$\begin{array} { | l | c | c | c | c | } \hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \\ \hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \\ \hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \\ \hline \end{array}$ 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) 1 × 1022 kg B) 3 × 1022 kg C) 1 × 1023 kg D) 3 × 1023 kg E) 1 × 1024 kg

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 × $10^{25}$ kg, (b) 1.2 kg ×$10 ^ { 31 }$ kg B) (a) 4.3 kg × $10^{25}$ kg, (b) 1.2 kg ×$10 ^ { 31 }$ kg C) (a) 2.4 kg × $10^{25}$ kg, (b) 7.1 kg ×$10^{30}$ kg D) (a) 4.3 kg × $10^{25}$ kg, (b) 7.1 kg ×$10^{30}$ kg A) (a) 2.4 kg × $10^{25}$ kg, (b) 1.2 kg ×$10 ^ { 31 }$ kg B) (a) 4.3 kg × $10^{25}$ kg, (b) 1.2 kg ×$10 ^ { 31 }$ kg C) (a) 2.4 kg × $10^{25}$ kg, (b) 7.1 kg ×$10^{30}$ kg D) (a) 4.3 kg × $10^{25}$ kg, (b) 7.1 kg ×$10^{30}$ kg

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 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

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 A) 8.0 m/s2 B) 16 m/s2 C) 128 m/s2 D) 4.0 m/s2 E) 2.0 m/s2

Exam 6: Gravity

Mass Radius Orbital radius Orbital period Moon A 4.0\times1 unknown 2.0\times1 4.0\times1 Moon B 1.5\times1 2.0\times1 3.0\times1 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)

(Multiple Choice)

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Question 61

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?

(Multiple Choice)

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Question 62

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?

(Multiple Choice)

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Question 63

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)

(Multiple Choice)

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Question 64

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?

(Multiple Choice)

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Question 65

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?

(Multiple Choice)

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Question 66

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

(Multiple Choice)

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Question 67

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.

(Multiple Choice)

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Question 68

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.

(Multiple Choice)

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Question 69

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?

(Multiple Choice)

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Question 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

(Multiple Choice)

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Question 71

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?

(Multiple Choice)

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Question 72

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)

(Multiple Choice)

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Question 73

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

(Multiple Choice)

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Question 74

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)

(Multiple Choice)

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Question 75

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)

(Multiple Choice)

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Question 76

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?

(Multiple Choice)

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Question 77

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?

(Multiple Choice)

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Question 78

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?

(Multiple Choice)

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Question 79

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)

(Multiple Choice)

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Question 80

Showing 61 - 80 of 96

Exam 6: Gravity

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 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 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?

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

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.

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.

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 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

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?

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)

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

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)

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?

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 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?

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)

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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.

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)

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)

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?

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)