Work done by a variable force
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
where, F and θ are variables. The total work done for a displacement from initial position ri to final position rf is given by the relation,
A graphical representation of the work done by a variable force is shown in Figure 4.6. The area under the graph is the work done by the variable force.
A box is pulled with a force of 25 N to produce a displacement of 15 m. If the angle between the force and displacement is 30o, find the work done by the force.
Force, F = 25 N
Displacement, dr = 15 m
Angle between F and dr, θ = 30o
Work done, W = Fdr cosθ
A variable force F = kx2 acts on a particle which is initially at rest. Calculate the work done by the force during the displacement of the particle from x = 0 m to x = 4 m. (Assume the constant k =1 N m-2)