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# Gravitation and Circular Motion Practice Problems for AP Physics B & C

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By — McGraw-Hill Professional
Updated on Feb 10, 2011

Review the following concepts if necessary:

### Multiple Choice:

Questions 1 and 2

Two stars, each of mass M, form a binary system. The stars orbit about a point a distance R from the center of each star, as shown in the diagram above. The stars themselves each have radius r.

1. What is the force each star exerts on the other?
2. In terms of each star's tangential speed v, what is the centripetal acceleration of each star?
3. Questions 3 and 4: In the movie Return of the Jedi, the Ewoks throw rocks using a circular motion device. A rock is attached to a string. An Ewok whirls the rock in a horizontal circle above his head, then lets go, sending the rock careening into the head of an unsuspecting stormtrooper.

4. What force provides the rock's centripetal acceleration?
1. The vertical component of the string's tension
2. The horizontal component of the string's tension
3. The entire tension of the string
4. The gravitational force on the rock
5. The horizontal component of the gravitational force on the rock
5. The Ewok whirls the rock and releases it from a point above his head and to his right. The rock initially goes straightforward. Which of the following describes the subsequent motion of the rock?
1. It will continue in a straight line forward, while falling due to gravity.
2. It will continue forward but curve to the right, while falling due to gravity.
3. It will continue forward but curve to the left, while falling due to gravity.
4. It will fall straight down to the ground.
5. It will curve back toward the Ewok and hit him in the head.
6. A Space Shuttle orbits Earth 300 km above the surface. Why can't the Shuttle orbit 10 km above Earth?
1. The Space Shuttle cannot go fast enough to maintain such an orbit.
2. Kepler's laws forbid an orbit so close to the surface of the Earth.
3. Because r appears in the denominator of Newton's law of gravitation, the force of gravity is much larger closer to the Earth; this force is too strong to allow such an orbit.
4. The closer orbit would likely crash into a large mountain such as Everest because of its elliptical nature.
5. Much of the Shuttle's kinetic energy would be dissipated as heat in the atmosphere, degrading the orbit.
7. ### Free Response:

8. Consider two points on a rotating turntable: Point A is very close to the center of rotation, while point B is on the outer rim of the turntable. Both points are shown above. A penny could be placed on the turntable at either point A or point B.
1. In which case would the speed of the penny be greater, if it were placed at point A, or if it were placed at point B? Explain.
2. At which point would the penny require the larger centripetal force to remain in place? Justify your answer.
3. Point B is 0.25 m from the center of rotation. If the coefficient of friction between the penny and the turntable is μ = 0.30, calculate the maximum linear speed the penny can have there and still remain in circular motion.
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