What horizontal force F must be constantly applied to M so that M1 and M2 do not move relative to M? neglet friction http://imageshack.us/photo/my-images/823/immaginelq.jpg/

Since M2 is not moving, the tension of the string is T=M2∗g. Plugging this into the euation T=M1∗a we find that the acceleration of M1 is a=(M2/M1)∗g Since M1 is at rest with respect to M, M have the same accelleration a So, F=(M+M2)∗a. or F=(M2/M1)∗(M+M2)∗g that's what i found. But the problem solution states that F=(M2/M1)∗(M+M1+M2)∗g which i don't see why it should be like that. Intuitively if i push on the block M, i push both M and M2, that's why i found (M+M2), but i don't push on M1, since there is no friction. It's movements are due to the force of M2 pulling down.

but the question states that the force should be applied on M, so Newton's law should be applied on M, as far as I know, Thus, \[F=(M.M _{2}.g)/M _{1}\]

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