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Conservation of energy

Energy cannot be created or destroyed, only changed from one form to another. Without friction the sum of kinetic and potential energy stays constant. With friction some of it turns into heat, and that part must be included.

E_k = \tfrac12 m v^2

kinetic energy

E_p = m g h

gravitational potential energy

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

energy conservation with friction losses

Symbols

$m$	mass	kg
$v$	speed	m/s
$h$	height	m
$g$	gravitational acceleration	m/s²
$W_f$	energy lost to friction	J

Example

A ball is dropped from 5 m:

$mgh = \tfrac12 mv^2 \Rightarrow v = \sqrt{2\cdot 9.81\cdot 5} \approx 9.9$ m/s.

Put the zero level for height wherever it is easiest. Only the height difference matters.

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Part of Statics and Dynamics: Work, energy and momentum.