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 found to be non-negligible.

On the axis 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 the free-body diagram of the forces acting on the ball during its fall. The diagram has been drawn by a student. 

Figure 2

A student sketches the free-body diagram in Figure 2 and makes the following claim:

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

Indicate whether the student’s sketch (Figure 2) and claim are or are not consistent with the graph of displacement as a function of time you sketched in part a). Justify your reasoning.

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 velocity of the satellite in terms of $M$, $r$, 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 with mass $m$, orbit a planet of mass $M$. At one instant, Moon A is twice as far from the planet as Moon B.

Draw and label force vectors acting on each moon.

Moon B suddenly falls out of its orbit and begins to fall towards the planet.

Starting with conservation of energy, derive an equation for the final velocity of Moon B upon impact with the planet.