Circular Motion & Gravitation Unit Exam

An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?

1/16

The figure above represents the orbits of two planets of equal mass that orbit their star in the counterclockwise direction as a double-planet system. From the point of view of an observer on either planet, the planets appear to orbit each other while also orbiting the star. The dots on the orbits represent the position of the planets at time t0, and X is the position of their center of mass at that time. Which of the following arrows best represents the acceleration of the center of mass of the double-planet system when it is at point X ?

down left arrow

An astronaut in the space station appears weightless because the astronaut seems to float. Which of the following claims is true about the force exerted on the astronaut by Earth?

equal short answer

A cart of mass mm is moving with speed vv on a smooth track when it encounters a vertical loop of radius RR, as shown above. The cart moves along the inside of the entire loop without leaving the track. All frictional forces are negligible.

equal to or greater than

A ball of mass MM swings in a horizontal circle at the end of a string of radius RR at a constant tangential speed v0v0. A student gradually pulls the string inward such that the radius of the circle decreases while keeping the tangential speed v0v0 of the ball constant, as shown above. Which of the following graphs best represents the acceleration aa of the ball as a function of time tt?

exponential

A planet travels in an elliptical path around a star, as shown in the figure. As the planet gets closer to the star, the gravitational force that the star exerts on the planet increases. Which statement of reasoning best supports and correctly identifies what happens to the magnitude of the force that the planet exerts on the star as the planet gets closer to the star?

increases because it is a part of Newton's third law

One end of a string is attached to a vertical pole with the other end of the string attached to a ball that swings in a horizontal circular path, as shown. Which of the following free body diagrams represents the forces exerted on the ball?

north west down

An astronaut stands on the surface of an asteroid. The astronaut then jumps such that the astronaut is no longer in contact with the surface. The astronaut falls back down to the surface after a short time interval. Which of the following forces CANNOT be neglected when analyzing the motion of the astronaut?

the gravitational force between the astronaut and the asteroid

A comet passes by a planet with a speed vovo such that the comet travels in a straight line at the instant shown in the figure. The comet's tangential acceleration, centripetal acceleration, and force due to gravity from the planet at this location are provided in the table. Astronomers observe that the comet continues to travel in a nearly straight line, even though calculations show that the gravitational force exerted by the planet should cause the comet to move in a circular orbit. Why does the comet not travel in a circular path around the planet after the instant shown in the figure?

there must be another force

Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?

star 1 has less mass