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Conservation of energy

Energy cannot be created or destroyed, only change form. Without friction, the sum of kinetic and potential energy is constant, so you can find a speed from a height or the other way around without knowing the forces along the way. With friction, part of the energy turns into heat.

E_{k1} + E_{p1} = E_{k2} + E_{p2}

conservation of energy without friction

E_{k1} + E_{p1} = E_{k2} + E_{p2} + W_f

with friction work

W_f

Symbols

$E_k$	kinetic energy	J
$E_p$	potential energy	J
$W_f$	friction work	J

Example

A ball is dropped from $h = 5.0$ m with no air resistance. Energy conservation gives $mgh = \tfrac12 mv^2$ , so $v = \sqrt{2gh} = \sqrt{2\cdot 9.81\cdot 5.0} \approx 9.9$ m/s.

The mass often cancels out in energy conservation – you rarely need it to find a speed from a height.

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Part of Foundations of Physics: Work, energy and power.