How Long Does It Take for m1 to Reach the Floor in an Atwood Machine?

[petereater]

Homework Statement

Consider the system shown in the image attached with m1 = 27.0 kg, m2 = 13.6 kg, R = 0.290 m, and the mass of the pulley M = 5.00 kg. Object m2 is resting on the floor, and object m1 is 4.70 m above the floor when it is released from rest. The pulley axis is frictionless. The cord is light, does not stretch, and does not slip on the pulley.

Calculate the time interval required for m1 to hit the floor.

Homework Equations

I*Angular Accleration=torque
Conservation of Mechanical Energy( K+U, final=K+U, initial)

The Attempt at a Solution

I played around with the formulas starting with the mechanical energy formula. I got this:

omega [final] = (1/R) [(2*(m2-m1)gh)/(m1+m2+(I/R^2))]^(1/2)
I=.5MR^2, M=mass of pulley

So I plugged in the values and got omega[final]= 119

Now, I got to find time, but I'm stuck. I plug in 119 in the formala:

Omega[final] = omega[initial] +angular acceleration*time, omega[initial]= 0

I have to determine the angular accleration (equals torque/Inertia)

Inertia equals to .21075 (.5*5kg*.29m^2). To find torque, I could use Tau=rFSin(theta), but I end trying to find Force and theta. I don't really know where to go from here...

 

[ehild]

Draw a free-body diagram first.

ehild