Solve Block & Pulley Problem: Find Mass

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The discussion revolves around solving a physics problem involving a cylindrical pulley and a block. The user successfully calculated the angular acceleration of the pulley as 3.12 rad/s² using the equation Ay = 2T/MR. However, they are struggling to find the mass of the block, attempting various equations without success. Other participants suggest using the relationship between mass, tension, and gravitational force, pointing out that the tension is given as 3.40 N. The conversation emphasizes the importance of correctly applying the equations of motion to solve for the unknown mass.
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I'm trying to solve this problem and I can get one part but not the other. Here is the information I was given: A uniform, cylindrical pulley of mass M=3.30 kg and radius R=0.660 m rotates freely about a fixed horizontal axis. A block which moves downward is attached to a string of tension T=3.40 N which is wrapped around the pulley.

The first part asks me to find angular acceleration of the pulley which I was able to do with this equation I rearranged Ay = 2T/MR. When plugging in the numbers I got 3.12 rad/s^2.

The second part asks me to find the mass of the block which I have not been able to figure out. I've tried using these equations T = .5MAy and
mg - .5MAy = mAy (rearranging them to find M). I was wondering if someone could guide me in the right direction to solve for the mass. Thanks.
 
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i could be wrong on this, but ill give it a crack anyway

can you find the linear acceleration of the cylindrical block? THis linear acceleration is the related to the tension this way

ma = mg - T
i think you can find the mass now

isnt the tension given to you at 3.40N??
 

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