Answer to Question #219271 in Mechanical Engineering for JOHN SMITH

Question

A ball is fastened by a light inextensible cord 5m long to a point 3m above the level of a smooth horizontal table, and is than caused to rotate in a horizontal circle. Determine the following:

(a) The angular velocity of the ball in rpm so as to just keep clear of the surface of the table.

(b) If the mass of the ball is 6kg determine the tension in the string when it rotates at 17.3 rpm

Answer 1

a)

$$mgh=0.5m\omega^2l^2\\9.8(3)=0.5(5)^2\omega^2\\\omega=1.53\frac{rad}{s}=14.6\ rpm$$

b)

$$T=6(1.82)^2(5)=99.4\ N$$