3- A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 89.5 kg that rests on a platform. The cylinder has a mass of 245 kg and a radius of 0.470 m. Assume that the cylinder can rotate about its axis without any friction and the rope is of negligible mass. The platform is suddenly removed from under the block. The block falls down toward the ground and as it does so, it causes the rope to unwind and the cylinder to rotate.(a) What is the angular acceleration, in rad/s², of the cylinder?[________] rad/s²(b) How many revolutions does the cylinder make in 5 s?[________] rev(c) How much of the rope, in meters, unwinds in this time interval?[________] m

Name: 3- A solid cylinder is mounted above the ground with its axis of rotat
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: 3- A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 89.5 kg that rests on a platform. The cylinder has a mass of 245 kg a

Given, mass of cylinder =245 kg radius of cylinder =0.470 m mass of block = 89.5 kgFree body diagramFor block, T=mg-maT=89.5*9.81-89.5aT=878-89.5a for cylinder, moment of inertia I=12MR2I=12*245*0.4702I=27.06025 kgm2 then ' τ=IαT*R=27.06α878-89.5a*0.470=27.06*aR878-89.5a=122.5a212a=878a=4.14 m/s2 and angular acceleration is α=aRα=4.140.470a=8.81 rad/s2using motion equation θ=ωt+12αt2θ=0+12*8.81*52θ=110.15 radθ=110.15rad*1 rev2π radθ=17.5 rev then linear displacement is l=Rθl=0.470*110.15l=51.77 mAnswer: (a) 8.81 rad/s2 (b) 17.5 rev (c) 51.77 m