A block of mass M is attached to a spring ofspring constant k and is moving with

Question

A block of mass M is attached to a spring ofspring constant k and is moving with constant speed in a horizontalcircle on a frictionless table. You measure that the time it takesthe mass to make one complete circle is T seconds. One end of thespring is secured at the center of the circle and the other end isattached to the mass. The spring has a length L when it isunstretched. The spring stretches an additional length l while themass is rotating so that its total length (and also the radius ofthe circular motion) is now L+l. The goal is to calculate l interms of the other quantities.
(a) What is the speed of themass? (b) What is the acceleration ofthe mass? (c) What force is needed tocreate this acceleration? (d) What is the magnitude of theforce exerted by the spring? Express your answer in terms of k anda length or lengths.


(a) What is the speed of themass? (b) What is the acceleration ofthe mass? (c) What force is needed tocreate this acceleration? (d) What is the magnitude of theforce exerted by the spring? Express your answer in terms of k anda length or lengths.

Explanation / Answer

centripetal force = Mv^2/(L+l) = spring force = kl speed v = [kl(L+l)/M] acceleration a = v^2/(L+l) = kl/M force needed = spring force magnitude of force = kl

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