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Part of JME-03 — Work, Energy & Power

Work — Complete Reference

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Definition

W = F . s = |F||s|cos(theta)

theta: angle between force and displacement vectors
SI unit: Joule (J) = kg* $m^2$ / $s^2$
Dimension: [ $ML^{2T}^{-2}$ ]

Work by Angle

Angle (theta)	cos(theta)	Work	Example
0 degrees	1	+Fd (max positive)	Pushing along motion
90 degrees	0	0	Normal force, centripetal
180 degrees	-1	-Fd (max negative)	Friction opposing motion
0 < theta < 90	positive	positive	Pulling at angle
90 < theta < 180	negative	negative	Braking force component

Variable Force

W = integral from $x_1$ to $x_2$ of F(x) dx = area under F-x graph

Work by Specific Forces

Gravity (down h): W = +mgh
Gravity (up h): W = -mgh
Spring ( $x_1$ to $x_2$ ): W = $\frac{1}{2}$ k( $x_1^2$ - $x_2^2$ )
Friction: W = - $mu_k$ Nd (always negative)
Normal: W = 0 (perpendicular to motion)

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