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atwood machine problem -- symbolically solving for mass?
Symbolically solve the equation derived for the acceleration of the Atwood's machine in part 1, A-3 for the mass m in terms of M, g, and the acceleration, a. (No numbers.)
This question is part of a lab, so of course some other information is necessary. We were finding theoretical and experimental acceleration for an Atwood's machine when the masses on both sides were the same except for a few pennies balanced on one of the masses. After finding this value, we were using it to fine the theoretical and experimental weights of the pennies.
We were distinguishing m from M: m was the much smaller mass of the pennies, and M was the mass of the weights on both sides.
How I solved for acceleration can be found in attached image #1. The basic equation used is Newton's second law.
My weak attempt at solving for mass is in the second attached image. It all seems to cancel out and I'm getting really confused. Can anyone tell me where I made a mistake, or whether I'm just using really faulty, circular logic?
Homework Statement
Symbolically solve the equation derived for the acceleration of the Atwood's machine in part 1, A-3 for the mass m in terms of M, g, and the acceleration, a. (No numbers.)
This question is part of a lab, so of course some other information is necessary. We were finding theoretical and experimental acceleration for an Atwood's machine when the masses on both sides were the same except for a few pennies balanced on one of the masses. After finding this value, we were using it to fine the theoretical and experimental weights of the pennies.
We were distinguishing m from M: m was the much smaller mass of the pennies, and M was the mass of the weights on both sides.
Homework Equations
How I solved for acceleration can be found in attached image #1. The basic equation used is Newton's second law.
The Attempt at a Solution
My weak attempt at solving for mass is in the second attached image. It all seems to cancel out and I'm getting really confused. Can anyone tell me where I made a mistake, or whether I'm just using really faulty, circular logic?