Question

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/

Answer 1

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.

Answer 2

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,
\[F=(M.M _{2}.g)/M _{1}\]