Calculating Acceleration and Tension in a Pulley System

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The discussion focuses on calculating the relationship between the accelerations and tensions in a pulley system involving two masses, m1 and m2, connected through pulleys. It is suggested that the accelerations a1 and a2 of the masses are equal due to their attachment, but clarification is needed on how the floating pulley affects these values. The tension in the strings must also be determined, with considerations for the fixed length of the string connected to m2. Understanding the movement of the pulleys and their impact on the system's dynamics is crucial for solving the problem. The conversation emphasizes the need for a clear visual representation to aid in comprehension.
Warrzie
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This one has me clueless. The problem reads:

"An object of mass m1 on a frictionless horizontal table is connected to an object of mass m2 through a very light pulley P1 and a light fixed pulley P2."

It wants me to state the relationship between the accelerations, with a1 and a2 corresponding to m1 and m2 respectively.

It then wants the tension in both strings, and finally the acceleration of each block in terms of m1, g, and m2

I've stared at the attached figure for a while and don't even understand how m2's string is connect to the floating pulley, or if that pulley even has an effect on the accelerations/tension. I want to say that a1=a2 since the blocks are attached to each other.

Any hints?
 

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I've stared at the attached figure for a while and don't even understand how m2's string is connect to the floating pulley, or if that pulley even has an effect on the accelerations/tension. I want to say that a1=a2 since the blocks are attached to each other.
The acceleration of m2 = acceleration of pulley P1. On has to determine the accleration of m1 and the acceleration of P1. When P1 moves (translates) \Delta{x}, by what distance does m1 translate? One may assume the string tied to m2 is fixed to the axis of P1 and is of fixed length.
 
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