On the surface of planet Mars, the gravitational constant is . Considering that earth's gravitational constant is , how high above the surface do you need to be on planet Mars to have the same gravitational potential energy as you would if you were up on Earth? Assume your mass is unchanged on both planets.

A roller coaster of mass is approaching a circular loop with a radius of . The average frictional force on the coaster is and the velocity of the coaster is as it enters the loop. How many g's are felt by the riders of the coaster when it reaches the top of the loop?

Mass of Pluto:

Radius of Pluto:

Determine the escape velocity for a lander on Pluto.

A ball rolls down a frictionless ramp of height , at the end of the ramp what will its velocity be?

Changing which of the following variables will cause the biggest increase in gravitational potential energy?

Consider the following system:

Two spherical masses, A and B, are attached to the end of a rigid rod with length l. The rod is attached to a fixed point, p, which is at the midpoint between the masses and is at a height, h, above the ground. The rod spins around the fixed point in a vertical circle that is traced in grey. is the angle at which the rod makes with the horizontal at any given time ( in the figure).

The rod is in it's vertical position (mass A is at the top, mass B is at the bottom). If mass A has twice as much gravitational potential energy as mass B, what is h?

A mountain biker goes off a jump with an initial vertical velocity of . If the biker lands a vertical distance of below the launch point, what is his vertical velocity the moment he lands?

A man weighing walks to the top of a tall building. How much gravitational potential energy does he have at the top of the building compared to when he was on the street below?

Planet A is twice as massive as Planet B. Compared to a person standing on Planet A, a person standing on Planet B will have __________ potential energy and __________ mass.

Mass of moon:

Radius of moon:

Determine the gravitational potential energy of a lander above the surface of the moon