A 50kg block and a 100kg weight are connected with a rope pa

A 50kg block and a 100kg weight are connected with a rope, passing over a pulley as shown in the picture. The 50-kg block is a surface with a coefficient of friction of uk=0.5. The pulley is a solid disc whos radius is 0.2m and whose mass is 2kg. The rope does not strech.

Solution

writting force and torque equations

100 - T1 = 100*a

T2 - Friction = 50a

T2*R - T1R = I*alpha = mR^2/2*alpha ( torque equation for disk)

alpha = a/R , friction = ukmg

adding all we get

=> 100*9.8 - 0.5*50*9.8 = (50+100+2/2)*a

=>a = 4.86 m/s^2