Question

In Problems 64 and 65 you are given the equation used to solve a problem. For each of these, you are to
a. Write a realistic problem for which this is the correct equation. Besure that the answer your problem requests is consistent with the equation given.
b. Finish the solution of the problem.
60 N = (0.30 kg)ω²(0.50 m)

Short answer

a) A ball of mass 300 gm , attached to a string , is rotating around a horizontal circle of 0.5 m radius. The tension on the string is 60 N . Find the angular velocity of the ball.

b) Angular velocity is 20 rad/sec or 190.985 rmp.

Step-by-step solution

Part(a) Step 1 : Given information

The equation given is 60 N = (0.30 kg)ω² (0.50 m)

Part(a) Step 2 : Explanation

Lets observe the equation given 60 N = (0.30 kg)ω² (0.50 m)

We have Force =60 N. Mass 0.3 kg and radius 0.5 m. Angular velocity is unknown.

We can state problem as

A ball of mass 300 gm , attached to a string , is rotating around a horizontal circle of 0.5 m radius. The tension on the string is 60 N . Find the angular velocity of the ball.

Part(b) Step 1 : Given information

The equation given is 60 N = (0.30 kg)ω² (0.50 m)

Part(b) Step 2 : Explanation

The centripetal force acting on a mass m revolving with angular speed ωaround a circle of radius r is given by mω² r.

The angular velocity of the ball is calculated as

$$\begin{gathered} 60N=(0.30kg){\omega }^2(0.50m) \\ {\omega }^2=\frac{60N}{(0.30kg)(0.50m)} \\ \omega =20rad/s \end{gathered}$$