In one of his novels author Jules Verne imagined that astronauts inside a spaceship walked on the floor of the cabin when the force exerted on the ship by Earth was greater than the force exerted by the Moon. When the force exerted by the Moon was greater, he thought the astronauts walked on the ceiling of the cabin. (a) At what distance from the center of Earth would the forces exerted on the spaceship by Earth and the Moon be equal? (b) Explain why Verne's description of gravitational effects is incorrect.

In many science fiction stories a rotating space station, provides "artificial gravity" for its inhabitants. How does this work?

Find the linear speed of the bottom of a test tube in a centrifuge if the centripetal acceleration there is 52,000 times the acceleration due to gravity. The distance from the axis of rotation to the bottom of the test tube is 7.5 cm.

Driving in your car with a constant speed of $12 \mathrm{~m} / \mathrm{s}$, you encounter a bump in the road that has a circular cross section, as indicated in Figure 6-35. If the radius of curvature of the bump is $35 \mathrm{~m}$, determine the apparent weight of a $67-\mathrm{kg}$ person in your car as you pass over the top of the bump.

Assume that the brakes in your car create a constant deceleration of $4.2 \mathrm{~m} / \mathrm{s}^2$ regardless of how fast you are driving. If you double your driving speed from $16 \mathrm{~m} / \mathrm{s}$ to $32 \mathrm{~m} / \mathrm{s}^2$, does the time required to come to a stop increase by a factor of two or a factor of four? Explain.

Driving in your car with a constant speed of $12 \mathrm{~m} / \mathrm{s}$, you encounter a bump in the road that has a circular cross section, as indicated in Figure 6-35. If the radius of curvature of the bump is $35 \mathrm{~m}$, determine the apparent weight of a $67-\mathrm{kg}$ person in your car as you pass over the top of the bump, at what speed must you go over the bump if people in your car are to feel "weightless"?

Does the radius of Mars's orbit sweep out the same amount of area per time as that of Earth? Explain.

In 2 months a planet sweeps out the area A. How much area does it sweep out in 1 month? In 3 months?

Friend 1 says that an orbiting satellite is in free fall. Friend 2 disagrees, reasoning that a satellite in free fall would crash to the ground. Who is right? How would you explain this phenomenon to your friends?

On June 22, 1978, James Christy made the first observation of a moon orbiting Pluto. Until that time the mass of Pluto was not known, but the discovery of its moon, Charon, allowed its mass to be calculated with some accuracy. Explain.

One day in the future you may take a pleasure cruise to the Moon. While there you might climb a lunar mountain and throw a rock horizontally from its summit. If, in principle, you could throw the rock fast enough, it might end up hitting you in the back. Explain.

One day in the future you may take a pleasure cruise to the Moon. While there you might climb a lunar mountain and throw a rock horizontally from its summit. If, in principle, you could throw the rock fast enough, it might end up hitting you in the back. Explain.

The force exerted by the Sun on the Moon is more than twice the force exerted by Earth on the Moon. Should the Moon be thought of as orbiting Earth or the Sun? Explain.

Satellites that make up the Global Positioning System, or GPS, orbit at an altitude of $2.02 \times 10^{7} \mathrm{m}$. Find the orbital period of a GPS satellite.