If there is an external force on a particle causing it to move in a certain direction by a displacement s, then there must be a component of that force acting in that direction and doing the work.

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This “work” is a mechanical quantity and is defined to be the product of that force times the displacement it moves:

W = F.s

Here, we have taken the dot product of the two vector quantities F and s. The dot product has the property that it takes the component of F which is in the direction of d and multiplies them to get a scalar quantity, W.

If the force F is applied at an angle θ, the component along the displacement is F cos θ

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and hence work becomes

W = F s cos θ

In the case of a varying force, net work done during a small displacement ds can be written as:

dW = F.ds

and the total work done along a path from initial point to the final point can be written as:

W =∫ dW = ∫ F.ds

Work
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