Question

A simple pendulum is constructed by attaching a bob of mass m to a string of length L fixed at the upper end. The bob oscillates in a vertical circle. It is found that the speed of the bob is v when the string makes an angle α with the vertical. Based on the above, find the tension in the string and the magnitude of net force on the bob at that instant.

Answer 1

Apply Newton’s second law on the bob in two perpendicular directions. One along the string and the other along the tangent to its circular path, i.e. along the perpendicular to the string. 

The forces acting on the bob are:

(a) Tension, T and

(b) Weight, mg

As observe that the bob moves in a circle of radius L with center at O, it is imperative that a centripetal force of magnitude \(\frac{mv^2}{l}\) is required toward O. 

However, this force will be provided by the resultant of T and mg cos α . 

Thus,