Question

A body, weight W, is attached by a string, length l, to a hook on a vertical wall. A horizontal force F acting on the body holds it at a distance d from the wall. Derive the equation which gives the force F in terms of W, l, and d.

Answer 1

The body is equilibroum So the forces acting on it can be represented by the three sides of the Right angle triangle.

OAB;

Here OA = L the length of the string; AB = D given

Angle α = Angle BOA

In this Δ, AO represents force T(tension in the string)

OB represents weight W of the bob

            BA represent the force, F acting horizontally.

So from Δlaw of forces in equilibrium.

             T/OA = F/BA = W /OB

Hence,    F/W = BA/OB =Tan α

                OB =√(L² -D²)

            F = W. (BA/OB) = W*[D/√(L² -D²)] ________ required equation.