Aball 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?

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

The formula can also be rewritten as

where 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:

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

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