Is there a difference between 10kg weight exerting 98N force vs. a person pulling the string with 98N force? My question is related to an AP Physics question (2.k acceleration of systems), which appears simple, but the premise of part 2 of the question is difficult to understand, hence asking the physics community here for the explanation of the question.
The part 2 of the questions asks why M in the second system reaches to the right earlier than the first system even if the force acting on the string (by someone pulling on the string) is same as the case 1 where a weight is attached.
So my question is in what ways these systems are different if 10kg weight induced 98N tension in the string same as someone pulling with 98N force? Why would the second system accelerate more than the first system?


 A: The first system has more mass (total mass M+10) than the second system (total mass M) and therefore accelerates more slowly when subjected to a particular force. In the first system, the 98N of force has to accelerate both blocks, while in the second system, the 98N of force just needs to accelerate one block. If you turn this into a horizontal problem by eliminating the pulley and treating both forces as a pull, it should be clear that you'll get lower acceleration when pulling a rope with two blocks on it, compared to pulling a rope with just one block on it.
As noted in the argumentation section of the answer, tension is not the same in both cases. In the first system, the hanging block is pulled down by the force of gravity (98N), and pulled up by a tension force - this tension force must be less than 98N, since the block is accelerating downwards (it's pulled down harder than it's pulled up). The actual tension value must be somewhere between 0 (as M approaches 0kg and the hanging block approaches free-fall) and 98N (as M approaches a very large value and the hanging block approaches not moving at all).
In the second system, the tension force of 98N is applied directly to the string connected to M, so that's the tension felt by M.
