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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.
Solution
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`
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