Question

A bob attached to the string oscillates back and forth. Resolve the forces acting on the bob into components. What is the acceleration experienced by the bob at an angle θ?

Answer 1

(i) Gravitational force(mg) acting downwards.

(ii) Tension (T) exerted by the string on the bob whose position determines the direction of T.
The bob is moving in a circular arc and so it has centripetal acceleration. At points, A and C bob comes to rest momentarily, and then its velocity increases when moving towards B.

Hence tangential acceleration is along the arc.

tangential acceleration = g sin θ

The gravitational force can be resolved into two components.

mg cos θ along the string

mg sin θ perpendicular to the string

At point A & C T=mg cos θ and at all other points T is greater than mg cos θ.

∴ Centripetal force = T – mg cos θ

∴ ma_c = T- mg cos θ

Centripetal acceleration a_c = `(T - mgcostheta)/2`m