherical ball of mass M and radius R rolls without slipping down an inclined plane from a height h. Compare the center of mass speed of the ball at the bottom of the plane with the speed obtained if the ball were simply dropped from a height h. A) rolling ball is (5/7) 1/2 times slower B) rolling ball is 7/5 times faster C) rolling ball is (2/3) 1/2 times slower D) rolling ball is 2/3 times faster E) rolling ball and dropped ball have the same speeds
51. A wheel is rotating clockwise on a fixed axis perpendicular to the page (x). A torque that causes the wheel to slow down is best represented by the vector A) B) C) D) E) 52. A man stands on the center of a platform that is rotating on frictionless bearings at a speed of 1.00 rad/s. Originally his arms are outstretched and he holds a 4.54-kg mass in each hand. He then pulls the weights in toward his body. Assume the moment of inertia of the man, including his arms, to remain constant at 5.42 kg m 2. If the original distance of the weights from the axis is 0.914 m and their final distance is 0.305 m, the final angular velocity is A) 1.14 rad/s B) 1.27 rad/s C) 1.58 rad/s D) 2.08 rad/s E) 7.70 rad/s 53. A woman sits on a stool that can turn friction-free about its vertical axis. She is handed a spinning bicycle wheel that has angular momentum and she turns it over (that is, through 180º). She thereby acquires an angular momentum of magnitude
A) 0 B) C) D) E) 54. In a playground there is a small merry-go-round of radius 1.25 m and mass 175 kg. Assume the merry-go-round to be a uniform disc. A child of mass 45 kg runs at a speed of 3.0 m/s tangent to the rim of the merry-go-round (initially at rest) and jumps on. If we neglect friction, what is the angular speed of the merry-go-round after the child has jumped on and is standing at its outer rim? A) 0.82 rad/s B) 2.4 rad/s C) 0.49 rad/s D) 1.2 rad/s E) 0.41 rad/s 55. A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible. A second identical wheel, initially at rest, is suddenly coupled to the same shaft. The angular speed of the coupled wheels is A) 10 rad/s B) 14 rad/s C) 20 rad/s D) 28 rad/s E) 40 rad/s 56. A wheel is set spinning and then is hung by a rope placed at one end of the axle. The precession vector of the spinning wheel points in the direction of
A) z B) y C) z D) x E) y 57. Two planets have masses M and m, and the ratio M/m = 25. The distance between the planets is R. The point P, is between the planets as shown, and the distance between M and P is x. At P the gravitational forces on an object due to M and m are equal in magnitude. The value of x is A) 5R/6 B) 25R/36 C) R/25 D) 6R/5 E) None of these is correct. 58. If the mass of Earth is 6 10 24 kg, the mass of the moon 7 10 22 kg, the radius of the moon's orbit 4 10 8 m, and the value of the gravitational constant 6 10 11 N m 2 /kg 2, the force between Earth and the moon is approximately A) 5 10 4 N B) 2 10 20 N
C) 3 10 50 N D) 7 10 30 N E) 3 10 28 N 59. A planet is made of two distinct materials in two layers. From the core to R/2, the density of the material is 4000 kg/m 3, and from R/2 to R the density is 3000 kg/m 3. What is the mass of the planet if R = 5000 km? A) 2.62 10 23 kg B) 1.37 10 24 kg C) 1.64 10 24 kg D) 1.57 10 24 kg E) 1.87 10 24 kg 60. The mass of Earth is M E = 6.0 10 24 kg, and the mass of the Sun is 2.0 10 30 kg. They are a distance of 1.5 10 8 km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 10 11 N m 2 /kg 2 ) A) 1.8 10 8 m/s 2 B) 6.0 10 3 m/s 2 C) 9.8 m/s 2 D) 6.0 m/s 2 E) 6.0 10 3 m/s 2 Use the following to answer questions 61-62. NASA's Weightless Wonder flights can simulate zero-g or some other extraterrestrial gravity by flying a C-9 jet plane in a parabolic path. One path the plane takes is expressed as y = y o + 0.8 x 1.02 10-4 x 2 where y o is the highest point, and x and y are the horizontal and vertical coordinates (in m). 61. What is the horizontal speed of the plane if the flight is to simulate lunar gravity, g Moon = 1.62 m/s 2. A) 50 m/s B) 100 m/s C) 150 m/s D) 200 m/s E) 250 m/s 62. Suppose y o = 10000 m and the lowest height is 2000 m, how long is the flight with a simulated lunar gravity g Moon = 1.62 m/s 2?
A) 44 s B) 100 s C) 40 s D) 60 s E) 66 s 63. If the mass of a planet is doubled with no increase in its size, the escape speed for that planet is A) increased by a factor of 1.4. B) increased by a factor of 2. C) not changed. D) reduced by a factor of 1.4. E) reduced by a factor of 2. 64. Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s 2 and R E = 6370 km.) A) 1.3 10 4 km B) 8.5 10 3 km C) 9.6 10 3 km D) 2.6 10 4 km E) 1.9 10 4 km 65. With what velocity must a body be projected vertically upward from the earth's surface, in the absence of friction, to rise to a height equal to the earth's radius (6400 km)? A) 4.3 10 5 m/s B) 2.6 10 3 m/s C) 10 5 m/s D) 3.6 10 2 m/s E) 7.9 10 3 m/s 66. The radius of the moon is R. A satellite orbiting the moon in a circular orbit has an acceleration due to the moon's gravity of 0.14 m/s 2. The acceleration due to gravity at the moon's surface is 1.62 m/s 2. The height of the satellite above the moon's surface is A) 3.4R B) 0.42R C) 11R D) 2.4R E) 1.7R
67. Four identical masses, each of mass M, are placed at the corners of a square of side L. The total potential energy of the masses is equal to xgm 2 /L, where x equals A) 4 B) C) D) E) 68. Suppose that a satellite is in a circular orbit at a height of 2.00 10 6 m above Earth's surface. What is the speed of a satellite in this orbit? A) 8.31 10 1 m/s B) 6.90 10 3 m/s C) 4.76 10 7 m/s D) 9.62 10 4 m/s E) None of these is correct. 69. The radius R of a stable, circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by A) R = Gv/M B) R = Gv/mM C) R = GmM/v D) R = GM/mv E) R = GM/v 2 70. The Roche Limit tells us about the point on a rotating planet where the gravitational force at the equator is just equal to the necessary centripetal force needed for rotation. Assuming the planet to be a uniform sphere of density 5520 kg/m 3, find the shortest period of rotation possible before exceeding the Roche Limit. (G = 6.67 10 11 N m 2 /kg 2 ) A) none of the following B) 50 mins C) 150 mins D) 48 mins E) 85 mins