# Homework Help: Torque and Velocity

1. Nov 17, 2009

### kelslee28

1. The problem statement, all variables and given/known data
An Atwood Machine consists of two masses m1 and m2 attached to each other by a single massless string passing over a cylindrical pulley of mass M without slipping. The masses are released from rest, and allowed to accelerate until each has moved a distance h = 1.8 m. Assuming that upwards is positive, rank the velocity of m2 (from most negative to most positive) at this moment for the following cases:
Case A: m1 = 21 kg, m2 = 16 kg, M = 28 kg

Case B: m1 = 13 kg, m2 = 16 kg, M = 31 kg

Case C: m1 = 25 kg, m2 = 16 kg, M = 26 kg

Case D: m1 = 18 kg, m2 = 16 kg, M = 34 kg

Case E: m1 = 17 kg, m2 = 16 kg, M = 33 kg

2. Relevant equations
sum of the torques = I*alpha
vf^2 = vi^2 + 2a (yf - yi)

3. The attempt at a solution
I did a free body diagram of the cylinder. I did sum of the Torques = I(alpha). I found that the acceleration was equal to
a = [2g(m1+m2)]/M

Then I used a constant acceleration equation Vf^2 = Vi^2 + 2a(yf-yi). I said the initial velocity is 0, I substituted [2g(m1+m2)]/M in for a, I said that yf is the height change (1.8 m) and yi is 0.
I simplified this to say Vf = the square root of [4gh(m1+m2)]/M

I plugged in the values for the examples A through E. I made B a negative velocity because mass 2 is heavier so it would go down.

My ranking was B<D=E<A<C
Thanks for helping :)