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Potential energy and falling

Potential energy in the gravitational field is the energy a body has because of its height. We may choose where the height is zero. Without friction and air resistance the sum of kinetic and potential energy is constant. If a body is dropped from rest, all of that potential energy has become kinetic just before it reaches the bottom. The speed can then be found without knowing the time.

Try it yourself

Energy conservation in free fall

E_p = mgh

potential energy

v = \sqrt{2gh}

speed after a fall from rest

Symbols

$E_p$	potential energy	J
$h$	height	m
$g$	acceleration of gravity, 9.81	m/s²

Example

A ball of 2 kg is held 5 m above the ground and dropped.

$E_p = 2 \cdot 9.81 \cdot 5 = 98.1$ J and $v = \sqrt{2 \cdot 9.81 \cdot 5} \approx 9.90$ m/s.

Air resistance takes energy, so the real speed is a little lower than the formula says.

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Part of Physics 1: Energy and work.