Question 1

What is the gravitational force between two 7.00-kg balls, when they are 35.0 cm apart?
G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

2.67 × 10^-8 N

Question 2

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to increase the forward speed of the rocket, what will happen?

Accepted Answer

The spacecraft will be put into an elliptical orbit with a perigee,the distance of closest approach to the center of Earth,equal to the original radius.The average radius of this orbit is larger,so it will take longer to complete one revolution.So when he completes one revolution,bringing him back to the original radius,he will have fallen further behind.

Question 3

For a satellite in orbit around Earth, the product of its speed times the distance from the center of Earth has the same value when the satellite is at the perigee, its closest approach to Earth, and at the apogee, its furthest point from Earth. Is the product the same at other points on the orbit?
 Why?

Accepted Answer

No.According to Kepler's second law,equal areas are swept in equal times.For a short time interval,this translates into the product of the perpendicular component of radius times the speed times one-half of the time interval.Since the velocity and the radius are perpendicular to each other only at those two points,the product has that value only at those two points.

Question 4

What is the ratio of potential energy to kinetic energy for a comet that has just enough energy to escape from the Sun's gravitational field?

Accepted Answer

A)  1/2 
B)  1 
C)  2 
D)  -1 
E)  -2 
A)  1/2 
B)  1 
C)  2 
D)  -1 
E)  -2

Question 5

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.0060 m/s2 and the escape velocity is only 10.1 m/s. What is the mass of Eros? G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  2.3 × 1016 kg 
B)  3.5 × 1012 kg 
C)  6.5 × 1015 kg 
D)  4.9 × 1014 kg 
E)  6.7 × 1013 kg 
A)  2.3 × 1016 kg 
B)  3.5 × 1012 kg 
C)  6.5 × 1015 kg 
D)  4.9 × 1014 kg 
E)  6.7 × 1013 kg

Question 6

A satellite is in an elliptical orbit around Earth. At one point on the ellipse, it is 40 × 106 m from the center of Earth and has a speed of 10,000 m/s. At another point on the ellipse its speed is 9100 m/s. How far from the center of Earth is the second point? The mass of Earth is 5.97 × 1024 kg and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  2.9 × 108 m 
B)  4.3 × 108 m 
C)  6.7 × 107 m 
D)  8.6 × 107 m 
E)  9.1 × 107 m 
A)  2.9 × 108 m 
B)  4.3 × 108 m 
C)  6.7 × 107 m 
D)  8.6 × 107 m 
E)  9.1 × 107 m

Question 7

A mass is attached to a fixed point by means of an ideal spring with zero unstretched length and is free to move in two dimensions. What would be the equivalent statement of Kepler's third law for this situation in the case of circular orbits around the fixed point?

Accepted Answer

The period of the or

Question 8

In 1994, fragments of Comet P/Shoemaker-Levy 9 collided with Jupiter. Assume that these fragments came from an infinite distance away with zero initial speed and fell into Jupiter. What was their speed when they arrived at Jupiter's surface? Jupiter has a mass of 1.90 × 1027 kg and a radius of 71.4 × 106 m, and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  10,400 m/s 
B)  11,200 m/s 
C)  35,500 m/s 
D)  42,100 m/s 
E)  59,600 m/s 
A)  10,400 m/s 
B)  11,200 m/s 
C)  35,500 m/s 
D)  42,100 m/s 
E)  59,600 m/s

Question 9

An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 106 m and that G = 6.67 x 10-11 N·m2/kg2. From this information, she can conclude that the mass of Mars is

Accepted Answer

A)  3.30 × 1023 kg. 
B)  6.62 × 1023 kg. 
C)  4.62 × 1023 kg. 
D)  8.09 × 1023 kg. 
E)  9.95 × 1023 kg. 
A)  3.30 × 1023 kg. 
B)  6.62 × 1023 kg. 
C)  4.62 × 1023 kg. 
D)  8.09 × 1023 kg. 
E)  9.95 × 1023 kg.

Question 10

Tides are approximately 24 hours apart.

Accepted Answer

A) True 
 B)False

Question 11

What is the ratio of potential energy to total energy for a planet in a circular orbit around the Sun?

Accepted Answer

A)  1/2 
B)  1 
C)  2 
D)  -1 
E)  -2 
A)  1/2 
B)  1 
C)  2 
D)  -1 
E)  -2

Question 12

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 × 106 m.

Accepted Answer

A)  9.81 m/s2 
B)  9.78 m/s2 
C)  9.75 m/s2 
D)  9.72 m/s2 
E)  9.69 m/s2 
A)  9.81 m/s2 
B)  9.78 m/s2 
C)  9.75 m/s2 
D)  9.72 m/s2 
E)  9.69 m/s2

Question 13

A satellite is in a circular parking orbit 6.98 × 106 m from the center of Earth. To initiate a Hohmann transfer, a rocket gives it an accelerating thrust so that its speed is increased to 8300 m/s. How far from the center of Earth will the satellite be when it reaches its apogee? The mass of Earth is 5.97 × 1024 kg and G = 6.67 x 10-11 N·m2/kg2.

Accepted Answer

A)  3.12 × 107 m 
B)  2.48 × 107 m 
C)  1.06 × 107 m 
D)  6.73 × 107 m 
E)  4.75 × 107 m 
A)  3.12 × 107 m 
B)  2.48 × 107 m 
C)  1.06 × 107 m 
D)  6.73 × 107 m 
E)  4.75 × 107 m

Question 14

The gravitational force between two objects is inversely proportional to

Accepted Answer

A)  the distance between the two objects. 
B)  the square of the distance between the two objects. 
C)  the product of the masses of the two objects. 
D)  the square of the product of the masses of the two objects. 
E)  none of the above 
A)  the distance between the two objects. 
B)  the square of the distance between the two objects. 
C)  the product of the masses of the two objects. 
D)  the square of the product of the masses of the two objects. 
E)  none of the above

Question 15

A projectile is shot from the surface of Earth by means of a very powerful cannon. If the projectile reaches a height of 35,000 m above Earth's surface, what was the speed of the projectile when it left the cannon?

Accepted Answer

A)  355 m/s 
B)  505 m/s 
C)  827 m/s 
D)  710 m/s 
E)  906 m/s 
A)  355 m/s 
B)  505 m/s 
C)  827 m/s 
D)  710 m/s 
E)  906 m/s

Question 16

The identical 50-kg masses are held at the corners of an equilateral triangle, 30 cm on each side. If one of the masses is released, what is its initial acceleration, if the only forces acting on it are the gravitational forces due to the other two masses?

Accepted Answer

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 
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

Question 17

The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon?

Accepted Answer

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 
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

Question 18

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?

Accepted Answer

A)  0.41 R 
B)  0.50 R 
C)  1.0 R 
D)  1.4 R 
E)  2.0 R 
A)  0.41 R 
B)  0.50 R 
C)  1.0 R 
D)  1.4 R 
E)  2.0 R

Question 19

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 x 10-11 N·m2/kg2. What is the force exerted by Venus on Earth at that point?

Accepted Answer

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)  1.10 × 1018 N 
B)  4.62 × 1028 N 
C)  5.43 × 1026 N 
D)  6.30 × 1020 N 
E)  1.72 × 1019 N

Question 20

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 on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

Accepted Answer

A)  g/3. 
B)  3 g. 
C)  6 g. 
D)  g/9. 
E)  9 g. 
A)  g/3. 
B)  3 g. 
C)  6 g. 
D)  g/9. 
E)  9 g.

Exam 12: Gravity

What is the gravitational force between two 7.00-kg balls, when they are 35.0 cm apart? G = 6.67 x 10-11 N·m2/kg2.

An astronaut is piloting a spacecraft, which is in a circular orbit around Earth. A space station is ahead, on the same circular orbit. If he fires his rockets briefly to increase the forward speed of the rocket, what will happen?

What is the ratio of potential energy to kinetic energy for a comet that has just enough energy to escape from the Sun's gravitational field?

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.0060 m/s2 and the escape velocity is only 10.1 m/s. What is the mass of Eros? G = 6.67 x 10-11 N·m2/kg2.

A mass is attached to a fixed point by means of an ideal spring with zero unstretched length and is free to move in two dimensions. What would be the equivalent statement of Kepler's third law for this situation in the case of circular orbits around the fixed point?

An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 106 m and that G = 6.67 x 10-11 N·m2/kg2. From this information, she can conclude that the mass of Mars is

Tides are approximately 24 hours apart.

What is the ratio of potential energy to total energy for a planet in a circular orbit around the Sun?

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 × 106 m.

The gravitational force between two objects is inversely proportional to

A projectile is shot from the surface of Earth by means of a very powerful cannon. If the projectile reaches a height of 35,000 m above Earth's surface, what was the speed of the projectile when it left the cannon?

The identical 50-kg masses are held at the corners of an equilateral triangle, 30 cm on each side. If one of the masses is released, what is its initial acceleration, if the only forces acting on it are the gravitational forces due to the other two masses?

The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon?

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?

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 x 10-11 N·m2/kg2. What is the force exerted by Venus on Earth at that point?

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 on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

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What is the gravitational force between two 7.00-kg balls, when they are 35.0 cm apart? G = 6.67 x 10^-11 N·m²/kg².

Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.0060 m/s² and the escape velocity is only 10.1 m/s. What is the mass of Eros? G = 6.67 x 10^-11 N·m²/kg².

An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 10⁶ m and that G = 6.67 x 10^-11 N·m²/kg². From this information, she can conclude that the mass of Mars is

You are on an airplane traveling with a constant velocity at an altitude of 20,000 m. What is the acceleration of gravity at that altitude? The radius of Earth is 6.37 × 10⁶ m.

The mass of the Moon is 7.4 × 10²² kg and its mean radius is 1.75 × 10³ km. What is the acceleration due to gravity at the surface of the Moon?

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?

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 x 10^-11 N·m²/kg². What is the force exerted by Venus on Earth at that point?