7.1.4 Gravitational Potential Energy

Question 1

Gravitational Potential Energy

Answer 1

• The formula for the gravitational potential energy between two objects with masses M1and M2is .
• Gravitational potential energy is negative. If ETOT is constant, as objects move closer together Ugrav becomes more negative and kinetic energy increases.
• The speed required for an object to escape from the Earth’s gravity (escape velocity) is about 11 km/s.

Question 2

Consider two stars moving under mutual gravitational force. Their masses are 6.010^35 kg and 9.010^35 kg respectively. They are far away from other stars. Several years ago, the distance between them was 6.010^15 m and they were moving at respective speeds of 2.010^5 m/s and 4.010^5 m/s (with respect to an inertial reference frame). Now the stars are moving at speeds of 1.510^5 m/s and 4.2*10^5 m/s respectively. What is the distance between them?

Answer 2

4.43*10^15 m

Question 3

Consider two balls of masses 100 kg and 200 kg and radii 0.1 m and 0.2 m respectively. Suppose their centers are separated by 2 m. What is the gravitational potential energy of the system?

Answer 3

-6.67*10^-7 J

Question 4

Consider a system consisting of a star and a planet with masses 6.010^36 kg and 9.010^25 kg respectively. They are far away from other stars. Several years ago, the planet was 6.010^15 m away from the star and moving at the speed 4.010^5 m/s (with respect to the star). Now the planet is moving at the speed 5.0*10^5 m/s. How far is it away from the star?

Answer 4

3.58*10^15 m

Question 5

Consider two stars S1 and S2 moving under mutual gravitational force. They are far away from other stars. Star S1 has a mass of 6.010^25 kg. Several years ago the distance between the stars was 6.010^15 m and S1 and S2 were moving at speeds of 2.010^5 m/s respectively (with respect to some inertial reference frame). No2, S1 and S2 are moving at speeds of 1.510^5 m/s and 4.210^5 m/s respectively. The distance between them is about 4.010^15 m. What is the mass of S2?

Answer 5

1.08*10^36 kg

Question 6

Suppose that you are on the surface of a planet and its mass and radius are 9.010^25 kg and 6.010^5 m respectively. You would like to send a projectile away from the planet. What is the smallest initial speed of the projectile (the so-called escape velocity)?

Answer 6

1.41*10^5 m/s

Question 7

Consider two balls of masses 100 kg and 200 kg and radii 0.1 m and 0.2 m respectively. The gravitational potential energy between them is -5.0*10^-7. What is the shortest distance between the surfaces of the two balls?

Answer 7

2.37 m

Question 8

Consider a system consisting of a star and a planet with masses 6.010^36 kg and 9.010^25 kg respectively. They are far away from other stars. Several years ago, the planet was 6.010^15 m away from the star and moving at the speed 4.010^5 m/s (with respect to the star). Now the planet is moving at the speed 4.0*10^5 m/s. What is the planet’s speed?

Answer 8

4.76*10^5 m

Question 9

Consider two balls of the same mass with radii 0.1 m and 0.2 m respectively. The gravitational potential energy between them is -5.0*10^-7. What is the mass of each ball?

Answer 9

1.22*10^2 kg