A spool consists of an axle of radius r and an outside circle of radius R which rolls on the ground. A thread is wrapped around the axle and is pulled with tension T, at an angle ? with the horizontal (see Fig).

(a) Given R and r, what should ??¸ be so that the spool does not move? Assume that the friction between the spool and the ground is large enough so that the spool doesn't slip.

(b) Given R, r, and the coefficient of friction ? between the spool and the ground, what is the largest value of T for which the spool remains at rest?

(c) Given R and ?, what should r be so that you can make the spool slip with as small a T as possible? That is, what should r be so that the upper bound on T from part (b) is as small as possible? What is the resulting value of T?

Transcribed Image Text:

R T