Practice Problems s3

AP PHYSICS C NAME______

CH. 12 GRAVITATION DATE______

PRACTICE PROBLEMS:

1. Two objects attract each other with a gravitational force of magnitude 1.00 x 10-8 N when separated by 20.0 cm. If the total mass of the two objects is 5.00 kg, what is the mass of each object?

2. A 200 kg mass and a 500 kg mass are separated by 0.400 m. (a) Find the net gravitational force exerted by these masses on a 50.0 kg placed midway between them. (b) At what position (other than infinitely remote ones) can the 50.0 kg mass be placed so as to experience a net force of zero?

3. Three uniform spheres of masses 2.00 kg, 4.00 kg, and 6.00 kg are placed at the vertices of a right triangle, as shown below. Calculate the resultant gravitational force on the 4.00 kg mass, assuming that the spheres are isolated from the rest of the universe.

2.00 kg

3.00 m

6. 00 kg 4.00 kg

4.00 m 4. Determine the gravitational field strength at an altitude of 500 km above the surface of the Earth.

5. Using the inverse square law, determine the gravitational field strength at a location of two Earth radii above its surface.

6. At the Earth’s surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance.

7. A satellite with a mass of 200 kg is placed in orbit around the Earth at a height of 200 km above the surface. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit? (b) What is the satellite’s speed? (c) What is the minimum energy necessary to place this satellite in orbit (assuming no air friction)? 8. Calculate the escape speed from the Earth for a 5000 kg spacecraft, and determine the kinetic energy it must have at the Earth’s surface in order to escape the Earth’s gravitational field.

9. A satellite in a geostationary orbit circles the Earth above the equator with a period of exactly 1 day, so it stays above a particular place all the time. Most of the satellites in such orbits act as relays for telephone calls and television programs. Find the altitude of a geostationary orbit.

10. Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has a speed of 2.0 x 104 m/s when at a distance of 2.5 x 1011 m from the center of the sun, what is its speed when at a distance of 5.0 x 1010 m?

11. Consider a spacecraft in an elliptical orbit around the Earth. At the low point, or perigee of its orbit, it is 400 km above the Earth’s surface; at the high point, or apogee, it is 4000 km above the Earth’s surface. (a) Using the conservation of angular momentum, find the ratio of the spacecraft’s speed at the perigee to its speed at the apogee. (b) Using the conservation of energy, find the speed at the perigee and at the apogee. 12. A 3000 kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?