State the law of conservation of energy. Show that it holds for a body of mass m falling freely from a height h.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the law. Energy can neither be created nor destroyed; it only changes from one form to another, so the total stays constant.
2 · At the top (height h, at rest). PE = mgh and KE = 0. Total = mgh.
3 · After falling a distance x.
Height is now h − x, so PE = mg(h − x)
From v² = u² + 2gs with u = 0: v² = 2gx, so KE = ½m(2gx) = mgx
Total = mg(h − x) + mgx = mgh
4 · Just before landing.
PE = 0
v² = 2gh, so KE = ½m(2gh) = mgh
Total = mgh
5 · Sketch. [Diagram: a vertical dashed line with the ball at the top (A), part way down (B) and just above the ground (C); write PE and KE beside each point]
6 · Real-life link. A hydroelectric dam uses the same change of PE into KE to make electricity.
7 · Close. So PE + KE = mgh at every point: energy is conserved.
Scoring tip: Work out PE and KE at three points: the top, part way down and the bottom. Show that the total is mgh each time.
