Question

Determine the amount of work done when an object is displaced at an angle of 30° with respect to the direction of the applied force.

Answer 1

Suppose, when a constant force `vecF` is applied on a body located at point 'O', the displacement of that body is `vecs` and the angle between force and displacement is θ.

Displacement of body O →P, direction of force O →Q

On the basis of the diagram,

`costheta = ("OR")/("OQ")`

∴ OR = OQ cosθ

= F cosθ

Here the force applied on the body in the direction of displacement

= F cosθ

∴ Work done by force = (F cosθ)s = Fs cosθ

Displacement of body O →P, direction of force O →Q

`cos theta = ("OS")/("OP")`

∴ OS = OP cosθ = s cosθ

Here the displacement of the body in the direction of the force = s cosθ

∴ work done by force on body = F(s cosθ) = Fs cosθ

When θ = 30°, work (W) = Fs cos 30°

= Fs`sqrt3/2`