Question 1

Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1RE and Satellite Two at an altitude of 2RE where RE = 6370 km is the radius of Earth. What is the ratio of the potential energy of Satellite One to Satellite Two?

Accepted Answer

A)   
B)  2/3 
C)  3/2 
D)   
E)  2

Question 2

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s2 and RE = 6370 km.)

Accepted Answer

A)  1.3 $\times$ 104 km 
B)  8.5 $\times$ 103 km 
C)  9.6 $\times$ 103 km 
D)  2.6 $\times$ 104 km 
E)  1.9 $\times$ 104 km

Question 3

The radius R of a stable, circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by

Accepted Answer

A)  R = Gv/M 
B)  R = Gv/mM 
C)  R = GmM/v 
D)  R = GM/mv 
E)  R = GM/v2

Question 4

Test masses are used to measure the gravitational field at various positions in and near a hollow spherical shell. The gravitational field will have its greatest value at point(s)

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  1, 2, and 5 
E)  1 and 2

Question 5

At the surface of the moon, the acceleration due to the gravity of the moon is  . At a distance from the center of the moon equal to three times the radius of the moon, the acceleration due to the gravity of the moon is

Accepted Answer

A)  9  
B)   /3 
C)   /4 
D)   /9 
E)  27

Question 6

A satellite in circular orbit 1.609 $\times$ 106 m above the surface of Earth (re = 6.436 $\times$ 106 m) has an acceleration toward Earth of

Accepted Answer

A)  9.76 m/s2  
B)  6.25 m/s2  
C)  7.80 m/s2  
D)  8.73 m/s2  
E)  15.3 m/s2

Question 7

Newton's law of gravity is F = GMm/r2. What are the SI units of the gravitational constant G?

Accepted Answer

A)  G has no dimensions 
B)  N · kg2/m2  
C)  N · m2/kg2  
D)  kg2/N · m2  
E)  None of these is correct.

Question 8

A satellite is orbiting Earth in an elliptical orbit. The distance of the satellite from Earth at the aphelion (rA) is twice that at the perihelion (rB). The total energy (potential and kinetic) of the satellite at A is _____ the total energy at B.

Accepted Answer

A)  the same as 
B)  twice 
C)  half 
D)  one quarter 
E)  four times

Question 9

An object whose mass is 6 kg experiences a gravitational force of 30 N  at some point P. The gravitational field at this point is

Accepted Answer

A)  6 m/s2  
B)  5 m/s2  
C)  180 m/s2  
D)  30 N/kg  
E)  36 N/kg

Question 10

Kepler's second law of planetary motion states that the radius vector from the sun to a planet sweeps out equal areas in equal times. This relationship is a consequence of which of the following conservation principles?

Accepted Answer

A)  speed 
B)  linear momentum 
C)  angular momentum 
D)  mechanical energy 
E)  potential energy

Question 11

Use the following scenario to answer the next problem. 
NASA's "Weightless Wonder" flights can simulate "zero-g" or some other extraterrestrial gravity by flying a C-9 jet plane in a parabolic path. One path the plane takes is expressed as y = yS1U1B1oS1U1B0 + 0.8 x - 1.02 $\times$ 10S1U1P1-4S1S1P0 xS1U1P12S1S1P0 where yS1U1B1oS1U1B0 is the highest point, and x and y are the horizontal and vertical coordinates (in m).
-What is the horizontal speed of the plane if the flight is to simulate lunar gravity,
GMoon = 1.62 m/s2.

Accepted Answer

A)  50 m/s 
B)  100 m/s 
C)  150 m/s 
D)  200 m/s 
E)  250 m/s

Question 12

The mass and radius of the planet Venus are 81% and 95% that of Earth, respectively. How much faster or slower (as a percentage) is the escape velocity from Venus compared to that of Earth?

Accepted Answer

A)  8% slower 
B)  8% faster 
C)  12% slower 
D)  12% faster 
E)  17% slower

Question 13

Four identical masses, each of mass M, are placed at the corners of a square of side L. The total potential energy of the masses is equal to -xGM 2/L, where x equals

Accepted Answer

A)  4 
B)   
C)   
D)   
E)

Question 14

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 106 m above Earth's surface. What is the speed of a satellite in this orbit?

Accepted Answer

A)  8.31 $\times$ 101 m/s 
B)  6.90 $\times$ 103 m/s 
C)  4.76 $\times$ 107 m/s 
D)  9.62 $\times$ 104 m/s 
E)  None of these is correct.

Question 15

The mass of Earth is ME = 6.0 $\times$ 1024 kg, and the mass of the Sun is 2.0 $\times$ 1030 kg. They are a distance of 1.5 $\times$ 108 km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 $\times$ 10-11 N·m2/kg2)

Accepted Answer

A)  1.8 $\times$ 10-8 m/s2  
B)  6.0 $\times$ 10-3 m/s2  
C)  9.8 m/s2  
D)  6.0 m/s2  
E)  6.0 $\times$ 103 m/s2

Question 16

Of the five masses in orbit around the central mass, the one with the longest period of revolution is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 17

An object weighs 37.0 N on Earth. If the mass of the moon is one eighty-first that of Earth and its radius one-fourth that of Earth, the weight of this object on the moon would be

Accepted Answer

A)  1.77 N 
B)  7.10 N 
C)  18.2 N 
D)  28.3 N 
E)  37.0 N

Question 18

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2 $\times$ 108 m above the surface of Earth (me = 5.99 $\times$ 1024 kg, re = 6.37 $\times$ 106 m) is

Accepted Answer

A)  ~3.92 $\times$ 109 m/s 
B)  ~6.26 $\times$ 104 m/s 
C)  ~1.10 $\times$ 104 m/s 
D)  ~1.21 $\times$ 108 m/s 
E)  None of these is correct.

Question 19

A planet is made of two distinct materials. From the core to R/2, the density of the material is 4000 kg/m3, and from R/2 to R the density is 3000 kg/m3. What is the gravity at the surface of the planet if R = 5000 km?

Accepted Answer

A)  0.699 m/s2 
B)  3.66 m/s2 
C)  4.19 m/s2 
D)  4.38 m/s2 
E)  4.99 m/s2

Question 20

Two objects with masses M1 = 30,000 kg and M2 = 70,000 kg are initially very far apart and at rest. If due to gravitational attraction the two objects attract each other, calculate their total kinetic energy when they are 100 km apart.

Accepted Answer

A)  1.4 $\times$ 10-3 J 
B)  1.4 $\times$ 10-11 J 
C)  1.4 $\times$ 10-6 J 
D)  0.7 $\times$ 10-3 J 
E)  0.7 $\times$ 10-6 J

Exam 11: Gravity

Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1R_E and Satellite Two at an altitude of 2R_E where R_E = 6370 km is the radius of Earth. What is the ratio of the potential energy of Satellite One to Satellite Two?

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s² and R_E = 6370 km.)

The radius R of a stable, circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by

Test masses are used to measure the gravitational field at various positions in and near a hollow spherical shell. The gravitational field will have its greatest value at point(s)

At the surface of the moon, the acceleration due to the gravity of the moon is . At a distance from the center of the moon equal to three times the radius of the moon, the acceleration due to the gravity of the moon is

A satellite in circular orbit 1.609 $\times$ 10⁶ m above the surface of Earth (r_e = 6.436 $\times$ 10⁶ m) has an acceleration toward Earth of

Newton's law of gravity is F = GMm/r². What are the SI units of the gravitational constant G?

A satellite is orbiting Earth in an elliptical orbit. The distance of the satellite from Earth at the aphelion (r_A) is twice that at the perihelion (r_B) . The total energy (potential and kinetic) of the satellite at A is _____ the total energy at B.

An object whose mass is 6 kg experiences a gravitational force of 30 N at some point P. The gravitational field at this point is

Kepler's second law of planetary motion states that the radius vector from the sun to a planet sweeps out equal areas in equal times. This relationship is a consequence of which of the following conservation principles?

The mass and radius of the planet Venus are 81% and 95% that of Earth, respectively. How much faster or slower (as a percentage) is the escape velocity from Venus compared to that of Earth?

Four identical masses, each of mass M, are placed at the corners of a square of side L. The total potential energy of the masses is equal to -xGM ²/L, where x equals

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface. What is the speed of a satellite in this orbit?

The mass of Earth is M_E = 6.0 $\times$ 10²⁴ kg, and the mass of the Sun is 2.0 $\times$ 10³⁰ kg. They are a distance of 1.5 $\times$ 10⁸ km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 $\times$ 10^-11 N·m²/kg²)

Of the five masses in orbit around the central mass, the one with the longest period of revolution is

An object weighs 37.0 N on Earth. If the mass of the moon is one eighty-first that of Earth and its radius one-fourth that of Earth, the weight of this object on the moon would be

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2 $\times$ 10⁸ m above the surface of Earth (m_e = 5.99 $\times$ 10²⁴ kg, r_e = 6.37 $\times$ 10⁶ m) is

A planet is made of two distinct materials. From the core to R/2, the density of the material is 4000 kg/m³, and from R/2 to R the density is 3000 kg/m³. What is the gravity at the surface of the planet if R = 5000 km?

Two objects with masses M₁ = 30,000 kg and M₂ = 70,000 kg are initially very far apart and at rest. If due to gravitational attraction the two objects attract each other, calculate their total kinetic energy when they are 100 km apart.

Exam 11: Gravity

Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1RE and Satellite Two at an altitude of 2RE where RE = 6370 km is the radius of Earth. What is the ratio of the potential energy of Satellite One to Satellite Two?

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s2 and RE = 6370 km.)

The radius R of a stable, circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by

Test masses are used to measure the gravitational field at various positions in and near a hollow spherical shell. The gravitational field will have its greatest value at point(s)

At the surface of the moon, the acceleration due to the gravity of the moon is . At a distance from the center of the moon equal to three times the radius of the moon, the acceleration due to the gravity of the moon is

A satellite in circular orbit 1.609 ×\times× 106 m above the surface of Earth (re = 6.436 ×\times× 106 m) has an acceleration toward Earth of

Newton's law of gravity is F = GMm/r2. What are the SI units of the gravitational constant G?

A satellite is orbiting Earth in an elliptical orbit. The distance of the satellite from Earth at the aphelion (rA) is twice that at the perihelion (rB) . The total energy (potential and kinetic) of the satellite at A is _____ the total energy at B.

An object whose mass is 6 kg experiences a gravitational force of 30 N at some point P. The gravitational field at this point is

Kepler's second law of planetary motion states that the radius vector from the sun to a planet sweeps out equal areas in equal times. This relationship is a consequence of which of the following conservation principles?

The mass and radius of the planet Venus are 81% and 95% that of Earth, respectively. How much faster or slower (as a percentage) is the escape velocity from Venus compared to that of Earth?

Four identical masses, each of mass M, are placed at the corners of a square of side L. The total potential energy of the masses is equal to -xGM 2/L, where x equals

Suppose that a satellite is in a circular orbit at a height of 2.00 ×\times× 106 m above Earth's surface. What is the speed of a satellite in this orbit?

The mass of Earth is ME = 6.0 ×\times× 1024 kg, and the mass of the Sun is 2.0 ×\times× 1030 kg. They are a distance of 1.5 ×\times× 108 km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 ×\times× 10-11 N·m2/kg2)

Of the five masses in orbit around the central mass, the one with the longest period of revolution is

An object weighs 37.0 N on Earth. If the mass of the moon is one eighty-first that of Earth and its radius one-fourth that of Earth, the weight of this object on the moon would be

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2 ×\times× 108 m above the surface of Earth (me = 5.99 ×\times× 1024 kg, re = 6.37 ×\times× 106 m) is

A planet is made of two distinct materials. From the core to R/2, the density of the material is 4000 kg/m3, and from R/2 to R the density is 3000 kg/m3. What is the gravity at the surface of the planet if R = 5000 km?

Two objects with masses M1 = 30,000 kg and M2 = 70,000 kg are initially very far apart and at rest. If due to gravitational attraction the two objects attract each other, calculate their total kinetic energy when they are 100 km apart.

Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1R_E and Satellite Two at an altitude of 2R_E where R_E = 6370 km is the radius of Earth. What is the ratio of the potential energy of Satellite One to Satellite Two?

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed. How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s² and R_E = 6370 km.)

A satellite in circular orbit 1.609 $\times$ 10⁶ m above the surface of Earth (r_e = 6.436 $\times$ 10⁶ m) has an acceleration toward Earth of

Newton's law of gravity is F = GMm/r². What are the SI units of the gravitational constant G?

A satellite is orbiting Earth in an elliptical orbit. The distance of the satellite from Earth at the aphelion (r_A) is twice that at the perihelion (r_B) . The total energy (potential and kinetic) of the satellite at A is _____ the total energy at B.

Four identical masses, each of mass M, are placed at the corners of a square of side L. The total potential energy of the masses is equal to -xGM ²/L, where x equals

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface. What is the speed of a satellite in this orbit?

The mass of Earth is M_E = 6.0 $\times$ 10²⁴ kg, and the mass of the Sun is 2.0 $\times$ 10³⁰ kg. They are a distance of 1.5 $\times$ 10⁸ km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 $\times$ 10^-11 N·m²/kg²)

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2 $\times$ 10⁸ m above the surface of Earth (m_e = 5.99 $\times$ 10²⁴ kg, r_e = 6.37 $\times$ 10⁶ m) is

A planet is made of two distinct materials. From the core to R/2, the density of the material is 4000 kg/m³, and from R/2 to R the density is 3000 kg/m³. What is the gravity at the surface of the planet if R = 5000 km?

Two objects with masses M₁ = 30,000 kg and M₂ = 70,000 kg are initially very far apart and at rest. If due to gravitational attraction the two objects attract each other, calculate their total kinetic energy when they are 100 km apart.