If the weight of m

_{1}and m_{2}are equal then there is no acceleration. However if they are unequal their acceleration would be as follows. We can define the forces acting on m_{1}as T the tension force of the rope and W1 the force due to the weight of the block. The forces acting on m_{2}are T the tension force and W_{2}the weight of the second block. As you can see the tension force has the same magnitude on each block and all that is left is to solve for our acceleration.
m

_{1}g - T = m_{1}a
T - m

_{2}g = m_{2}a
We then combine this system of equations by adding them together to get

m

_{1}g - m_{2}g = m1 a + m2 a
This is the same as distributing g and a over m1 and m2 so our acceleration is

a = g(m

_{1}- m_{2})/(m_{1}+ m_{2})
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