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.

 

[tomcue]

Your solution is correct. The force F required to keep M3 in equilibrium can be calculated using Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, M3 is not accelerating, so the net force on it must be zero. This means that the force of gravity acting on M3, M3.g, must be balanced by an equal and opposite force. This force can be provided by the tension in the string, which is equal to the force applied on M2, (M2.F)/M1. Therefore, F = (M3.g.M1)/M2 is the correct equation to use. It is possible that you made a calculation error, so it would be helpful to double check your calculations. Additionally, it is always a good idea to draw a free body diagram to help visualize the forces acting on each object in the system.