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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?
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Solution
(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
∴ mac = T- mg cos θ
Centripetal acceleration ac = `(T - mgcostheta)/2`m
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