Gravitational Force (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A moon of mass $m_M$ is moving clockwise in a circular orbit around a planet of mass $M$ and radius $R$, as shown in Figure 1.

Figures 2, 3, and 4 each show the planet and a portion of the moon's orbit.

i) On the diagram in Figure 2, draw an arrow to indicate the direction of the moon's velocity. If the velocity is zero, write "$v=0$" next to the dot.

ii) On the diagram in Figure 3, draw an arrow to indicate the direction of the moon's acceleration. If the acceleration is zero, write "$a=0$" next to the dot.

iii) On the diagram in Figure 4, draw an arrow to indicate the direction of the net force exerted on the moon. The force must be represented by a distinct arrow starting on and pointing away from the dot.

A ball is dropped from rest from a height $h$ above the ground. Air resistance is not negligible. The ball reaches terminal velocity before it hits the ground.

On the axes provided in Figure 1, sketch a graph of the displacement of the ball as a function of time, from its release to the time just before it hits the ground.

Figure 1

Figure 2 shows a free-body diagram drawn by a student to represent the forces exerted on the ball as it falls.

Figure 2

The student makes the following claim:

"The free-body diagram shows the forces exerted on the ball for the entire time the ball falls."

Indicate whether the student's free-body diagram and claim are or are not consistent with the graph of displacement as a function of time that you sketched in part a). Justify your answer.

A satellite of mass $m$ orbits a planet of mass $M$ in a circular orbit at an altitude $h$ above the planet's surface. The radius of the planet is $R$.

Derive an expression for the orbital speed of the satellite in terms of $M$, $R$, $h$ and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 1

A spacecraft of mass $m$ is in a clockwise circular orbit of radius $R$ around Earth, as shown in Figure 1. The mass of Earth is $M_E$.

i) On the diagram in Figure 2, draw and label arrows that represent the forces (not components) that act on the spacecraft. Each force on your diagram must be represented by a distinct arrow starting on, and pointing away from, the spacecraft.

Figure 2

ii) Determine an equation for the net gravitational force on the spacecraft due to the Earth in terms of $m$, $M_E$, $R$ and physical constants as appropriate.

Two identical moons, each of mass $m$, orbit a planet of mass $M$. At one instant, Moon A is twice as far from the center of the planet as Moon B.

Draw and label an arrow to represent the gravitational force exerted on each moon by the planet. Each arrow must start on the moon, and the relative lengths of the arrows must represent the relative magnitudes of the forces. Ignore the gravitational force between the two moons.

Moon B is a distance $r$ from the center of the planet. The planet has radius $R$.

Moon B is suddenly brought to rest in its orbit and then falls from rest directly toward the planet. Assume the planet remains at rest, and ignore the gravitational force exerted on Moon B by Moon A.

Starting with conservation of energy, derive an expression for the speed of Moon B just before it reaches the surface of the planet. Express your answer in terms of $M$, $R$, $r$ and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.