Question 1

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)

Accepted Answer

A)   12,000 N
B)   8,000 N
C)   16,000 N
D)   6,200 N
E)   18,000 NF) None of the above
G) A) and C)

Question 2

Mass  Radius  Orbital radius  Orbital period  Moon A 4.0×1020 kg unknown 2.0×108 m4.0×106 s Moon B 1.5×1020 kg2.0×105 m3.0×108 m unknown \begin{array} { | l | c | c | c | c | } \hline & 	ext { Mass } & 	ext { Radius } & 	ext { Orbital radius } & 	ext { Orbital period } \\hline 	ext { Moon A } & 4.0 	imes 10 ^ { 20 } \mathrm {~kg} & 	ext { unknown } & 2.0 	imes 10 ^ { 8 } \mathrm {~m} & 4.0 	imes 10 ^ { 6 } \mathrm {~s} \\hline 	ext { Moon B } & 1.5 	imes 10 ^ { 20 } \mathrm {~kg} & 2.0 	imes 10 ^ { 5 } \mathrm {~m} & 3.0 	imes 10 ^ { 8 } \mathrm {~m} & 	ext { unknown } \\hline\end{array} Moon A  Moon B ​ Mass 4.0×1020 kg1.5×1020 kg​ Radius  unknown 2.0×105 m​ Orbital radius 2.0×108 m3.0×108 m​ Orbital period 4.0×106 s 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)

Accepted Answer

A)   1 × 1022 kg
B)   3 × 1022 kg
C)   1 × 1023 kg
D)   3 × 1023 kg
E)   1 × 1024 kg F) A) and B)
G) B) and C)

Question 3

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?

Accepted Answer

A)   8.0 m/s2
B)   16 m/s2
C)   128 m/s2
D)   4.0 m/s2
E)   2.0 m/s2F) All of the above
G) C) and D)

Question 4

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

Accepted Answer

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) All of the above
F) A) and D)

Question 5

The captain of a spaceship orbiting planet X discovers that to remain in orbit at  410 km410 \mathrm {~km}410 km  from the planet's center, she needs to maintain a speed of  68 m/s68 \mathrm {~m} / \mathrm { s }68 m/s  What is the mass of planet X? (G = 6.67 × 10-11 N ∙ m2/kg2)

Accepted Answer

A)   2.8 × 1019 kg
B)   4.2 × 1017 kg
C)   2.8 × 1016 kg
D)   4.2 × 1014 kg E) B) and C)
F) A) and D)

Question 6

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

Accepted Answer

A)   4T.
B)   2T.
C)   T.
D)   T/2.
E)   T/4.F) C) and E)
G) A) and E)

Question 7

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)

Accepted Answer

A)   (a)  2.4 kg ×  102510^{25}1025  kg, (b)  1.2 kg × 103110 ^ { 31 }1031  kg
B)   (a)  4.3 kg ×  102510^{25}1025  kg, (b)  1.2 kg × 103110 ^ { 31 }1031  kg
C)   (a)  2.4 kg ×  102510^{25}1025  kg, (b)  7.1 kg × 103010^{30}1030  kg
D)   (a)  4.3 kg ×  102510^{25}1025  kg, (b)  7.1 kg × 103010^{30}1030  kg E) B) and D)
F) A) and C)

Question 8

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?

Accepted Answer

A)   zero
B)   g
C)   g/2
D)   g/4
E)   g/  2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​F) C) and D)
G) None of the above

Question 9

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?

Accepted Answer

A)   200 N
B)   390 N
C)   790 N
D)   490 N
E)   590 NF) B) and D)
G) A) and B)

Question 10

A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

Accepted Answer

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.E) B) and D)
F) A) and D)

Question 11

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?

Accepted Answer

A)   0 N
B)   20 N
C)   40 N
D)   50 N
E)   100 NF) D) and E)
G) A) and C)

Question 12

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?

Accepted Answer

A)   719 N
B)   2.95 × 103 N
C)   1.31 × 104 N
D)   4.31 × 104 NE) None of the above
F) All of the above

Question 13

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?

Accepted Answer

A)   9.4 m/s
B)   28 m/s
C)   780 m/s
D)   The curve cannot be taken safely at any speed.E) B) and D)
F) None of the above

Question 14

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.

Accepted Answer

A)   1.3 × 108 m
B)   2.6 × 108 m
C)   1.3 × 1010 m
D)   2.6 × 1010 mE) B) and C)
F) All of the above

Question 15

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.

Accepted Answer

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.F) B) and D)
G) All of the above

Question 16

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?

Accepted Answer

A)   v /  2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)   2v
C)   v  2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)   v/2 E) All of the above
F) C) and D)

Question 17

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?

Accepted Answer

A)   F/32
B)   F/16
C)   16F
D)   32F
E)   2FF) A) and E)
G) B) and C)

Question 18

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?

Accepted Answer

A)   108 N
B)   48.0 N
C)   27.0 N
D)   305 N
E)   144 NF) A) and B)
G) All of the above

Question 19

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)

Accepted Answer

A)   1.2 × 1024 kg
B)   1.7 × 1024 kg
C)   2.4 × 1024 kg
D)   3.4 × 1024 kg
E)   4.8 × 1024 kgF) A) and D)
G) B) and E)

Question 20

At a given point above Earth's surface, the acceleration due to gravity is equal to  7.8 m/s27.8 \mathrm {~m} / \mathrm { s } ^ { 2 }7.8 m/s2  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)

Accepted Answer

A)   770 km
B)   970 km
C)   1500 km
D)   2000 km
E)   2400 km F) All of the above
G) C) and E)

Exam 6: Gravity

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?

Correct Answer
verified

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?

Correct Answer
verified

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

Correct Answer
verified

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)

Correct Answer
verified

Correct Answer
verified

At a given point above Earth's surface, the acceleration due to gravity is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the altitude of this point above Earth's surface? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, R_earth = 6.38 × 10⁶ m)

Correct Answer
verified

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

Correct Answer
verified

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?

Correct Answer
verified

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?

Correct Answer
verified

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?

Correct Answer
verified

Correct Answer
verified

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?

Correct Answer
verified

A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

Correct Answer
verified

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?

Correct Answer
verified

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?

Correct Answer
verified

The captain of a spaceship orbiting planet X discovers that to remain in orbit at $410 \mathrm {~km}$ from the planet's center, she needs to maintain a speed of $68 \mathrm {~m} / \mathrm { s }$ What is the mass of planet X? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

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.

Correct Answer
verified

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.

Correct Answer
verified

Exam 6: Gravity

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?

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

At a given point above Earth's surface, the acceleration due to gravity is equal to 7.8 m/s27.8 \mathrm {~m} / \mathrm { s } ^ { 2 }7.8 m/s2 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)

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

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?

Correct AnswerverifiedShow Answer

The captain of a spaceship orbiting planet X discovers that to remain in orbit at 410 km410 \mathrm {~km}410 km from the planet's center, she needs to maintain a speed of 68 m/s68 \mathrm {~m} / \mathrm { s }68 m/s What is the mass of planet X? (G = 6.67 × 10-11 N ∙ m2/kg2)

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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Correct Answer
verified

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)

Correct Answer
verified

Correct Answer
verified

At a given point above Earth's surface, the acceleration due to gravity is equal to $7.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ What is the altitude of this point above Earth's surface? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, R_earth = 6.38 × 10⁶ m)

Correct Answer
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Correct Answer
verified

Correct Answer
verified

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?

Correct Answer
verified

Correct Answer
verified

Correct Answer
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Correct Answer
verified

Correct Answer
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Correct Answer
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Correct Answer
verified

The captain of a spaceship orbiting planet X discovers that to remain in orbit at $410 \mathrm {~km}$ from the planet's center, she needs to maintain a speed of $68 \mathrm {~m} / \mathrm { s }$ What is the mass of planet X? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

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.

Correct Answer
verified

Correct Answer
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