Two blocks on a pulley, finding magnitudes, tension, and rotational acceleration...?

Question

There are two blocks hanging on a pulley attached by a cord. One block has a mass M = 500 g, the other has mass m = 460 g, and the pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 s (without the cord slipping on the pulley).

(a) What is the magnitude of the blocks’ acceleration?

What is the tension in the part of the cord that supports (b) the heavier block, and (c) the lighter block?

(d) What is the magnitude of the pulley’s rotational acceleration?

(e) What is its rotational inertia?

Explain your work. Thanks :)

Answer 1

a) given y(5)=0.75 m
and y(t)=.5*a*t^2

a=0.75*2/25

a=0.06 m/s^2

the tension is related to a as
0.5*0.06=0.5*9.81-T
solve for T
T=4.875 N


since the a is the same for the smaller block

T=0.460*0.06
T=0.0276

The net torque on the pulley is related to the translational acceleration as

torque=I*a/R
since the cord doesn't slip
alpha=0.06/0.005
12 rad/s^2
The net torque is
0.005*(4.875-0.0276)
or 0.024237

and
I=0.02437*0.005/0.06
I=0.00203

j