# What's the "d" in that formula? (work formula)

What's the definition of the "d" in that formula?

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ZapperZ
Staff Emeritus
This equation assumes a constant force?
No it doesn't. This is because to find W, you have to integrate F over the appropriate range of dr.

Zz.

Austin Gibson
robphy
Homework Helper
Gold Member
$dW=\vec F \cdot d\vec r$ is an infinitesimal amount work done over the infinitesimal displacement $d\vec r$,
where $\vec F$ is approximately constant during that displacement.

When this is evaluated over a path, then $\vec F$ and $d\vec r$ will vary as you progress along the path.

It's probably not a good idea to think of these $d$'s as differentials (as in $dW$ is a differential of $W$
since there is generally no such $W$ because the work done generally depends on the path. In thermodynamics books, this is sometimes written as $đW$.)

Last edited:
Austin Gibson