- #1

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## Homework Statement

See Picture, The problem gives three boxes(M

_{1}, M

_{2}, and M

_{3}) and a few pulleys, no value for the coefficient of friction is given. None of the masses are known, and we are told to assume M1 and M3 are sliding. The objective is to find F

_{t}

## Homework Equations

F=ma

F

_{f}=µma

## The Attempt at a Solution

First I started of by drawing free body diagrams for all of the boxes, Using these(and assuming M

_{1}and M

_{2}are sliding towards the middle) I came up with

M

_{1}:

F

_{NET}=F

_{t}-F

_{f}

M

_{1}a=F

_{t}-µM

_{1}a

F

_{t}=M

_{1}a+µM

_{1}a

M

_{2}Would then have the same equations except M

_{1}would be M

_{2}because it also has

F

_{NET}=F

_{t}-F

_{f}

(I feel like that might be wrong but I'm not sure)

I'm not sure about the signs on all of those either.

Then I have for M

_{3}

F

_{NET}=F

_{g}-F

_{t}

At this point I'm not sure what to do, (the lack of values is killing me) I would think putting F

_{t}from the M

_{1}equation into the F

_{t}equation would be a good start, but then everything except mass would cancel wouldn't it? So that doesn't seem right. I feel like I'm going in the right direction and I need to use these equations simultaneously some how but I'm not sure what to do for the next step as I don't see how this is going to get me F

_{t}.

Also I'm starting to think M

_{2}Net force is different

F

_{NET}=F

_{f}-F

_{t}(Since the ropes would be moving in opposite directions) and that would also change the equation for M

_{2}to

M

_{2}a=µM

_{2}a-F

_{t}

F

_{t}=µM

_{2}a+M

_{2}a

But even if that's right, what would i do with it...?

Any help is appreciated, I'm currently stumped.