How Do You Calculate Vertical Acceleration in a Block and Pulley System?

AI Thread Summary
In a block and pulley system, a mass m_1 is connected to a massless string that goes over two massless pulleys, with a second block m_2 on a frictionless table. The tension T in the string is calculated as (m_2*a_2)/2, where a_2 is the horizontal acceleration of m_2. The next step involves determining the vertical acceleration a_1 of block m_1 in terms of its mass m_1, gravitational acceleration g, and the tension T. The discussion emphasizes the need for clarity in expressing these relationships and calculations. Understanding these dynamics is crucial for solving problems related to acceleration in pulley systems.
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appreciate if Sum1 can help

Two Blocks and Two Pulleys(Other answer didn't include T?)


A block of mass m_1 is attached to a massless, ideal string. This string wraps around a massless pulley and then wraps around a second pulley that is attached to a block of mass m_2 that is free to slide on a frictionless table. The string is firmly anchored to a wall and the whole system is frictionless.

Assuming that a_2 is the magnitude of the horizontal acceleration of the block of mass m_2, what is T , the tension in the string? Express the tension in terms of m_2 and a_2

I figured out the T to be (m_2*a_2)/2

but got stuck on the next question

Given T, the tension in the string, calculate a_1, the magnitude of the vertical acceleration of the block of mass . Express the acceleration magnitude a_1 in terms of m_1,g , and T.

I know there was a post like this, but the answer wasn't given in T...
Thanks a lot again...


(thanks cartoon for the last post)
 
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