What is the expression of work for three different situations for force and displacement?

• Work done by a constant force-The scalar product of the force vector () and the displacement vector ()

w = $\underset{F.}{\rightarrow}\underset{S}{\rightarrow}$

• work done by the variable force is given by

$W=\int \vec{F}\cdot \vec{ds}$

Where $\vec{F}$ is a variable force and $\vec{ds}$ is a small displacement.

The area under the force-displacement curve with the proper algebraic sign represents work done by the force.

Work done by the frictional force :

•   is zero:  When the force applied on a body is insufficient to overcome the friction.

•  is negative: When the force is large enough to overcome the friction

•  is positive: When force is applied on a body, which is placed above another body, the work done by the frictional force on the lower body

may be positive.

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