A student whirls a 0.25 kg rubber stopper in a horizontal circle on the end of a…
PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
A student whirls a 0.25 kg rubber stopper in a horizontal circle on the end of a light string of length 1.1 m. Initially the string sweeps out 1.5 revolutions each second. The student then increases the revolutions to 4.5 per second while keeping the radius of the circle unchanged.
(a) Show algebraically how the magnitude of the centripetal acceleration depends on the rotational frequency f (revolutions per second) for an object moving in a horizontal circle of fixed radius.
(b) Using your result from part (a), determine the factor by which the centripetal acceleration increases when the frequency is changed from 1.5 Hz to 4.5 Hz.
(c) Calculate the numerical values of the centripetal acceleration before and after the speed-up. Express both answers to two significant figures.
(d) If the string has a maximum sustainable tension of 180 N, assess whether the string will remain intact at the higher frequency. Support your answer with calculations and reasoning.