For the system shown below, find the force required to prevent the mass m2 from descending. Use the values of m1 = 9.00kg, m2 = 1.75kg and m3 = 1.000 kg. Assume that all the surfaces are frictionless and the ropes do not stretch (also, in the figure, assume that mass m2 is flush against m1).
F = ma
W = mg
The Attempt at a Solution
I've drawn the free body diagrams for each of the masses.
For mass m2, i've drawn the tension (upwards) and the weight (downwards).
For mass m3, i've drawn the force that m1 exerts on m3, the weight (but these two wouldn't count as the mass isn't moving vertically), and the tension directed to the pulley (or must it be in the opposite direction?).
For mass m3, i've drawn the force that the surface exerts on m1, the force that exerts m3 on m1, the force that we are applying and it's weight (also, i didn't take into accoutn the vertical forces for m1 and m3).
By this, i concluded that m3 is also moving with the acceleration that the force on m1 provides, but the tension must cancel out the acceleration (force) so that m2 doesn't move.
How can i proceed from this information or have i made a mistake in my assumptions?