How Do You Calculate the Unknown Mass in an Atwood's Machine?

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To calculate the unknown mass in an Atwood's machine with one known mass of 5 kg and an acceleration of 2 m/s², the relationship between the forces acting on the system must be established. Given that the unknown mass is greater than the known mass and friction is negligible, the equation can be set up using Newton's second law. The user derived the equation correctly, leading to the conclusion that the unknown mass is approximately 7.56 kg. This calculation confirms the principles of dynamics in a pulley system. The final answer is validated by the forum participants.
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I dislike simply having answers told to me, so I won't give the actual number values of the question. However, I need some insight on how I would solve this:

There are two masses on an atwood's machine, but only one of the masses is known (let's say 5 kilograms). I am told that the unknown mass is greater than the known mass, and that the system is accelerating at 2 m/s^2. I am also told that friction is negligible, and to assume that the string is weightless. How would I solve for the unknown mass?

edit:
I think it came to me:
2(5) + 2(x) = 9.81(x) -9.81(5)
2(5) + 9.81(5) = 9.81(x) - 2(x)
10 + 49.05 = 7.81(x)
59.05/7.81 = (x) = 7.56kg

Is that right?
 
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Yup! You've got it.:wink:
 
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