All subjects · Physics · WPH11 (Unit 1)

Conservation of energy

Energy cannot be created or destroyed, only transferred. In mechanics this lets you find speeds and heights without knowing the forces in detail.

The principle

The total energy of a closed system stays constant. In mechanics, energy moves between kinetic energy, gravitational potential energy and work done (often against friction or air resistance).

No resistive forces

Loss of GPE = gain of KE: mgΔh = (1/2)mv2, so v = sqrt(2gΔh). The mass cancels, so all objects dropped from the same height reach the same speed (ignoring air resistance). The same idea works for pendulums, roller coasters and smooth slopes.

With resistive forces

Energy at the start = energy at the end + work done against resistive forces. The work done against friction is dissipated, mostly as thermal energy. If the average resistive force F acts over a distance d, work done = Fd.

Worked example

A roller-coaster car starts from rest at a height of 20 m. Ignoring friction, find its speed at the bottom.

  1. mgΔh = (1/2)mv2
  2. v = sqrt(2 x 9.81 x 20) = sqrt(392.4)

Answer: v = 19.8 m/s

Key idea: Energy in = energy out. Without friction mgΔh = (1/2)mv2; with friction, the difference is work done against resistance.

Check yourself

  1. A ball is dropped from rest from 5.0 m. Ignoring air resistance, find its speed just before it lands, in m/s, to 3 s.f.
    Show answer

    9.90 m/s. v = sqrt(2 x 9.81 x 5.0) = sqrt(98.1) = 9.90 m/s.

  2. A pendulum bob moves at 2.0 m/s at the bottom of its swing. How high above the bottom does it rise, in m? Give 3 s.f.
    Show answer

    0.204 m. Δh = v2 / 2g = 4.0 / 19.62 = 0.204 m.

  3. A ball is thrown straight up at 8.0 m/s. Ignoring air resistance, find its maximum height in m, to 3 s.f.
    Show answer

    3.26 m. Δh = 64 / 19.62 = 3.26 m.

  4. A 60 kg skier starts from rest and descends a vertical height of 30 m, reaching 20 m/s at the bottom. How much energy was dissipated, in J? Give 3 s.f.
    Show answer

    5660 J. GPE lost = 60 x 9.81 x 30 = 17658 J; KE gained = 0.5 x 60 x 400 = 12000 J; dissipated = 5660 J.

  5. The skier's slope in the last question is 150 m long. Find the average resistive force in N, to 3 s.f.
    Show answer

    37.7 N. F = work done / distance = 5658 / 150 = 37.7 N.

  6. Why do a heavy ball and a light ball dropped from the same height reach the same speed (ignoring air resistance)?
    • Heavier objects have less GPE
    • Air resistance is the same for both
    • The mass cancels in mgΔh = (1/2)mv2
    • They have the same kinetic energy
    Show answer

    The mass cancels in mgΔh = (1/2)mv2. Dividing both sides by m gives v = sqrt(2gΔh), which has no m in it.

  7. A book slides across a table and stops. What happens to its kinetic energy?
    • It is transferred to thermal energy of the book, table and surroundings
    • It is destroyed by friction
    • It becomes gravitational potential energy
    • It stays in the book as kinetic energy
    Show answer

    It is transferred to thermal energy of the book, table and surroundings. Friction does work, dissipating the energy as thermal energy. Energy is never destroyed.

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Last updated 7 November 2026. Spotted a mistake? Tell us.