Work Done By Variable Force - Practice Questions & MCQ

• Force is a vector quantity. So it has a magnitude as well as direction. A variable force means when its magnitude or its direction or both varies with position.

           And work done by the variable force is given by - 

$$
W=\int \vec{F} \cdot \overrightarrow{d s}
$$

Where $\vec{F}$ is a variable force and $\overrightarrow{d s}$ is a small displacement
- When Force is time-dependent

And we can write $d \vec{s}=\vec{v} d t$
${ }_{\text {So, }} W=\int \vec{F} \cdot \vec{v} d t$
Where $\vec{F}$ and $\vec{v}$ are force and velocity vector at any instant.

• Work Done Calculation by Force Displacement Graph

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

1. Work done by the frictional force is zero - 

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

2. Work done by the frictional force is negative

             When the force is large enough to overcome the friction

3. Work done by the frictional force 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

             maybe positive.