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

Explanation

Work done by a constant force: 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=(Fcostheta)dr` ....(1)
The total work done in producing a displacement from initial position `r_(i)` to final position is `r_(f)` is, `W=underset(r_(i))overset(r_(f))intdW` ....(2)
`W=underset(r_(i))overset(r_(f))int(Fcostheta)dr=Fcostheta underset(r_(i))overset(r_(f))intdr=(Fcostheta)(r_(f)-r_(i))` ...(3)
The graphical representation of the work done by a constant force is shown in figure given below. The area under the graph shows the work done by the constant force,
Work done by a variable force: When the component of a variable force Facts on a body, the small work done (dW) by the force in producing a small displacement dr is given by the relation
`dW=Fcosthetadr` [`Fcostheta` is the component of the variable force F]
where,` F and theta` are variables. The total work done for a displacement from initial position to final position `r_(i)` to final position `r_(f)` given by the relation,
`w=underset(r_(f))overset(r_(i))intFcosthetadr` ...(4)
A graphical representation of the work done by a variable force is shown in figure given below. The area under the graph is the work done by the variable force, Work done by a variable force