Question

a light string can support a stationary hanging mass of 40kg before breaking. determine the maximum speed of a 5kg object tied to one end of a string, while rotating in a circle of radius 0.8m , on a horizontal friction less table while the other end of the string is held fixed.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Maximum hanging mass the string can support = M = 40 kg

Maximum tension the string can handle = T

T = Mg

T = (40)(9.81)

T = 392.4 N

Mass of the object tied to the string = m = 5 kg

Radius of the circle = R = 0.8 m

Maximum speed of the object = V

For maximum speed the tension in the string will be maximum.

The tension in the string will provide the centripetal force for the circular motion of the object.

$T = \frac{mV^{2}}{R}$

$392.4 = \frac{(5)V^{2}}{(0.8)}$

V = 7.92 m/s

Maximum speed of the 5 kg object rotating = 7.92 m/s