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Please explain the theory in the image.
Asked by kandappan | 30 Dec, 2018, 09:15: AM
When a force F acting on a body to make a disolacement d, then the workdoneW  by the force is defined as  W = f×d.
In this definition, it is assumed that force and displacement is in same direction. But if they are in different direction,
we need to find the workdone either in the direction of force or in the direction displacement.

If θ is the angle between line of action of force and the direction of displacement,
then the component of force along the direction of displacement is F×cosθ.
Hence workdone along the direction of displacement = F×cosθ×d = F×d×cosθ.

If we find the workdone along the direction of force, then displacement along the direction of force is d×cosθ.
Hence workdone along the direction of force F×d×cosθ.

Hence to know the workdone we need to calculate F×d×cosθ, where F is the force, d is the displacement
and θ is the angle between the direction of force and direction of displacement.

If force and displacement are in same direction, θ=0 and cosθ = 1, hence workdone = F×d .

If force and displacement are perpendicular to each other, θ= π/2 and cos (π/2) = 0, hence workdone = 0.

If the angle between the force and displacement is in between 0 and π/2 , then workdone is in between 0 and F×d
Answered by Thiyagarajan K | 31 Dec, 2018, 03:18: PM

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