A simple pendulum is constructed by attaching a bob of mass 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 `alpha` with the vertical. Find the tension in the string and the magnitude of net force on the bob at that instant.

Explanation

a. The forces acting on the bob are
i. the tension `T`
ii. The weight `mg`
As the bob moves in a circls of radius `L` with center at O,A centripetal force of magnitude `mv^(2)//L` is required toward o.
This force will be provided by the resitant of `T` and `mg cos alpha`

Thus `T - mg cos theta = (mv^(2))/(L)`
`T = m(g cos alpha + (v^(2))/(L))`
ii. `a_("net") = sqrt(a_(1)^(2) + a_(1)^(2)) = sqrt((g^(2) sin alpha)^(2) + ((v^(2))/(l))^(2))`
`|barF_("net")| = ma_("net") = m sqrt(g^(2) sin^(2) alpha + (v^(4))/(L^(2))`