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## Homework Statement

A 4KG mass is connected by a weightless cord to a 3 kg mass on a smooth surface. The pully rotates about a frictionless axle and has a moment of inertia of 0.5 kgm^2 and radius of 0.3m. Assuming that the cord does not slip on the pully, find a.) the acceleration of the two masses and b.) the tensions T1 and T2.

Click the image below to expand it to see what this looks like.

http://img98.imageshack.us/img98/1032/47770145rn2.th.png [Broken]

## Homework Equations

T1=39.24-ma

T2=3a

Torque1=0.3T1

Torque2=0.3T2

I=mr^2

Torque=Parallel force x radius

Net Torque=Ialpha

## The Attempt at a Solution

I started by finding the mass(M) of the pully.

0.5=0.09M

M=5.56

I then used the net torque equation, substituting a/r for alpha.

nettorque=1.67a

I then summed my torques to this.

torque1-torque2=1.67a

0.3T1-0.3T2=1.67a

0.3(T1-T2)=1.67a

T1-T2=5.56a

Next I substituted my tensions in.

(39.24-4a)-3a=5.56a

39.24=12.56a

3.12a

I figured that now I could substitute the acceleration back in my original tension equations to find the tensions.

T2=3(3.12)

T2=9.37

T1=39.24-12.48

T1=26.76

There is no answer in the back of the book for this one, and I want somebody to check(rather than skim) my work and tell me if I have come to the right conclusion. If not, please tell me what I have done wrong. It's important that I can do this kind of equation for this week's test.

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