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Kinetic, gravitational potential and elastic energy

Three stores can be calculated with equations you need to know. Use g = 10 N/kg near the Earth's surface.

Moving body. Kinetic energy = ½ × mass × speed squared, or Ek = ½ m v2, with mass in kg and speed in m/s. A 2 kg trolley moving at 3 m/s has ½ × 2 × 32 = 9 J. Doubling the speed makes the kinetic energy four times bigger, because the speed is squared.

Object raised above the ground. Gravitational potential energy = mass × gravitational field strength × height, or Ep = m g h. Lifting a 3 kg object through 2 m gives 3 × 10 × 2 = 60 J.

Stretched spring. Energy transferred in stretching = ½ × spring constant × extension squared, or E = ½ k e2. For a spring with spring constant 100 N/m and an extension of 0.2 m, the energy is ½ × 100 × 0.22 = 2 J. The extension must be in metres.

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