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# 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 .

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. ## Solved Example Problems for Work

### Example 4.1

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. ### Solution

Force, F = 25 N

Displacement, dr = 15 m

Angle between F and dr, θ = 30o

Work done, W = Fdr cosθ ## Solved Example Problems for Work done by a variable force

### Example 4.6

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)

### Solution

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11th Physics : UNIT 4 : Work, Energy and Power : Work done by a variable force |