Gravitation and Circular Motion Practice Problems for AP Physics B & C
Review the following concepts if necessary:
- Gravitation and Circular Motion for AP Physics B & C
- Newton's Law of Gravitation for AP Physics B & C
- Gravitation and Circular Motion: Of Special Interest to Physics C Students
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.
- What is the force each star exerts on the other?
- In terms of each star's tangential speed v, what is the centripetal acceleration of each star?
- What force provides the rock's centripetal acceleration?
- The vertical component of the string's tension
- The horizontal component of the string's tension
- The entire tension of the string
- The gravitational force on the rock
- The horizontal component of the gravitational force on the rock
- 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?
- It will continue in a straight line forward, while falling due to gravity.
- It will continue forward but curve to the right, while falling due to gravity.
- It will continue forward but curve to the left, while falling due to gravity.
- It will fall straight down to the ground.
- It will curve back toward the Ewok and hit him in the head.
- A Space Shuttle orbits Earth 300 km above the surface. Why can't the Shuttle orbit 10 km above Earth?
- The Space Shuttle cannot go fast enough to maintain such an orbit.
- Kepler's laws forbid an orbit so close to the surface of the Earth.
- 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.
- The closer orbit would likely crash into a large mountain such as Everest because of its elliptical nature.
- Much of the Shuttle's kinetic energy would be dissipated as heat in the atmosphere, degrading the orbit.
- 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.
- 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.
- At which point would the penny require the larger centripetal force to remain in place? Justify your answer.
- 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.
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.