Explain with graphs the difference between work done by a constant force and by a variable force.

Explanation

When a constant force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by,
`dW=(Fcostheta)dr`
The total work done in producing a displacement from initial position `r_(i)` to final position `r_(f)` is, given by
`W=underset(r_(i))overset(r_(f))intdW`
`W=underset(r_(i))overset(r_(f))int(Fcostheta)dr`
`=(Fcostheta)underset(r_(i))overset(r_(f))intdr`
`=(Fcostheta)(r_(f)-r_(i))`

the graphical representation of the work done by a constant force is as shown in the figure. The work done by the constant force is given by the area under the graph.
Work done by a variable force: When the component of a variable force F acts on a body, the small amount of work done (dW) by the force in producing a small displacement dr is given by the relation,
`dW=(Fcostheta)dr`
where, F and `theta` are variables. The total work done by a body for a displacement from initial position `r_(i)` to final position `r_(f)` is given by the relation
`W=underset(r_(i))overset(r_(f))intdW=underset(r_(i))overset(r_(f))intFcosthetadr`

The work done by a variable force is as represented by a graph as shown in figure. The area under the graph is the work done by the variable force.