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

Explanation

Work done by a constant force :
(i) 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 the relation,
`dW=(F cos theta)`
(ii) The total work done in producing a displacement from initial position `r_(i)` to final position `r_(f)` is,
`W=int_(r_(i))^(r_(f))dW`
`W=int_(r_(i))^(r_(f))(F cos theta)dr = (F cos theta) int_(r_(i))^(r_(f))dr=(F cos theta) (r_(f)-r_(i))`
(iii) The graphical representation of the work, done by a constant force is shown in Figure, The area under the grap shows the work done by the constant force.

Work done by the constant force
Work done by a variable force :
The work done by the gravitational force on the object is positive.
(i) When the component of a variable force F acts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation
`dW=(F cos theta)dr`
[F cos `theta` is the component of the variable force F]
where F and `theta` are variables.
(ii) The total work done for a displacement from initial position `r_(1)` to final position `r_(f)` is given by the relation,
`W= int_(r_(i))^(r_(f))dW = int_(r_(i))^(r_(f))F cos theta dr` .... (1)
(iii) A graphical representation of the work done by a variable force is shown in Figure. The area under the graph is the work done by the variable force.