Trouble finding the acceleration

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The discussion focuses on finding the vertical acceleration a1 of a block m1 in a system involving two blocks connected by a string over pulleys. Participants agree that the tension T is consistent throughout the string and that the accelerations of both blocks are equal. The challenge arises in expressing a1 in terms of m1, g, and T, with some confusion regarding the correct formulation. One participant suggests a formula for a1, but another points out that the units do not correspond to acceleration, indicating a potential error in the calculation. The conversation highlights the complexities of analyzing the dynamics of interconnected masses in a frictionless environment.
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A block of mass m1 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 m2 that is free to slide on a frictionless table. The string is firmly anchored to a wall and the whole system is frictionless.


I want to find the vertical acceleration a1 in terms of m1, g and T

I know that the tension T is equal everywhere in the string and also that the acceleration af block m1 must be equal to the acceleration of block m2.


I've tried some calculations but I always seem to get stuck with m2 in my equations.

T = m1*g and T = (m2*a2)/2
 
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The setup is that a falling weight M1 pulls a mass M2 horizontally - correct.
The force downward on M1 is just f = M1 g and the force upward from the string is f = M2 a
 
Yeah, I figured that one out but that was not the question (but thanks thanks anyway for replying! :)

My problem is to find the a1 in terms off m1, g and T (When T = (m2*a2)/2)
 
Ok. I've got the answer! Was a bit hard but finally.

a1 = (m1-g)/m1
 

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