Define Work

Work is the product of force and the distance through which that force is applied. Work can be simplified as force times displacement only when the force and the displacement are in the same direction.

Work can be defined mathematically in several ways, all of which are equivalent.

$W=|F x| cos \theta$ $W=\vec{F} \cdot \vec{x}$ $W=\int F dx$

$Where\ W\ is\ Work,\ F\ is\ the\ force,\ x\ is\ the\ displacement,\ and\ \theta\ is\ the\ angle\ between\ them.$

Work is a scalar quantity. It does not have direction. The sign does give you information however.

Notice that if the displacement vector is in the opposite direction as the force vector, you can still find the work by simply multiplying the force and displacement. However, the work has a negative value. A negative value for work denotes that the work is being done by the object or system to the environment. When it is positive, work is being done to the system or object that is moving.

#Mechanics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$