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Potential energy, conservation of mechanical energy, and conservative forces sheet
5-mark answer frame

State the law of conservation of energy. Show that the mechanical energy of a freely falling body stays constant, and draw the energy graph.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · State the law. Energy can neither be created nor destroyed; it only changes form. The total energy of an isolated system stays constant.
  2. 2 · Top point. At height h, at rest: U = mgh and K = 0, so E = mgh.
  3. 3 · Middle point.
    • After falling h₁, to a height h₂ = h − h₁: U = mgh₂.
    • v² = 2gh₁, so K = ½mv² = mgh₁.
    • E = mgh₁ + mgh₂ = mgh.
  4. 4 · Bottom point. Just before the ground: U = 0 and v² = 2gh, so K = mgh and E = mgh.
  5. 5 · Draw the graph. [Energy against distance fallen: a horizontal line E = mgh; U falling from mgh to 0; K rising from 0 to mgh; the two lines cross at h/2]
  6. 6 · Real-life link. In a hydroelectric plant, the potential energy of stored water becomes kinetic energy and then electrical energy.
  7. 7 · Close in one line. So K + U = mgh at every point: mechanical energy is conserved when only gravity acts.

Scoring tip: Check the total at three points: top, middle and bottom. The middle-point working is what proves the law for every point, so examiners look for it.