Work, Energy, and Conservation of Energy

Manual: General · Subject: Newtonian Mechanics

Learn how forces can transfer energy and how energy methods simplify mechanics problems.

Energy in Mechanics

Work is done when a force causes displacement. For a constant force, $W = Fd\cos\theta$ , where $\theta$ is the angle between force and displacement.

Kinetic energy is energy of motion: $K = \frac{1}{2}mv^2$ .

Gravitational potential energy near Earth is often written as $U = mgh$ . Elastic potential energy in a spring is $U = \frac{1}{2}kx^2$ .

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Energy conservation

If only conservative forces act, the total mechanical energy $E = K + U$ stays constant.

What is the formula for kinetic energy?

mv

\frac{1}{2}mv^2

mgh

Fd

What does the cosine factor in work account for?

Energy forms in basic mechanics

Type	Formula	Common use
Kinetic	$\frac{1}{2}mv^2$	Moving objects
Gravitational potential	$mgh$	Height changes
Spring potential	$\frac{1}{2}kx^2$	Compressed or stretched springs