Physics Chapter 5
A
16) In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25? A) 8.9 m/s B) 2.3 m/s C) 3.0 m/s D) 4.9 m/s E) It depends on the mass of the passengers.
A
2) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding? A) 9000 N B) 9800 N C) 300 N D) 900 N E) 3000 N
C
26) What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? A) 31° B) 41° C) 51° D) 61°
1.8 × 10-6 m/s2, toward B
33) A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along the line connecting A and B. When the third mass is suddenly released, find the magnitude and direction (toward A or toward B) of its initial acceleration. (G = 6.67 × 10-11 N ∙ m2/kg2)
E
38) Three identical 50-kg balls are held at the corners of an equilateral triangle, 30 cm on each side. If one of the balls is released, what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 3.7 × 10-8 m/s2 B) 2.5 × 10-8 m/s2 C) 1.9 × 10-8 m/s2 D) 4.2 × 10-8 m/s2 E) 6.4 × 10-8 m/s2
C
46) What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius? A) 580 N B) 290 N C) 1160 N D) 2320 N E) 1200 N
B
5) If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water. A) True B) False
C
53) An object weighs 432 N on the surface of the earth. The earth has radius R. If the object is raised to a height of 3R above the earth's surface, what is its weight? A) 108 N B) 48.0 N C) 27.0 N D) 305 N E) 144 N
B
54) By how many newtons does the weight of a 100-kg person decrease when he goes from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is 6.38 × 106 m. A) 0.60 N B) 1.5 N C) 2.6 N D) 3.6 N E) 9.8 N
A
55) The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit? A) 61 N B) 110 N C) 9000 N D) 16,000 N
C
56) A spherically symmetric planet has four times the earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet? A) 3.0 N B) 6.0 N C) 12 N D) 24 N E) 36 N
1.4 m/s2 toward the center of the earth
58) A satellite orbits the Earth once every 6.0 hours in a circle. What are the magnitude and direction of the acceleration of the satellite? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg)
D
6) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying? A) 640 m B) 1200 m C) 7100 m D) 9200 m
A
60) The captain of a spaceship orbiting planet X discovers that to remain in orbit at from the planet's center, she needs to maintain a speed of What is the mass of planet X? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 2.8 × 1019 kg B) 4.2 × 1017 kg C) 2.8 × 1016 kg D) 4.2 × 1014 kg
A
64) Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon, which has been named Dactyl. From the dimensions of Ida and its general features, one can estimate the mass of Ida to be 4.5 × 1016 kg, and the distance between Dactyl and Ida is approximately 90 km. Assuming a circular orbit, what would be the orbital speed of Dactyl? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.8 m/s B) 11 m/s C) 2.3 m/s D) 2.9 m/s E) 30 m/s
(a) 5.5 ×103 s (b) 7.7 ×103 m/s
67) The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 1024 kg, the radius of the earth is 6.38 × 106 m, and G = 6.67 × 10-11 N ∙ m2/kg2. Assume a circular orbit. (a) What is the period of the International Space Station's orbit? (b) What is the speed of the International Space Station in its orbit?
3.4 × 103 N
71) A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 6.0 × 1024 kg)
D
72) Europa, a satellite of Jupiter, has an orbital diameter of 1.34 × 109 m and a period of 3.55 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.53 × 1027 kg B) 1.65 × 1027 kg C) 1.07 × 1027 kg D) 1.89 × 1027 kg E) 3.08 × 1027 kg
D
73) The innermost satellite of Jupiter orbits the planet with a radius of 422 × 103 km and a period of 1.77 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.33 × 1027 kg B) 1.50 × 1027 kg C) 1.72 × 1027 kg D) 1.89 × 1027 kg E) 3.08 × 1027 kg
B
75) The average distance from Earth to the sun is defined as one astronomical unit (AU). If an asteroid orbits the sun in 1/3 of a year in a circular orbit, the asteroid's distance from the sun is closest to A) 0.19 AU. B) 0.48 AU. C) 2.1 AU. D) 5.2 AU. E) 0.33 AU.
C
78) Two moons orbit a planet in circular orbits. Moon A has orbital radius R, and moon B has orbital radius 4R. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit? A) 20 days B) 80 days C) 160 days D) 320 days E) 5 days
A
23) The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked? A) 32° B) 34° C) 30° D) 28° E) 26°
B
11) A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump? A) 200 N B) 390 N C) 790 N D) 490 N E) 590 N
D
11) A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity? A) when it gets above the atmosphere B) when it is half-way there C) when it is closer to the Moon than it is to Earth D) It is never beyond the pull of Earth's gravity.
C
12) A car moving at a steady 10 m/s on a level highway encounters a depression that has a circular cross-section with a radius of 30 m. The car maintains its speed as it drives through the depression. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the bottom of the depression? A) 200 N B) 390 N C) 790 N D) 490 N E) 590 N
A
12) If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh A) the same as you do on Earth. B) two times more than you do on Earth. C) two times less than you do on Earth. D) four times more than you do on Earth.
E
13) An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is A) zero. B) the same as on the surface of the earth. C) one-half of its weight on the surface of the earth. D) one-third of its weight on the surface of the earth. E) one-quarter of its weight on the surface of the earth.
A
13) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70-kg pilot at that point? A) 3300 N B) 690 N C) 2600 N D) 490 N E) 1400 N
A
1) A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car. A) 11.4 m/s B) 12.5 m/s C) 10.1 m/s D) 14.9 m/s
C
1) You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the ice, it A) moves along a straight-line path away from the center of the circle. B) moves along a straight-line path toward the center of the circle. C) moves along a straight-line path in its original direction. D) continues to follow a circular path, but with a radius larger than the original radius. E) moves along a path that is neither straight nor circular.
D
21) If Earth had twice its present mass but it orbited at the same distance from the sun as it does now, its orbital period would be A) 4 years. B) 3 years. C) 2 years. D) 1 year. E) 6 months.
6.75 × 108 kg
31) Two identical tiny balls of highly compressed matter are 1.50 m apart. When released in an orbiting space station, they accelerate toward each other at 2.00 cm/s2. What is the mass of each of them? (G = 6.67 × 10-11 N ∙ m2/kg2)
C
32) As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 1022 kg, the distance to the Moon is 3.82 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2. A) 0.24 N B) 0.024 N C) 0.0024 N D) 0.00024 N
B
44) Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is A) g/3. B) 3g. C) 6g. D) g/9. E) 9g.
A
59) Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg) A) 1.44 × 107 m B) 0.69 × 107 m C) 7.22 × 107 m D) 2.11 × 107 m
D
8) Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one? A) 16F B) 8F C) 4F D) F E) F/4
C
80) It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiter's orbit is truly circular, what is the distance from Jupiter to the sun, given that the distance from the earth to the sun is 1.5 × 1011 m? A) 3.9 × 1011 m B) 5.2 × 1011 m C) 7.9 × 1011 m D) 9.7 × 1011 m E) 3.2 × 1012 m
E
10) A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.35. At what speed will the car begin to skid sideways? A) 9.3 m/s B) 24 m/s C) 34 m/s D) 35 m/s E) 19 m/s
D
10) Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the distance is changed to r/4. What is the magnitude of the new gravitational force? A) F/32 B) F/16 C) 16F D) 32F E) 2F
E
14) A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the location of the satellite? A) gm/9 B) 0 C) gm D) gm/3 E) gm/16
A
14) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7.0 times his true weight? A) 1700 m B) 1500 m C) 2200 m D) 230 m E) 42 m
D
15) A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth? A) g B) g/2 C) g/4 D) g/8 E) g/16
D
15) In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km? A) 79 m/s B) 310 m/s C) 260 m/s D) 160 m/s E) 510 m/s
D
16) The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of Planet B? A) 1/6 B) 1/16 C) 1/24 D) 1/96 E) 1/12
D
17) A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to be 25°? A) 0.089 N B) 0.041 N C) 0.20 N D) 0.22 N E) 0.46 N
D
17) Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B? A) m/ B) m C) m D) 4m E) m/4
E
18) A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18°, what is the speed of the mass? A) 0.55 m/s B) 2.0 m/s C) 3.8 m/s D) 1.3 m/s E) 1.1 m/s
C
18) Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B? A) r/ B) r C) r D) 4r E) 2r
(a) 79.0 m/s2 toward the center of the circle (b) 13.8 N
19) A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s. (a) What are the magnitude and direction of the acceleration of the ball? (b) Find the tension in the string.
E
19) Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B? A) The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B. B) The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B. C) The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B. D) The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater. E) We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets.
B
2) When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path? A) the normal force from the road B) the friction force from the road C) gravity D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.
D
20) A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the road surface is the same in both cases? A) 160 m/s B) 80 m/s C) 70 m/s D) 40 m/s E) 30 m/s
B
20) The reason an astronaut in an earth satellite feels weightless is that A) the astronaut is beyond the range of the earth's gravity. B) the astronaut is falling. C) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel. D) this is a psychological effect associated with rapid motion. E) the astronaut's acceleration is zero.
D
21) A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth? A) 91 min B) 8.7 min C) 4.6 min D) 1.5 min E) 0.011 min
A
22) A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction? A) 29.1° B) 13.5° C) 33.8° D) 56.2° E) 60.9°
D
22) Satellite A has twice the mass of satellite B, and moves at the same orbital distance from Earth as satellite B. Compare the speeds of the two satellites. A) The speed of B is twice the speed of A. B) The speed of B is one-half the speed of A. C) The speed of B is one-fourth the speed of A. D) The speed of B is equal to the speed of A. E) The speed of B is four times the speed of A.
B
23) Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions? A) 1/4 as long as the present year B) 1/2 as long as the present year C) the same as the present year D) twice as long as the present year E) four times as long as the present year
(a) 37° (b) 9200 N (normal force), 0 N (friction)
24) A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a) What banking angle should you specify for this curve? (b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed?
B
24) Halley's Comet is in a highly elliptical orbit around the sun. Therefore the orbital speed of Halley's Comet, while traveling around the sun, A) is constant. B) increases as it nears the Sun. C) decreases as it nears the Sun. D) is zero at two points in the orbit.
C
25) Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits? A) T/R B) T/R2 C) T2/R3 D) T3/R2 E) T2/R
C
25) Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger-radius curve? A) v / B) 2v C) v D) v/2
B
27) A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated without friction at a speed of A) 22 m/s. B) 31 m/s. C) 44 m/s. D) 67 m/s.
B
28) A highway curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road? A) 9.4 m/s B) 28 m/s C) 780 m/s D) The curve cannot be taken safely at any speed.
A
29) What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere. (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.8 × 10-8 N B) 8.5 × 103 N C) 1.2 × 10-7 N D) 9.8 × 10-10 N E) 2.0 × 10-9 N
D
3) A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road? A) tangent to the curve in the forward direction B) tangent to the curve opposite to the direction of the car's motion C) perpendicular to the curve outward D) perpendicular to the curve inward E) There is no friction on the car because its speed is constant.
A
3) The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway? A) 54 m/s B) 52 m/s C) 50 m/s D) 48 m/s E) 46 m/s
2.67 × 10-8 N
30) What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? (G = 6.67 × 10-11 N ∙ m2/kg2)
B
34) When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 1024 kg, the sun's mass is 1.99 × 1030 kg, and the Earth-sun distance is 1.5 × 1011 m. A) 1.3 × 108 m B) 2.6 × 108 m C) 1.3 × 1010 m D) 2.6 × 1010 m
E
35) Mass Radius Orbital radius Orbital period Moon A 4.0 × 1020 kg unknown 2.0 × 108 m 4.0 × 106 s Moon B 1.5 × 1020 kg 2.0 × 105 m 3.0 × 108 m unknown Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.6 × 1013 N B) 4.4 × 1013 N C) 1.0 × 1014 N D) 2.0 × 1014 N E) 4.0 × 1014 N
A
36) At their closest approach, Venus and Earth are 4.20 × 1010 m apart. The mass of Venus is 4.87 × 1024 kg, the mass of Earth is 5.97 × 1024 kg, and G = 6.67 × 10-11 N ∙ m2/kg2. What is the magnitude of the gravitational force exerted by Venus on Earth at that point? A) 1.10 × 1018 N B) 4.62 × 1028 N C) 5.43 × 1026 N D) 6.30 × 1020 N E) 1.72 × 1019 N
A
37) A spaceship with a mass of 2.8 × 106 kg is traveling toward two spherical asteroids, each with a mass of 5.0 × 1016 kg, that are 40 km apart center-to-center. Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 12,000 N B) 8,000 N C) 16,000 N D) 6,200 N E) 18,000 N
B
39) What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, the center-to-center distance between Earth and the Moon is 3.84 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2. A) 3.45 × 108 m B) 3.84 × 107 m C) 4.69 × 106 m D) 3.83 × 106 m E) 4.69 × 107 m
C
4) A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h. What is the magnitude of the net force on the motorcycle? A) 719 N B) 2.95 × 103 N C) 1.31 × 104 N D) 4.31 × 104 N
C
4) When an object moves in uniform circular motion, the direction of its acceleration is A) in the same direction as its velocity vector. B) in the opposite direction of its velocity vector. C) is directed toward the center of its circular path. D) is directed away from the center of its circular path. E) depends on the speed of the object.
A
40) From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54g? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg, Rearth = 6.38 × 106 m) A) 2300 km B) 1700 km C) 5400 km D) 2900 km
A
41) At a given point above Earth's surface, the acceleration due to gravity is equal to What is the altitude of this point above Earth's surface? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg, Rearth = 6.38 × 106 m) A) 770 km B) 970 km C) 1500 km D) 2000 km E) 2400 km
C
42) In another solar system, a planet has an airless moon Zygo that is 4.0 × 105 m in diameter. Experiments reveal that a freely falling object at the surface of Zygo accelerates at 0.20 m/s2. What is the mass of Zygo? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 2.4 × 1019 kg B) 4.8 × 1019 kg C) 1.2 × 1020 kg D) 2.4 × 1020 kg E) 4.8 × 1020 kg
D
43) Mass Radius Orbital radius Orbital period Moon A 4.0 × 1020 kg unknown 2.0 × 108 m 4.0 × 106 s Moon B 1.5 × 1020 kg 2.0 × 105 m 3.0 × 108 m unknown Mithra is an unknown planet that has two airless moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 0.10 m/s2 B) 0.15 m/s2 C) 0.20 m/s2 D) 0.25 m/s2 E) 0.30 m/s2
B
45) What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius? A) 580 N B) 290 N C) 1160 N D) 118 N E) 1200 N
D
47) The mass of the Moon is 7.4 × 1022 kg, its radius is 1.74 × 103 km, and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 2.8 × 106 m/s2 B) 9.8 m/s2 C) 4.9 m/s2 D) 1.6 m/s2 E) 0.80 m/s2
D
48) An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point? A) zero B) g C) g/2 D) g/4 E) g/
A
49) The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? A) 0.41 R B) 0.50 R C) 1.00 R D) 1.41 R E) 0.25 R
B
5) A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string? A) 700 m/s B) 26 m/s C) 19 m/s D) 13 m/s
A
50) The mass of Pluto is 1.31 × 1022 kg and its radius is 1.15 × 106 m. What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 0.661 m/s2 B) 9.81 m/s2 C) 1.62 m/s2 D) 3.72 m/s2 E) 0.140 m/s2
B
51) An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest. She also knows that the radius of Z-49 is 3.39 × 106 m. From this information, what will she determine for the mass of Z-49? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 3.30 × kg. B) 6.62 × kg. C) 4.62 × kg. D) 8.09 × kg. E) 9.95 × kg.
A
52) At a distance of 14,000 km from the center of Planet Z-99, the acceleration due to gravity is 32 m/s2. What is the acceleration due to gravity at a point 28,000 km from the center of this planet? A) 8.0 m/s2 B) 16 m/s2 C) 128 m/s2 D) 4.0 m/s2 E) 2.0 m/s2
20.6 N (on Earth), 3.40 N (on the Moon)
57) A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 × 106 m, its mass is 7.35 × 1022 kg, and G = 6.67 × 10-11 N ∙ m2/kg2. How much does the hammer weigh on Earth and on the Moon?
A
6) When a car goes around a banked circular curve at the proper speed speed for the banking angle, what force cause it to follow the circular path? A) the normal force from the road B) the friction force from the road C) gravity D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration.
A
61) Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 1026 kg, and use an orbital radius of 1.00 x 105 km. (G = 6.67 × 10-11 N ∙ m2/kg2) A) 19.5 km/s B) 27.5 km/s C) 13.8 km/s D) 9.40 km/s
A
62) You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m. You have previously determined that the planet orbits 2.9 × 1011 m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 19.5 m/s2. What are the masses of (a) the planet and (b) the star? (G = 6.67 × 10-11 N ∙ m2/kg2) A) (a) 2.4 kg × kg, (b) 1.2 kg × kg B) (a) 4.3 kg × kg, (b) 1.2 kg × kg C) (a) 2.4 kg × kg, (b) 7.1 kg × kg D) (a) 4.3 kg × kg, (b) 7.1 kg × kg
C
63) A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min. The radius of Zeeman-474 is 6.38 × 106 m. What is the mass of this planet? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.0 × 1024 kg B) 5.5 × 1024 kg C) 6.0 × 1024 kg D) 6.5 × 1024 kg
E
65) In another solar system, a planet has a moon that is 4.0 × 105 m in diameter. Measurements reveal that this moon takes 3.0 x 105 s to make each orbit of diameter 1.8 × 108 m. What is the mass of the planet? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.2 × 1024 kg B) 1.7 × 1024 kg C) 2.4 × 1024 kg D) 3.4 × 1024 kg E) 4.8 × 1024 kg
D
66) Mass Radius Orbital radius Orbital period Moon A 4.0 × 1020 kg unknown 2.0 × 108 m 4.0 × 106 s Moon B 1.5 × 1020 kg 2.0 × 105 m 3.0 × 108 m unknown Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the mass of Mithra? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1 × 1022 kg B) 3 × 1022 kg C) 1 × 1023 kg D) 3 × 1023 kg E) 1 × 1024 kg
(a) 3900 N (b) 7.5 × 105 m
68) A satellite of mass 500 kg orbits the earth with a period of 6,000 s. The earth has a mass of 5.97 × 1024 kg, a radius of 6.38 × 106 m, and G = 6.67 × 10-11 N ∙ m2/kg2. (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the earth's surface.
D
69) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much mass, the orbital speed of the satellite at the same distance from the center would be A) V . B) 2V. C) V. D) V/ . E) V/2.
A
7) One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts walk on the inside surface of the space station. How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts? A) 28 s B) 39 s C) 6.2 s D) 4.4 s
C
7) Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve? A) the car with the new tires B) the car with the bald tires C) Neither car will slide. D) It depends on if the pavement is wet or dry.
C
70) A satellite of mass M takes time T to orbit a planet. If the satellite had twice as much mass, the time for it to orbit the planet at the same altitude would be A) 4T. B) 2T. C) T. D) T/2. E) T/4.
47 years
74) As you know, the earth has an orbital period of 1.0 year at an orbital radius of 1.0 AU (astronomical unit, the average distance between the earth and the sun). If a new "minor planet" were to be found in a circular orbit with radius 13 AU, what would be its orbital period?
B
76) If the earth were twice as far from the sun as it presently is, how long (in terms of the present year) would it take it to make one orbit around the sun? A) 2.0 years B) 2.8 years C) 4.0 years D) 5.7 years E) 16 years
B
77) If NASA wants to put a satellite in a circular orbit around the sun so it will make 2.0 orbits per year, at what distance (in astronomical units, AU) from the sun should that satellite orbit? The earth's orbit is 1.0 AU from the sun. A) 7.6 AU B) 0.63 AU C) 0.50 AU D) 2.0 AU E) 0.71 AU
D
79) The planet Jupiter is 7.78 × 1011 m from the sun. How long does it take for Jupiter to orbit once about the sun given that the distance from the earth to the sun is 1.50 × 1011 m? A) 2.3 years B) 5.2 years C) 6.0 years D) 12 years E) 27 years
460 N
8) A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?
E
9) A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball? A) 0 N B) 20 N C) 40 N D) 50 N E) 100 N
B
9) Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is changed to 4r. What is the magnitude of the new gravitational force? A) F/16 B) F/4 C) 16F D) 4F E) F/2
