Question

A uniform, solid cylinder with mass 3M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string (the figure (Figure 1)). The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the tabletop.

ЗМ 2R м М

1.) Find the magnitude of the acceleration of the block after the system is released from rest?

2.) Find the static friction between solid cylinder and table top?

3.) If all the masses start to move from rest what is speed Vf of M2 after it starts to move?

Answer 1

n Let blick Mass starts to accelerate by an acceleration a f ga. Applying Newtondecond law (пр. -Т= mg (fter ) - T-faima (forcy Ander) Torque generated by friction force, 1=((2R) {for pure rolling a = 8/2R) } e = I2 g flar) = I2 = 3M (2R)? ( 21 ) a f = 3mg 3 Adding eqr , and ♡ ng = matomart3ma = lima for states condition of cylinder Tafalsa [T = mg (No motion of horging block) mg = ls (3ng) [Ms = 1 : 0.33 ② of energy (3m) ve of mass in fall by a distance h. using conservation 1. mgh = 1 mvp + ( Ipwet I wa fp = mph, Ic = 3m 12R² mgha tmye ttcmpe won 8+2 (3M(2832) We . (wp=ove weat (30) ngh = tmpt amue + 3m y + 3 m ² migh = 4 mv ly=fugh