# How can I understand work conceptually?

I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?

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## 2 Answers

Start with force; force does work when it acts on a body. This displaces the body from its original position. A force does work when it results in this body moving.

Unit wise, it is Joules [J] or Newton-Meters [Nm] or [N-m]. this would imply $W=F \cdot d$ where $d$ is the distance.

I prefer this definition; the work done by some force on an object travels along some curve S is given by a line integral $$W=\int_{S} \vec{F} \cdot d\vec{x}$$ when path dependent. When path independent, one obtains instead that $$W=U(d_{1})-U(d_{2})$$ where $U$ is called the potential energy, measured in joules. $d$ is a point at which the potential is evaluated; this can be time dependent.

Hope this helps!

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This website has an excellent definition of work: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

This chart from the same website explains how work relates to other mechanical concepts: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

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