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?

mgh = \frac{1}{2}mv^2

gh = \frac{1}{2}v^2

v = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 3} = 7.67\mbox{ ms}^{-1}

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

\frac{GMm}{0.5r} = \frac{1}{2}mv^2

\frac{GM}{0.5r} = \frac{1}{2}v^2

\frac{4GM}{r} = v^2

v = 2\sqrt{\frac{GM}{r}} = 2\sqrt{\frac{6.67 \times 10^{-11} \times 10^{25}}{10^{12}}} = 52\mbox{ ms}^{-1}

(Not too sure about this one. Please check.)

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

mgh = 2000 \times 9.81 \times 100 = 1.962\mbox{ MJ}

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.

Last modified on 12 June 2009, at 14:01