Solving for Tension & Acceleration in M1 & M2

[Harmony]

Assume there is negligible friction between the blocks and the table. Compute the tension in the cord and the acceleration of m2 if m1 = 300g, m2 = 200g, and F=0.4N

I figured out that T=m2*a2, F-2T=m1a1.
According to the answer, 2a1=a2. But I don't undestand why.

 

[Doc Al]

acceleration constraint

Your force equations are correct, but incomplete. You need to incorporate the constraint imposed by the fact that the masses are connected via a pulley and ropes--that's what will give you the additional equation a2 = 2 a1. To understand where that relationship comes from, answer this question: If m1 moves one meter to the right, how far does m2 move? (If you have trouble visualizing the motion, use a piece of string or a paper strip.)