Hello, This is an advanced forces problem from introductory Calculus with Physics. I have mostly solved the problem I am posting here but am just missing a force on my diagram somewhere. M. The jpeg below "MassCartTheProblem_1.jpg" shows a picture of the situation and the goal is to find the constant acceleration. There are three masses, ([M][/B], [M][/1], [M][/2]. There is a force F applied to the right and the goal is to find the accelerations everywhere, assuming the two masses connected by the tension do not accelerate with respect to the big block. No friction anywhere, pulley is massless. The problem is that I know that the answer should be F = ([M][/B] + [M][/1] + [M][/2] )a but I only come up with F = ([M][/B] + [M][/2] )a Somehow, the mass on top of the block is not making its way into the final "F = ma". Of course, I know that if the whole system moves together, the system behaves as one big block of [M][/B] + [M][/1] + [M][/2]. However, I cannot find any other forces further than what I drew in figure "MassCartForces_2.jpg". I provide Newton's Laws for these forces for each mass in each direction in the figure "MassCartEquations_3.jpg. I cannot find a way to draw some other force in "MassCartForces_2.jpg" that couples the [M][/1] term into equation 7) on the figure "MassCartAlgebra_4.jpg". One explanation I came up with is that maybe when [N][/B] pushes on [M][/2], [N][/B] is not the only force in the x-direction acting on [M][/2]; that is, perhaps since [M][/1] and [M][/2] are connected, there is some inertia of [M][/1] transmitted through the cable. I drew this "horizontal tension" in the figure "HorizTensionMaybe.jpg". If I do this, I can put another term in equation 7) of figure "MassCartAlgebra_4.jpg" by using equation 2) of the figure "MassCartForces_2.jpg". If the above is wrong, can anyone show me how to draw the subtle missing force on the force diagram that will make the equations on "MassCartEquations_3.jpg" yield the correct F = ([M][/B] + [M][/1] + [M][/2] )a ?