a1 = a2 a1 = F/(M+m1+m2) | Force/(Mass of entire system) = acceleration of entire system *a2 = (m1g)/(m2+m1) | Force = m1g; acceleration of m2 and m1 = m1g/(m1+m2) My answer: F = (m1g)(M+m1+m2)/(m2+m1) The book's answer: F = (m1g)(M+m1+m2)/(m2) *This step is what leads me to a slight variation of the book's provided answer. I've looked through the forums, and have done a lot of thinking myself, and I believe what it comes down to is a false assumption. I understand that the force pulling m1 and m2 is m1g, and that the tension that then pulls m2 is equal to m1g, leading to an acceleration of m1g/m2 and subsequently the correct answer, but I do not understand what is incorrect about concluding that the system (looking at m2 and m1) as a whole accelerates at m1g/(m1+m2). Gut feeling tells me that the conclusion I've made is incorrect because the acceleration would be m1g/(m1+m2) in an inertial frame, but not in this case because it is part of an accelerating system. Why does a2 = m1g/m2 rather than a2 = m1g/(m1+m2)?