Force problem involving two pulleys and three masses

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The problem involves a system with an 8.00 kg block on a frictionless table connected to two hanging masses, 3.40 kg on the left and 12.0 kg on the right, via frictionless pulleys. The main objective is to determine the tension in the cord on the right side. Key concepts include analyzing the forces acting on each block, including gravity and normal force, and applying Newton's second law (F=ma) to solve for tension. The discussion emphasizes the need to consider the effects of gravity on the hanging blocks and the resultant forces on the block on the table. A systematic approach to examining forces and applying the relevant equations is crucial for finding the solution.
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Homework Statement



A block with a mass of 8.00 kg rests on a frictionless table. On both sides of the table are frictionless pulleys. Two hanging blocks are attached to the block on the table though these pulleys with two cords (one block on each side). On the left side of the table the block has a mass of 3.40 kg. On the right side the mass of the block is 12.0 kg.

What is the tension of the cord on the right?


Homework Equations



F=ma...

The Attempt at a Solution



My only idea is that the pulleys cause the tension to all take effect upon the x-axis. Gravity obviously takes effect on both hanging blocks. The normal force is taking effect upon the block on the table. I'm at a loss on how to proceed with this problem.
 
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You should start by examining all the forces acting on each block and then applying Newton's second law to each block individually.
 

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