Problem on an atwood's machine given an upward acceleration

[mnlaguerta]

The pulley in an atwood's machine is given an upward acceleration a. Find the acceleration of each mass and the tension in the string that connects them.

so my problem here is deriving the equation for the acceleration of both masses considering that the system was applied with an upward force. what will the upward acceleration do to the system? well, if the system wasn't given any upward acceleration i know that:

$$\sum$$Fy₁= T₁-m₁g=-m₁a
$$\sum$$Fy₂= T₂-m₂g=m₂a

are the tensions equal?
my professor didn't give us any values for the masses which make this problem even tougher for me. please help me.

 

[mtr]

are the tensions equal?

It depends on friction. Is there any friction in this task? If yes, tensions are not equal. What about masses? Are they among the data?
Considering acceleration, it seems it will be a-g. In your equations you just have to change g for g-a and a for b-a, where b is acceleration of each mass if the pulley is not given any acceleration. If you have masses, it is not a very difficult problem.