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Work and energy conservation

The total work done on a body equals the change in its kinetic energy. Without friction, the sum of kinetic and potential energy is constant throughout the motion, which lets you find speeds and heights without knowing the forces or times along the way.

W_{net} = \Delta E_k

work-energy theorem

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

energy conservation without friction

Symbols

$W$	work	J
$E_k$	kinetic energy	J
$E_p$	potential energy	J

Example

A solid block slides without friction from $h = 1.5$ m. Energy conservation gives $mgh = \tfrac12 mv^2$ , so $v = \sqrt{2\cdot 9.81\cdot 1.5} \approx 5.42$ m/s.

Set the energy before equal to the energy after, and add the friction work on the right side if there is a loss.

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