Q: A 2 kilogram ball is attached to a string that is 10 meters in length. If the tension in the string exceeds 50 Newtons, it will snap. If the ball is swung into rotational motion, what is the maximum speed it can attain and remain intact?

A: The tension in the string exerts a ” center seeking ” force upon the ball. This force is a centripetal force ( F_c ). According to Newton’s Third Law of Motion, “ Every force has an equal and opposite force. “ The string exerts a force upon the ball that prevents it from flying off its rotational path of motion, and the ball exerts 50 N of force upon the string.

F_c = ( mv²/ r ). If 50N of force keeps the ball in orbit, 50N = ( mv²/ r ). The ball has a mass of 2 kg, and the radius ( r ) of the centripetally accelerating ball is 10 m. Therefore, √ [ ( 10 m )( 50 N )/( 2 kg ) ] = v.

v = 15.8 m/s.