Suppose the solid cylinder in the apparatus described in Example 9.8 (Section 9.4) is replaced by a thin-walled, hollow cylinder with the same mass ?M? and radius ?R?. The cylinder is attached to the axle by spokes of a negligible moment of inertia. (a) Find the speed of the hanging mass ?m? just as it strikes the floor. (b) Use energy concepts to explain why the answer to part (a) is different from the speed found in Example 9.8.
Solution 46E Step 1: Step 2: There are no other (non-gravitational) ground forces acting on the system the total energy must be conserved. 2 2 mgh = 1/2mv + 1/2Iw (1) Where w = v/R (2) Moment of inertia of hollow cylinder is I = MR (3) Substitute eq(2) and eq(3) in eq(1) mgh = 1/2mv + 1/2( MR )(v/R) 2 mgh = (m/2 + M/2m) v 2 2 v = gh/(m/2 + M/2m)