Question

A 150-g weight is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R 3 cm and mass Ms 100 g. Find the tension in the thread and the magnitude of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. R-3 em Number M,-100g acceleration m/ s Number tension m-150 g

Answer 1

Given data, Mass of hanging weight (M_w) = 150 - g A uniform solid cylinder of radius (R) = 2 cm Mass (M_s) = 100 g The given diagram as shown below, The above diagram shows, the spool is uniform solid cylinder and can rotate about central axis. And the Moment of inertia of solid cylinder about central axis. I_cm = 1/2 M_s R^2 \r\n here thread has negligible mass. So the string does not slip so, acceleration of a point on the rim of spool Must be Equal to acceleration of hanging Mass. Mass (M_w) has downward acceleration a The Angular acceleration of spool alpha = a/R here, alpha is counter clockwise. where T = Tension in rope. By taking Newton's 2^nd law, M_w g - T = M_w a rightarrow (a) for spool, tau_net = T_R counter clockwise we know, tau_net = I alpha I_cm alpha = TR T = I_cm alpha/R rightarrow (b)