1. A mass of 20.0 kg is located 4.0 m to the right of a mass of 30.0 kg.
a. What is the force on the 20.0 kg mass?
b. What is the force on the 30.0 kg mass?

2. A spaceship is traveling along a line connecting the centers of the Earth and the Moon. At what distance from the earth does the spaceship find the gravitational pull of the Earth equal in magnitude to that of the moon (as a percentage of the distance between the centers of the 2 bodies)?

3. Find the altitude above the Earth's surface where Earth's gravitational field strength would be two-thirds of its value at the surface.

Gravitatonal force can be determined for the four bodies shown in the corners of a rectangle.

Four masses form the vertices of a 1 m X 1 m square as shown. What is the gravitational force on the 3 kg mass due to the other three masses?

5. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

6. The gravitational field intensity at the surface of a planet is 3.4N/kg. If a planet's mass is 7.2*10²² kg, what is its radius?

7. Suppose that material ejected from a volcano on Io reaches a height of 5.08 km after being projected straight upward with an initial speed of 127 m/s. Given that the radius of Io is 1820 km, calculate Io's mass.

8. A neutron star might have as much as five times the mass of our sun packed into a sphere about 10 km in radius! Estimate the surface gravity on this monster.

9. If the mass of Titan is 1.35*10²³ kg and it's radius is 2570 km determine

a. the force at the surface on a 500 kg probe.

b. the acceleration due to titans mass.

10. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

11. What is the acceleration due to gravity at an altitude of 2*10⁶m above the earth\'s surface? Earth's mass is 5.98*10²⁴kg and of Earth's radius is 6.37*10⁶ m .

12. A 492kg uniform solid sphere has a radius of .405m. Find the magnitude of the gravitational force (in N) exerted by the sphere on a 50.4g particle located 0.197m from the center of the sphere?

13. A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

ANSWERS
1. F = Gm₁m₂/R²

F = (6.67 x 10^-11)(20.0 kg)(30.0 kg)/(4.0 m)²

F = 2.50 x 10^-11 N

a. 2.50 x 10^-11 N [left]

b. 2.50 x 10^-11 N [right]

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