Question

A simple pendulum is constructed by attaching a bob of mas m to a string of length L fixed at its 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 `theta` with the vertical. Find the tension in the string at this instant.

Answer 1

(a) The force acting on the bob are
(a) the tension T (b) the weight mg

As the bob moves in a circle of radius L with centre at O. A centripetal force of magnitude `(mv^(2))/(L)` is required towards O. This force will be provided by the resultant of T and mg `cos alpha`. Thus,
`T-"mg cos"alpha=(mv^(2))/(L)`
or `T=m("g cos"alpha+(v^(2))/(L))`
(ii) `|F_("net")|=sqrt(("mg sin"alpha)^(2)+((mv^(2))/(L))^(2))`
`=msqrt(g^(2)sin^(2)alpha+(v^(4))/(L^(2)))`