Find Force to Keep M3 in Equilibrium: K&K Problem

[WiFO215]

Homework Statement

I got this problem from K&K. A pedagogical machine is illustrated in the sketch above. Refer link : http://www.slideshare.net/brigittperalta/sol-maquina-pedagogica-1546585 . What force F must be applied on M1 to keep M3 from moving up or down. All surfaces frictionless.

Homework Equations

The Attempt at a Solution

If I go and sit on the M1 block, I can mark a fictitious force on M2 to the left with magnitude (M2.F)/M1. On M2 there is also tension from the string (T) to the right. If M3 is to remain in equilibrium, M3.g = T and T = (M2.F)/M1 to prevent block 2 from moving which will cause block 3 to move.

Therefore, I get my answer to be F = (M3.g.M1)/M2. I am making a mistake here but cannot see where. Can someone please tell me where?

 

[alphysicist]

Hi anirudh215,

Homework Statement

I got this problem from K&K. A pedagogical machine is illustrated in the sketch above. Refer link : http://www.slideshare.net/brigittperalta/sol-maquina-pedagogica-1546585 . What force F must be applied on M1 to keep M3 from moving up or down. All surfaces frictionless.

Homework Equations

The Attempt at a Solution

If I go and sit on the M1 block, I can mark a fictitious force on M2 to the left with magnitude (M2.F)/M1.

I believe this is incorrect here. According to this expression, the overall horizontal acceleration would be given by F=(m1) a, which is not true.

Instead, begin by considering the entire setup as one mass to find the horizontal acceleration, and then continue from there as you already have done.