(Questions #4,5,6,27,37,38,42 and 58 each have TWO correct answers.) 1) A record player has four coins at different distances from the center of rotation. Coin A is 1 cm away, Coin B is 2 cm away. Coin C is 4 cm away, and Coin D is 8 cm away. If the player is spinning at 45 rotations/min, which coin has the greatest tangential velocity? a) Coin A b) Coin B c) Coin C d) Coin D e) All the coins have equal tangential velocities
2) The Moon orbits the Earth once every 27.3 days with an orbital radius 385,000 km. What is the orbital speed of the Moon? a) 0.163 m/s b) 27.3 m/s c) 163 m/s d) 1,030 m/s e) 1.22 x 10 12 m/s 3) The Moon takes 27.3 days to orbit the Earth at an average radial distance of 385,000 km from the center of the Earth. What is the acceleration of the Moon? a) 2.73 x 10-3 m/s 2 b) 4.96 x 10-3 m/s 2 c) 9.8 x 10 0 m/s 2 d) 1.94 x 10-3 m/s 2 e) 6.92 x 10-5 m/s 2
4) An object that s moving with constant speed travels once around a circular path. Which of the following statements are true concerning this motion? Select two answers. a) The displacement is zero. b) The average speed is zero. c) The acceleration is zero. d) The velocity is changing. 5) When an object is moving in circular motion, what accelerations are NOT possible? a) Inward radial acceleration b) Tangential acceleration c) Angular acceleration d) Outward radial acceleration e) Zero acceleration 6) An object moves at a constant speed in a circular path. Which of the following statements is true? Select two answers, a) The velocity is changing. b) The velocity is constant. c) The magnitude of acceleration is constant. d) The magnitude of acceleration is changing.
7) If a ball attached to a string is being twirled in a horizontal circle, what happens to the ball if the string is suddenly cut? (Ignore any effects from the gravitational force.) a) The ball spirals away from the center of the circle. b) The ball spirals toward the center of the circle. c) The ball continues in a circle because of Newton s first law. d) The ball flies off tangent to the circle. e) The ball falls to the ground. 8) An object moves at a constant speed in a circular path of radius r at a rate of 1 rev/sec. What is its acceleration? a) 0 b) 2π 2 r c) 2π 2 r 2 d) 4π 2 r 9) A car moves in a horizontal circle with a radius of 10 m. The tangential velocity of the car is 30 m/s. What is the car s acceleration? a) 3 m/s 2 toward the center b) 3 m/s 2 away from the center c) 90 m/s 2 toward the center d) 90 m/s 2 away from the center e) 270 m/s 2 toward the center
10) If the car in the previous question has a mass of 1,000 kg, then what is the force of friction acting on the car? a) 3,000 N toward the center b) 3,000 N away from the center c) 90,000 N away from the center d) 90,000 N toward the center e) 90,000 N vertically 11) The mass, turn radius, and speed of each car in the table below are shown relative to Car A. Which of the following best ranks the centripetal force on the cars? a) D > A = B > C b) D > C = B > A c) D = A = B > C d) D > B > A > C e) D = B > A > C
12) The centripetal acceleration of a 1,000 kg car in a turn is 1 x 10 5 m/s 2. The radius of the turn is 10 m. What is the car s speed? a) 1 x 10 1 m/s b) 1 x 10 2 m/s c) 1 x 10 3 m/s d) 1 x 10 4 m/s e) 1 x 10 5 m/s 13) An ice skater skates around a circular rink with a diameter of 20 m. If it takes her 62.8 s to go around the rink once, what is the coefficient of friction of the ice? a) 0.01 b) 0.10 c) 0.20 d) 0.30 e) 0.50
14) A warrior spins a slingshot in a horizontal circle above his head at a constant speed. The sling is 1.5 m long, and the stone has a mass of 50 g. The tension in the string is 3.3 N. When he releases the sling, what will the stone s speed be? a) 5 m/s b) 10 m/s c) 25 m/s d) 30 m/s e) 50 m/s 15) A 1,000-kg car experiences a centripetal force of 1.8 x 10 5 N while making a turn. The car is moving at a constant speed of 30 m/s. What is the radius of the turn? a) 0.2 m b) 1 m c) 2 m d) 4 m e) 5 m
16) A skater holds out her arms level to the ground as she spins. In one hand she holds a tennis ball. Each of her arms is 1 m long. If the tennis ball travels at 5 m/s, what is its centripetal acceleration? a) 5 m/s 2 b) 10 m/s 2 c) 15 m/s 2 d) 20 m/s 2 e) 25 m/s 2 17) Friction allows a car to make a turn at a speed of 10 miles per hour. By what factor will the friction have to change to allow the driver to make the same turn at twice the speed? a) Four times the friction b) Twice the friction c) The same amount of friction d) One-half the friction e) One-fourth the friction
18) This graph depicts the tangential velocities of several circular space stations with different radii. All the stations are spinning. Which of the following statements is true? a) The centripetal accelerations of the three shorter radii space stations are greater than 10 m/s 2 ; those of the larger ones are less than 10 m/s 2 b) The centripetal accelerations of the three shorter radii space stations are greater than 5 m/s 2 ; those of the larger ones are less than 5 m/s 2 c) The centripetal accelerations of all the stations are nearly 5 m/s 2 d) The centripetal accelerations of all the stations are nearly 10 m/s 2 e) The centripetal accelerations of the three shorter radii space stations are less than 10 m/s 2 ; those of the larger ones are greater than 10 m/s 2
19) A bicycle wheel has a radius of 0.5 m. When it spins, it completes one full turn in 1.6 s. A pebble wedged in the tread has a mass of 10 g. What is centripetal force on the pebble? a) 0.01 N b) 0.08 N c) 0.1 N d) 0.8 N e) 1 N 20) A tetherball swings in a horizontal circle. If the radius of the swing tripled but the tangential speed remains the same, by what factor does the centripetal force change? a) Nine times greater b) Three times greater c) Remains the same d) One-third as much e) One-ninth as much
21) The coefficient of friction between the rubber tires of a car and dry concrete is µ = 0.64. If a car enters a horizontal turn with a radius of 10 m, what is the maximum speed that the car can have and still hold the road? a) 4 m/s b) 8 m/s c) 32 m/s d) 64 m/s e) 144 m/s 22) A spinning top has a radius of 2 cm. If the top takes 0.06 s to complete one rotation, what is the centripetal acceleration at the edge of the top? a) 10 m/s 2 b) 22 m/s 2 c) 100 m/s 2 d) 220 m/s 2 e) 1,000 m/s 2
23) You swing a 100-g object attached to a 2-m string in a circle above your head. The speed of the object is 12 m/s. What is the centripetal force on its mass? a) 0.72 N b) 7.2 N c) 72 N d) 720 N e) 7,200 N 24) A tetherball is whirled in a horizontal circle above your head. If the string breaks, the ball will follow what type of path if it is observed from above? a) Straight outward from the center b) Straight toward the center c) An expanding spiral d) A curved path that gradually approaches a straight line e) Tangent to the original circular path
25) The driver of a racecar takes a turn on a track at a constant speed. What can be said about the acceleration of the driver? a) it is outward from the center. b) It is in the direction of motion. c) It is toward the center. d) It is a vector combination of forward and toward the center. e) It has a value of zero. 26) Two identical cars are moving at the same speed as they take different exit ramps from the highway. Ramp 1 is a circular arc with a radius of 25 m. Ramp 2 is a circular arc with a radius of 50 m. How does the centripetal force on the car taking Ramp 2 compare with that for the car taking Ramp 1? a) Ramp 2 requires four times the centripetal force b) Ramp 2 requires two times the centripetal force c) Ramp 2 requires the same centripetal force d) Ramp 2 requires one-half the centripetal force e) Ramp 2 requires one-fourth the centripetal force
27) A child swings from the end of a rope tied to the branch of a tree. As she swings through the bottom of the arc, which forces act on her? a) A downward force of air pressure b) A downward centrifugal force c) The gravitational force d) The forward force of motion e) The upward tension from the rope
28) A small block slides without friction through a loop-theloop as shown in the diagram below. Which of the force diagrams best illustrates the forces on the block at the bottom of the loop-the-loop? a) I b) II c) III d) IV
Questions #29 and 30 relate to the following scenario: A 60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is 3 kg. 29) At the lowest point in its path, the tension in the rope is 50 N. What is the speed of the bucket? a) 1 m/s b) 2 m/s c) 3 m/s d) 4 m/s 30) What is the critical speed below which the rope would become slack when the bucket reaches the highest point in the circle? a) 0.6 m/s b) 1.8 m/s c) 2.4 m/s d) 4.8 m/s
31) A counter-clockwise rotating platform, with a diameter of 1 m, shown in the diagram below, slows from 4 rad/s to 2 rad/s in 1 s. Which of the acceleration vectors shown best illustrates the magnitude and the direction of the acceleration of the point on the rim when its angular velocity is 2 rad/s? a) I b) II c) III d) IV
32) A 0.25 kg mass is attached to a string and swung in a vertical circle whose radius is 0.75 m. At the bottom of the circle, the mass is observed to have a speed of 10 m/s. What is the magnitude of tension in the string at that point? a) 2.45 N b) 5.78 N c) 22.6 N d) 35.7 N e) 44.7 N 33) A car and driver have a combined mass of 1000 kg. The car passes over the top of a hill that has a radius of curvature equal to 10 m. The speed of the car at that instant is 5 m/s. What is the force of the hill on the car as it passes over the top? a) 7300 N up b) 7300 N down c) 12,300 N up d) 12,300 N down e) 0 N
34) Two satellites orbit the Earth at the same speed in identical orbits. Satellite A is twice the mass of Satellite B. How does the centripetal acceleration of Satellite A compare with that of Satellite B? a) Four times as much b) Twice as much c) The same d) One-half as much e) One-fourth as much 35) A satellite is in circular motion at a distance of 3 R E above the surface of the Earth. The acceleration experienced by the satellite at that location is closest to a) 9.8 m/s 2 b) 1.1 m/s 2 c) 0.61 m/s 2 d) 0 m/s 2
36) A small moon is in circular orbit around its planet as shown below. Which of the vectors displayed below gives the correct direction for the velocity and the acceleration of the moon at the point indicated in its orbit? a) I b) II c) III d) IV
37) The planet Jupiter orbits the Sun at a nearly constant speed. Which of the following statements is true? a) There is a force on Jupiter toward the center of the orbit. b) There is a force on Jupiter pulling it out from the center of the orbit. c) There is a force on Jupiter in the direction of its motion d) Jupiter is accelerating toward the center of the orbit e) There are no forces on Jupiter 38) What can be said about the Moon as it orbits the Earth at a constant speed? a) The Moon s velocity is constant. b) The Moon experiences acceleration toward the center of the orbit. c) There is an unbalanced force on the Moon. d) The Moon experiences acceleration away from the center of the orbit. e) The Moon experiences a constant acceleration.
39) A small piece of space junk has a mass of 3 kg and is orbiting the Earth every 90 min at an altitude of 300 km. The Earth s radius is 6.38 x 10 6 m. What is the junk s orbital velocity? a) 3,710 m/s b) 5,160 m/s c) 0.001 rad/s d) 15,500 m/s e) 7,770 m/s 40) You are looking at a top view of a planet orbiting the Sun in a clockwise direction. Which of the following would describe the velocity, acceleration, and force acting on the planet due to the Sun s pull, when the planet is at Point P? a) vê aé Fé b) vê aç Fç c) vê aè Fè d) vé aç Fç
41) If the distance between two point particles is doubled, the gravitational force between them a) decreases by a factor of 4 b) decreases by a factor of 2 c) increases by a factor of 2 d) increases by a factor of 4 42) Two masses, M 1 and M 2, are separated a distance d. What changes in the variables will result in NO CHANGE in the gravitational force between the masses? a) M 1 is doubled, and d is doubled b) M 2 is doubled, and d is quadrupled c) Both M 1 and M 2 are tripled, and d is tripled d) M 2 is quadrupled, and d is doubled e) M 1 is cut in half, M 2 is cut in half, but d is doubled 43) Two masses separated by a distance R exert a gravitational force F on each other. To triple the force, the separation must be changed to a) 3R b) R/3 c) R/9 d) 3 R e) R/ 3
44) The gravitational force between two point masses A and B is F when they are r meters apart. When the mass of A is increased by a factor of 4, the mass of B is halved and the distance of separation is increased by a factor of three, what is the new force acting between them? a) 2F 1 /9 b) 2F 1 /3 c) 2F 1 d) 3F 1 45) Which of the following graphs best represents the gravitational force as a function of distance between two point masses m 1 and m 2 as they are moved further apart? a) I b) II c) III d) IV
46) A 70-kg astronaut floats at a distance of 10 m from a 50,000 kg spacecraft. What is the force of attraction between the astronaut and the spacecraft? a) 2.4 x 10-6 N b) 2.4 x 10-5 N c) Zero; there is no gravity in space d) 2.4 x 10 5 N e) 2.4 x 10 6 N 47) A moon of mass M orbits a planet of mass 100M. Let the strength of the gravitational force exerted by the planet on the moon be denoted by F 1, and let the strength of the gravitational force exerted by the moon on the planet be F 2. Which of the following is true? a) F 1 = 100 F 2 b) F 1 = 10 F 2 c) F 1 = F 2 d) F 2 = 10 F 1
48) Four planets, A through D, orbit the same star. The relative masses and distances from the star for each planet are shown in the table. For example, Planet A has twice the mass of Planet B, and Planet D has three times the orbital radius of Planet A. Which planet has the highest gravitational attraction to the star? a) Planet A b) Planet B c) Planet C d) Planet D e) All have the same gravitational attraction to the star. 49) A moon of Jupiter has a nearly circular orbit of radius R and an orbital period of T. Which of the following expressions gives the mass of Jupiter? a) 4π 2 R/T 2 b) 2πR 3 /(GT 2 ) c) 4πR 2 /(GT 2 ) d) 4π 2 R 3 /(GT 2 )
50) Which of the following statements are true for a satellite in outer space orbiting the Earth in uniform circular motion? Select two answers. a) There are no forces acting on the satellite. b) The force of gravity is the only force acting on the satellite. c) The force of gravity is balanced by the outward force of the object. d) The mass of the satellite has no effect on the orbital speed. 51) Two satellites of equal mass orbit a planet. Satellite B orbits at twice the orbital radius of Satellite A. Which of the following statements is true? a) The gravitational force on Satellite A is four times less than that on Satellite B. b) The gravitational force on Satellite A is two times less than that on Satellite B. c) The gravitational force of the satellites is equal. d) The gravitational force on Satellite A is two times greater than that on Satellite B. e) The gravitational force on Satellite A is four times greater than that on Satellite B.
52) A satellite orbits the Earth at a distance of 100 km. The mass of the satellite is 100 kg, while the mass of the Earth is approximately 6 x 10 24 kg. The radius of the Earth is approximately 6.4 x 10 6 m. What is the approximate force of gravity on the satellite? a) 4,140 N b) 1,695 N c) 1,412 N d) 947 N e) 432 N 53) A satellite orbits the Earth at a distance of 200 km. If the mass of the Earth is 6 x 10 24 kg and the Earth s radius is 6.4 x 10 6 m, what is the satellite s speed? a) 1 x 10 3 m/s b) 3.5 x 10 3 m/s c) 7.8 x 10 3 m/s d) 5 x 10 6 m/s e) 6.1 x 10 7 m/s
54) A block with a mass of 30 kg is hanging from a string. If you place another block with a mass of 10 kg at a distance of 2 m away, what is the gravitational attraction between the two blocks? a) 1 x 10-11 N b) 5 x 10-10 N c) 1 x 10-10 N d) 5 x 10-9 N e) 1 x 10-9 N 55) Mars orbits the Sun at a distance of 2.3 x 10 11 m. The mass of the Sun is 2 x 10 30 kg, and the mass of Mars is 6.4 x 10 23 kg. Approximately what is the gravitational force that the Sun exerts on Mars? a) 1.6 x 10 20 N b) 1.6 x 10 21 N c) 3.7 x 10 21 N d) 3.7 x 10 32 N e) 3.7 x 10 42 N
56) The Moon has a mass of 7.4 x 10 22 kg and a radius of 1.7 x 10 6 m. What is the force of gravity experienced by a 70 kg astronaut standing on the lunar surface? a) 10 N b) 50 N c) 100 N d) 120 N e) 150 N 57) The dwarf planet Pluto has 1/500 the mass and 1/15 the radius of Earth. What is the value of g (in m/s 2 ) on the surface of Pluto? a) 50/225 b) 50/15 c) 15/50 d) 225/50
58) Which of the following affect the strength of the gravitational field on the surface of a planet? a) The mass of the object at the surface b) The mass of the planet c) The radius of the planet d) The volume of the object at the surface e) The presence of air at the surface of the planet 59) What is the value of g at a height above the Earth s surface that is equal to the radius of the Earth? a) 9.8 N/kg b) 4.9 N/kg c) 6.93 N/kg d) 2.45 N/kg e) 1.6 N/kg 60) A planet has half the mass of Earth and half the radius. Compared to the acceleration due to gravity near the surface of the Earth, the acceleration of gravity near the surface of this planet is a) twice as much b) one-fourth as much c) half as much d) the same e) zero
61) Which of the following is an expression for the acceleration due to gravity for a planet with uniform density ρ and radius R? a) G(4πρ/3R 2 ) b) G(4πρR 2 /3) c) G(4πρ/3R) d) G(4πρR/3) e) None of the above. 62) When climbing from sea level to the top of Mount Everest, a hiker changes elevation by 8,848 m. By what percentage will the gravitational field of the Earth change during the climb? (The Earth s mass is 6 x 10 24 kg, and its radius is 6.4 x 10 6 m.) a) It will increase by approximately 0.3 % b) It will decrease by approximately 0.3 % c) It will increase by approximately 12 % d) It will decrease by approximately 12 % e) The gravitational field strength will not change.
63) What is the gravitational acceleration on the surface of a planet that has three times the mass and twice the radius of the Earth? a) 3g/4 b) g c) 4g/3 d) 2g 64) A 600 N astronaut travels from the Earth to the Moon. The mass of the astronaut as measured on the Moon is a) zero b) 1/6 of the mass of the astronaut on the Earth c) equal to the mass of the astronaut on the Earth d) 6 times the mass of the astronaut on the Earth 65) At the surface of the Earth, an object of mass m has weight w. If this object is transported to an altitude, above Earth s surface, that is twice the radius of the Earth, a) its mass is m and its weight is w/2 b) its mass is m/2 and its weight is w/4 c) its mass is m and its weight is w/4 d) its mass is m and its weight is w/9
66) A student with mass 60 kg imagines she travels to a planet with twice the mass of the Earth and four times the radius of the Earth. Her weight on this planet would be closest to a) 7.5 N b) 30 N c) 75 N d) 300 N e) 4,800 N\
Questions 67 and 68 are based on the following graph: 67) Engineers have designed a centrifuge for studying the effects of high gravity environments on plants and animals. This graph shows the results of the relationship between the radius and the centripetal acceleration. If the scientists want to simulate a 3-G environment, then what would the radius of the centrifuge be? a) 1 m b) 2 m c) 3 m d) 5 m e) 10 m
68) Given that the mean radius of the Moon s orbit is 3.84 x 10 8 m and its period is 2.36 x 10 6 s, at what altitude above the surface of the Earth does a geostationary satellite orbit? (The radius of the Earth is 6.38 x 10 6 m.) a) 4.23 x 10 7 m b) 3.59 x 10 7 m c) 6.2 x 10 8 m d) 2.2 x 10 7 m e) 5.8 x 10 7 m 69) What is the orbital velocity of a satellite at a height of 300 km above the surface of the Earth? (The mass of the Earth is approximately 6 x 10 24 kg and its radius is 6.4 x 10 6 m.) a) 5.42 x 10 1 m/s b) 1.15 x 10 6 m/s c) 7.7 x 10 3 m/s d) 6 x 10 6 m/s e) 3 x 10 8 m/s
70) What is the gravitational force of attraction between two trucks, each of mass 20,000 kg, separated by a distance of 2 m? a) 0.057 N b) 0.013 N c) 0.0067 N d) 1.20 N e) 0 N 71) The gravitational force between two masses is 36 N. If the distance between the masses is tripled, the force of gravity will be a) the same b) 18 N c) 9 N d) 4 N e) 27 N
72) The Earth moves in an elliptical orbit around the Sun as shown in the diagram below. Rank the positions for the force acting on the Earth due to the Sun from highest to lowest. a) A > C > B > D b) A > B > D > C c) C > D > B > A d) C > A > D > B 73) If you could place an object at the center of the Earth, which of the following statements would be true for the object at that location? a) The mass and the weight of the object would be the same as the values on the surface of the Earth. b) The mass would be zero and the weight would be the same as on the surface. c) The mass and the weight would both be zero. d) The weight would be zero and the mass would be the same as the value on the surface of the Earth.
74) Three spheres m 1 = 10 kg, m 2 = 20 kg, and m 3 = 30 kg are located along the x-axis as shown below. What is the resultant force on m 2 due to the other two spheres? a) 1.33 x 10-8 N directed toward m 1 b) 2.67 x 10-8 N directed toward m 3 c) 4.00 x 10-8 N directed toward m 3 d) 5.33 x 10-8 N directed toward m 1 75) Two large bodies, Body A of mass m and Body B of mass 4m, are separated by a distance R. At what distance from Body A, along the line joining the bodies, would the gravitational force on a third object be equal to zero? (Ignore the presence of any other bodies.) a) R/16 b) R/8 c) R/4 d) R/3
76) Two satellites of different masses are in the same circular orbit around Earth. Which of the following statements is correct? a) The magnitude of the gravitational force is the same for both satellites since they are in the same orbit, and both satellites have the same period. b) The magnitude of the gravitational force is zero for the smaller satellite because it is in the same orbit as the larger satellite. Thus the gravitational force exerted on the larger satellite gives it a larger period. c) The magnitudes of the gravitational force depend on the masses of the satellites, and the orbital periods are the same. d) The magnitude of the gravitational force is zero for both satellites, and they have the same period.
77) Astronauts float around inside the space shuttle as it orbits because a) the effects of gravity are almost negligible b) the net force on them is zero because centrifugal force cancels out gravity c) they are accelerating toward the Earth s surface at the same rate as the shuttle and everything within it d) the buoyant force of air is comparable to the force of gravity e) the gravitational attraction of the astronauts to each other and the shuttle is comparable to their attraction to the Earth