Multiple Pullys and determing Tension

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SUMMARY

The discussion focuses on determining the tension in a multi-pulley system and relating the accelerations of different blocks. The equations presented include: 2T - 2g = 2*a1 for the left block-pulley system, 2T - 2g = 3*a2 for the middle block-pulley system, and T - 20*9.8*sin(60) = 20a3 for the block on the ramp. The user seeks to derive a relationship between the three accelerations using the conservation of string principle, which is essential for solving the problem correctly. The final answer to the midterm question is confirmed as option d.

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  • Basic principles of conservation of string in mechanics
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Multiple Pulleys and determing Tension Dynamics

So i started out with the the equation for the tension of the block-pulley system on the far left in the y direction being: 2T-2g = 2*a1
the equation for the middle block-pulley system is: 2T-2g = 3*a2
the equation for the block on the ramp is: T - 20*9.8*sin60 = 20a3

I need an equation to relate the three accelerations using conservation of string but i do not know how to write it.
 

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I am studying for a midterm and this is a question from a previous years midterm the answer is d, but i do not know how to get it.
 

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