Question

Consider a small point object of mass m attached to a massless cord passing through a hole in a frictionless horizontal surface. The object is originally moving in a circle of radius with a speed us. The goal is to determine the speed of the object if the string is pulled so that the radius is changed to ry. This can be done in steps: (a) What force is required to keep the object moving in a circle of radius ri and speed vi? (b) How much work is done to pull in the string an amount dr;? (c) This work goes toward increasing the kinetic energy of the object. Use energy conservation to find expression for the new speed of the object after the string is shortened a small amount dr. (d) Derive a relationship for the change pf the speed of the object dv in terms of the change in length of the string dr. Your expression should also have ri, and vi it, but you should only keep first order terms in dr. (e) Assuming that du and dr are so small as to be differential quantities, integrate the equation to show that vr is a constant Show the steps and complete the derivation.

Answer 1

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