Question

1977M2. A uniform cylinder of mass M, and radius R is initially at rest on a rough horizontal surface. The moment of inertia of a cylinder about its axis is ½MR. A string, which is wrapped around the cylinder, is pulled upwards with a force T whose magnitude is 0.0Mg and whose direction is maintained vertically upward at all times. In consequence, the cylinder both accelerates horizontally and slips. The coefficient of kinetic friction is 0.5 On the diagram below, draw vectors that represent each of the forces acting on the cylinder identify and clearly label each force. a. b. c. d. Determine the line ar acceleration a of the center of the cylinder. Calculate the angular acceleration a of the cylinder. Your results should show that a and ?R are not equal. Explain.

Answer 1

Mass r eylinod es = M %3D Tenhion=T = Mx = to-Mhuent of kine he Ioich'on T= tenh'on N = Normal erle fx = kine he horhon F B.ort ylendes AT Mg= wergnt oelinder b) Fnet = Net lorre = Ma %3D Inves hical olrr fnet =0 S N+T=Mg > fr= Ma %3D > He-N = Ma =0.4ng =) a = 0.29 = 2m)s2 lineal atrelerahon t tylinedes = a = m)s? %3D Net Jor ene about ils cenreof mass=Znet = I %3D => T.R - fK R=Id s o.bmg.R-{0-sxo.4 Mg) R= MR? > 0-6M9R-0'4MJR=MR? 0.4 8 Angulas a ccelira h'on trylinder = & =. 0.4g a = am/s2 dR=4 m/s2 net are" f bottm faint = dR-a = 4-22m/s?