Homework Answers
force balance on m2
T2 - m2g = m2*a
force balance on m1
m1*g*sin(32) - T1 = m1*a
torque balance on pulley
(T1 - T2)R = 0.5*M*R^2*a/R = 0.5MR*a
T1 - T2 = 0.5M*a
so, from 3 equations
m1*g*sin(32) - m2g - 0.5M*a = (m2 + m1)a
a = (m1*g*sin(32) - m2*g)/(m2 + m1 + 0.5M) = 2.1728 m/s/s
Tensions are different as pulley has mass, and hence it needs net torque to rotate as well (with the system) and the net torque can only be generated by different tensions of the strings
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