Question

A 0.30 kg rock is rotating in a vertical plane on a 0.25 m long string. At the top of the path, the velocity is 4.0 m/s. Find the tension in the string at that point.

Answer 1

The force needed to produce the circular motion is m v^2/r, where m is mass, v is tangential velocity, a r is the radius, the string length. At the top of the circle the string is aided by gravity pulling the mass down (radially at that point), so that T = m v^2/r - mg. T=(0.3kg)(4m/s)^2/(0.25m)-(0.3kg)(10N.kg)=16.2. At the bottom of the circle, we would have to support mg rather than being aided by mg, so T=22.2N.