Question

A light string can support a stationary hanging load of 23.0 kg before breaking. An object of mass m = 2.95 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.791 m, and the other end of the string is held fixed as in the figure below. What range of speeds can the object have before the string breaks?

Answer 1

A hanging mass of 23 kg will exert a force of:
23 * 9.81 = 225.6 Newtons on the string
Thus, during rotation, the force exerted should remain less than this. Force on an object in circular motion is given by:
F = (m * v^2) / r
225.6 = (2.95 * v^2) / 0.791
v = sqrt(60.491)
v = 7.78 m/s
Thus, the magnitude of the velocity should not exceed 7.78 meters per second.