Question

A light string can support a stationary hanging load of 24.4 kg before breaking. An object of mass m = 2.93 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.819 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

The maximum tension for the string is:
T = m g
T = (24.4 kg) (9.81 m/s²)
T = 239.36 N

The tension in a string when the mass is moving in circular motion is given by:
T = m v² / r
so
(239.364 N) = (2.93 kg) v² / (0.819 m)
v = 8.179m/s

Answer:
(0 m/s) ≤ v ≤ (8.179 m/s)