A-level Physics (Advancing Physics)/Gravitational Potential Energy/Worked Solutions

1. A ball rolls down a 3m-high smooth ramp. What speed does it have at the bottom?

2. In an otherwise empty universe, two planets of mass 1025 kg are 1012 m apart. Both the planets have a radius of 106 m. What are their speeds when they collide?

Let be the mass of planet 1 and be the mass of planet 2. Both are kg

Assume planet 1 to be stationary and planet 2 to be accelerating towards it (relative).

Let D = meters = distance between the center of the two planets. Let d = meters = radius of planets.

Gravitational Potential Energy

3. What is the least work a 2000 kg car must do to drive up a 100m hill?

4. How does the speed of a planet in an elliptical orbit change as it nears its star?

As it nears the star, it loses gravitational potential energy, and so gains kinetic energy, so its speed increases.