AP Physics C: Mechanics : Understanding Gravity

Study concepts, example questions & explanations for AP Physics C: Mechanics

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Example Questions

Example Question #1 : Understanding Gravity

A block with a mass of  is traveling at  when it impacts the ground. From how many meters off the ground was the block dropped?

Round to the nearest whole number.

Possible Answers:

Correct answer:

Explanation:

Set the gravitational potential energy and kinetic energy equal to each other and solve for the height.

Mass cancels.

Isolate the height and plug in our values.

Rounding this gives .

Example Question #2 : Understanding Gravity

An object of mass  is dropped from a tower. The object's drag force is given by  where  is a positive constant. What will the objects terminal velocity be?

Possible Answers:

Correct answer:

Explanation:

To find terminal velocity, set the magnitude of the drag force equal to the magnitude of the force of gravity since when these forces are equal and opposite, the object will stop accelerating:

Solve for 

Example Question #3 : Understanding Gravity

A ship of mass  and an initial velocity of  is coasting to a stop. The water exerts a drag force on the ship. The drag force is proportional to the velocity:

 where the negative sign indicates that the drag force acts in a direction opposite the motion. After the ship has coasted for a time equal to , how fast (in terms of ) will the ship be moving?

Possible Answers:

Correct answer:

Explanation:

The ship's equation of velocity (found by solving the first-order differential equation) is 

Substitute  and solve.

Example Question #4 : Understanding Gravity

A spherical asteroid has a hole drilled through the center as diagrammed below:

Hole through planet

Refer to the diagram above. An object that is much smaller than the asteroid is released from rest at the surface of the asteroid, at point a. How do the velocity and acceleration of the object compare at point b at the surface, and point a, located at the center of the asteroid?

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

Because the gravitational force depends only on the mass beneath the object (which is the gravitational version of Gauss's Law for charge), the acceleration steadily decreases as the object falls, and drops to zero at the center. Nevertheless, the velocity keeps increasing as the object falls, it just does so more slowly.

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