A bob attached to a light string of length R is given an initial velocity u = 7 g R at the bottommost point of a vertical circle. (a) What is the velocity at topmost point? (b) What is tension at th

Question

A bob attached to a light string of length R is given an initial velocity u = 7 g R ​ at the bottommost point of a vertical circle. (a) What is the velocity at topmost point? (b) What is tension at the topmost point? (c) What is tension at the bottommost point?

TestHub · Accepted Answer

(a) Energy: 2 1 ​ m v top 2 ​ = 2 1 ​ m ( 7 g R ) − m g ( 2 R ) , giving v top ​ = 3 g R ​ . (b) At the top: T top ​ + m g = R m v top 2 ​ ​ = 3 m g , so T top ​ = 2 m g . (c) At the bottom: T b o t ​ − m g = R m u 2 ​ = 7 m g , so T bot ​ = 8 m g .

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