Physics
Physics
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 (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.Intuitive explanation
This problem is about centripetal force and how it changes when you alter the speed of circular motion. The key insight is that centripetal force depends on (or equivalently, on ), so tripling the rotation rate increases the required inward force by a factor of nine. You'll need to find the tension in the string at both speeds to see how much harder the student must pull to maintain the larger circular motion.
Intuitive explanation
This problem is about centripetal force and how it changes when you alter the speed of circular motion. The key insight is that centripetal force depends on (or equivalently, on ), so tripling the rotation rate increases the required inward force by a factor of nine. You'll need to find the tension in the string at both speeds to see how much harder the student must pull to maintain the larger circular motion.