How do mass affect the acceleration of a pulley?

[boii]

Hi, i am doing physics 20 and i am still quite new at this stuff. I have a base understanding of how the mass affect the acceleration but i can't find a way to explanation of why the the mass affects the acceleration by making it faster or slower of a pulley for my lab like this one http://cnx.org/content/m14060/latest/fap1.gifAnd i believe Newton 2nd law has to do something as well but i don't understand it if there's no force applied how acceleration could be found? If anyone could help me with this thanks!

 

[Simon Bridge]

Welcome to PF;
Without an unbalanced force, there is no acceleration.
In the example you give, there is an unbalanced force. The weight on one side of the pulley is greater than the weight on the other.

The effect of the pulley is to change the direction of action of the force ... draw a free body diagram for each component of the setup just like you'd normally do.

 

[paisiello2]

Assume the pulley itself is negligible mass and negligible friction.

Intuitively first, you would expect the heavier to mass to accelerate down pulling the smaller mass up. Look at three limiting cases:
1) m2 >> m1
2) m2 = m1
3) m2 << m1

So for the case where m2 = 2*m1 you are somewhere between the limiting cases 1) and 2).

 

[Simon Bridge]

m2 > m1 = 2*m1

This statement is nonsense.
m1 ≠ 2*m1 ...

I can see what you are trying to do ... but how about letting OP do the fbd's first?