A 300 g ball slides on the horizontal surface of a smooth table, circumscribing a circle.

A 300 g ball slides on the horizontal surface of a smooth table, circumscribing a circle. The ball is tied with a weightless and inextensible thread 20 cm long to a nail driven into the table. Determine the speed of the ball if the thread tension is 6 N?

m = 300 g = 0.3 kg.

L = 20cm = 0.2m.

F = 6 N.

V -?

The ball moves along a circle with a radius R equal to the length of the thread L, under the action of the tension force of the thread F.

m * a = F – 2 Newton’s law.

Since the ball moves in a circle, it moves with centripetal acceleration a, the value of which is expressed by the formula: a = V2 / L.

m * V2 / L = F.

The speed of the ball V will be determined by the formula: V = √ (F * L / m).

V = √ (6 N * 0.2 m / 0.3 kg) = 2 m / s.

Answer: the ball is rotated with a linear speed V = 2 m / s.