1. The problem statement, all variables and given/known data In the Atwood’s machine, what should M be, in terms of m1 and m2, so that it doesn’t move? 2. Relevant equations F=ma 3. The attempt at a solution I've set T1=Mg as T1 is the tension of the rope attached to M. m1 and m2 are both connected together by the same rope so I assumed T1=2T2 . I set up the equations T2-m1g=m1a T2-m2g=-m2a (negative due to m1 and m2 moving in opposite directions). I then added the two together to get T2=[m1(g+a)+m2(g-a)]/2. Which, since T1=2T2=Mg, it can be expressed as M=[m1(g+a)+m2(g-a)]/g (I think). Which is where I'm stuck now. I'm unsure of how to get rid of g and a in order to have my answer in terms of just m1 and m2. It's probably pretty simple, but I can't quite get it.. It seems as g can be canceled out from the current equation, but I'm not sure about a. I've tried canceling out the g and then solving for a which gives me a=M/m1-m2 But upon plugging that in as a, I am unsure of how to proceed.