Atwood's machine accelerating upward with two unknown mass accelerations

[diegojco]

well, I have tried many ways to get the solution to this problem, but i have two great obstacles:

We have atwood's machine with to masses m1 and m2, machine is accelerated upwards with an acceleration a. Find accelerations a1 and a2 for masses m1 and m2 respectively and find the tension.

Well, I have wrote the ecuations:

-T+(m1)g+(m1)(a1)=(m1)(a)
T-(m2)g-(m2)(a2)=(m2)(a)

since net force at m1 and m2 are the sum of the forces, including the fictious force introduced because this is a non-inertial system.

But I must find a new ecuation because this system has infinite solutions since I have the variables T, a1, a2. where are the other ecuation, or what's the mistake in thinking?

Please answer me the fast as it can be possible.

 

[Doc Al]

https://www.physicsforums.com/showthread.php?t=44305

 

[M98Ranger]

Hello,

I understand that you are struggling with finding the solution to the accelerated Atwood's machine problem. It seems like you have set up the equations correctly, but you are missing one more equation to solve for the three variables (T, a1, a2).

One additional equation that you can use is the fact that the masses are connected by a string and therefore, their accelerations must be the same. This means that a1 = a2 = a. This should help you to solve for the tension and accelerations of the masses.

I would also recommend checking your calculations and making sure that you have the correct signs for the forces and accelerations. Sometimes, a mistake in signs can lead to incorrect solutions.

I hope this helps and please let me know if you have any further questions. Good luck!