What force must be applied horizontally to the mass M such that neither m1 or m2

Question

What force must be applied horizontally to the mass M such that neither m1 or m2 move relative to the cart? Assume all surfaces, wheels, and pulleys are FRICTIONLESS. Your answer should be in terms of M, m1, m2 and g. (Hint: what system is easiest to determine the acceleration of all three masses?) Also, the surface that the cart is on is level. Can someone please show me step by step. I am very confused with this problem. It is from a practice problem, and I know something like it will be on my test this week. I really appreciate it.

Explanation / Answer

http://www.physics.oregonstate.edu/~mcintyre/COURSES/ph211_S04/PHpdfs/hw5_solns.pdf

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