Question

A ball is attached to the end of a massless string. A circus clown twirls the string with a pulling force of 12 N, and the ball travels in a horizontal circle of radius 87 cm. The ball completes one revolution every 1.4 seconds. What is the mass of the ball?

Answer 1

Answer: 0.68 kg

Step-by-step explanation:

The ball in this example moves by uniform circular motion. In a uniform circular motion, an object of mass m moves in a circular orbit of radius r, with constant tangential speed v. This type of motion is produced by a force F (called centripetal force) that "pushes" the object towards the centre of the circular path. The magnitude of this force is given by

`F=m(v^2)/(r)`

The formula can also be rewritten as

`F=m\omega^2 r`

where
`\omega=(2 \pi)/(T)` the angular frequency, and T is the period of revolution.

In this problem, we have the following data:

- centripetal force: F = 12 N

- radius: r = 87 cm = 0.87 m

- period of revolution: T = 1.4 s

Using the last formula, we can find the angular frequency:

`\omega=(2 \pi)/(T)=(2 \pi)/(1.4 s)=4.49 rad/s`

And now we can substitute
`\omega` inside the formula of the centripetal force, and by re-arranging it we can find the mass of the ball:

`m=(F)/(\omega^2 r)=(12 N)/((4.49 rad/s)^2 (0.87 m))=0.68 kg`