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

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

$F=m\frac{v^2}{r}$

The formula can also be rewritten as

$F=m\omega^2 r$

where $\omega=\frac{2 \pi}{T}$ 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:

$\omega=\frac{2 \pi}{T}=\frac{2 \pi}{1.4 s}=4.49 rad/s$

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:

$m=\frac{F}{\omega^2 r}=\frac{12 N}{(4.49 rad/s)^2 (0.87 m)}=0.68 kg$

Answer 2

The mass of the ball has to be 2.36 depending on the size and width