A satellite of mass m is in a circular orbit around a spherical planet of mass mp. The kinetic energy of the satellite is KA when its orbit radius is rA. In terms of rA, what must the orbit radius be in order for the kinetic energy of the satellite to be 2KA?

The three spheres in the figure, with masses mA = 75 g, mB = 9 g, and mc = 23 g, have their centers on a common line, with L = 23 cm and d = 4 cm. You move sphere B along the line until its center-to-center separation from C is d = 4 cm. How much work is done on sphere B(a) by you and (b) by the net gravitational force on B due to spheres A and C? B L ·d C

If a 1000 kg car is exiting a highway through an above-the-ground ramp of 5.0 m radius at 12 m/s, what is the potential energy?

A 2.50 kg mass is drop from rest. If it falls a distance of 25.0 m, what will its change in kinetic energy be? Assume only the gravitational force acts.

A satellite in Earth orbit has a mass of 105 kg and is at an altitude of 1.95 x 10° m. (Assume that U = 0 as r → ∞.) (a) What is the potential energy of the satellite-Earth system? (b) What is the magnitude of the gravitational force exerted by the Earth on the satellite? (c) What force, if any, does the satellite exert on the Earth? (Enter the magnitude of the force, if there is no force enter 0.)

The figure below shows the potential energy function U(r) of a projectile plotted outward from the surface of a planet of radius Rs.  What is the minimum velocity required for a 1.8 kg object to "escape" the gravitational field of the planet.

(a) What is the gravitational potential energy of a two-particle system with masses 6.8 kg and 3.0 kg, if they are separated by 1.7 m? If you triple the separation between the particles, how much work is done (b) by the gravitational force between the particles and (c) by you?

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In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work ?W applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 969 kg969 kg and 241 km.241 km. Earth's mass and radius are 5.98×1024 kg5.98×1024 kg and 6370 km.

In deep space, sphere A of mass 30 kg is located at the origin of an x axis and sphere B of mass 10 kg is located on the axis at x = 0.85 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 0.25 m toward A? Additional Materials eBook Powers of Ten