I am having difficulty reconciling this in my head. Imagine two Atwood machines (example). In both machines, the pulley is massless, there is no friction, but the rope is not massless, though it is inextensible. The rope and pulley in each machine are identical. The first is a traditional Atwood machine, with a 10N block hanging on the left of the pulley and a 50N block hanging on the right of the pulley. The second Atwood machine also has a 10N block on the left, but on the right there is a constant applied force of 50N downward. I am not sure whether the 10N block will accelerate at different rates in each Atwood machine. On the one hand I could see an argument that the block will accelerate faster in the second one simply because there is less overall mass to accelerate with identical forces. However, if this were the case, it would imply that the tension in the rope is greater in the second Atwood machine, and I cannot figure out how this would happen when both the mass in the first machine and the applied force in the second machine are exerting the same constant downward force. Help?