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Work and energy

The work–energy method is fastest when you want the speed after a distance without tracking the acceleration along the way. Kinetic and potential energy convert into each other, while friction and motors add or remove energy as work.

E_k = \tfrac12mv^2

kinetic energy

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

the work–energy theorem

Symbols

$E_k,\ E_p$	kinetic/potential energy	J
$W_{other}$	work from friction etc.	J

Example

A fall from $h = 5$ m, no air resistance:

$mgh = \tfrac12mv^2 \Rightarrow v = \sqrt{2\cdot 9.81\cdot 5} \approx 9.9$ m/s.

Friction does negative work – subtract it from the energy instead of adding it.

Practise dynamics for free →

← Newton's second law · Momentum and impact →

Part of Statics and Dynamics: Dynamics.