Solving Physics Problem with an Atwood Device

[monotonousJ]

I am in high school, taking a college Physics for Scientists and Engineers class. I am stuck on one problem concerning an atwood device.

I have an atwood device with two masses (m1<m2, m2 higher than m1, connected via a massless string) and a pulley with a mass Mp and radius Rp. The pulley rotates without friction about it's axis which is attached to the celing via a massless string.

There are 6 questions I need to answer about this device:
1. The magnitude of the acceleration of M2 is ... that of m1.
2. T2 is ... M2g.
3. The C.M. of Mp+M1+M2 does not accelerate.
4. m1g + M2g + Mpg is ... T3.
5. T3 is ... T1 + T2
6. T2 is ... T1;
My choices are less than, greater than, equal, true, and false.
For #1, I'm pretty sure the accelerations are equal, ditto #6.
#2, m2g-T2=m2a, so T2=m2g-m2a, and is therefore less than m2g
#3, I thought the center of mass accelerates
#4, if the C.M. accelerates upward, T3 (the celing string) would be less, more if CM accelerates down, and equal if there is no acceleration.
(T3=M(system)*(a(system))+g))
#5, I'm really not sure how to relate T3 and T1 and T2, because I'm not sure if the CM accelerates.

If I could get help on whether or not the CM accelerates, I'm sure I could finish this, but right now I am stuck. Thank you.

 

[Doc Al]

m1 and m2 are connected by a string, so they must have the same acceleration (at least the same magnitude of acceleration). Now use that fact to answer your question about the C.M. of the system. (You know that the C.M. of the pulley can't move.)

Regarding tension in the string, answer this question: Does the pulley accelerate?