Pully System on an Inclined Plane: Understanding Direction of Acceleration

[Yellowkies_3275]

Homework Statement

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So I am pretty okay with most of this problem. And I asked my teacher for clarification but he just sort of said "because it's positive" and I get that's it's positive. Apparently "everyone's" struggling with that, and therefore we are going over this problem to cement the fact that we consider the direction of acceleration to be positive...but that doesn't help me. I get, clearly, how why whatever that we consider m2g positive in this problem. What I don't get is why we can put m2g, a y direction force, into an other wise x direction equation...the fact that it's positive...I don't see how that negates or affects the fact that it's a y direction force in this problem

Homework Equations

See first picture
ΣF=ma

The Attempt at a Solution

As I was writing this I had a thought:

Do we use m2g because m2g is equivalent to Ft2...and Ft2 is equal to Ft1+Ft3...and ft1 and ft3 are x direction forces?? Is that why?

 

[Chandra Prayaga]

Please start your explanation at the beginning.

I get that's it's positive

. What is positive?
The photo that you posted does not show a lot of data.
There is no problem statement. What are you trying to calculate?
Please follow the guidelines when you post a problem.

 

[haruspex]

I suspect the diagram is wrong. It appears to show that a rope goes straight across between two pulleys, with a second rope tied at the middle. The instantaneous acceleration of m₂ would be g, since it would not immediately cause any significant acceleration of the other two masses.

To arrive at the equation shown, there would need to be two more pulleys in the middle. One rope would go over one of these to connect m₁ to m₂, and another rope over the other to connect m₃ to m₂.
If that is correct, you can arrive at the equation using virtual work. If m₂ descends a small distance dy then each of the other masses moves up slope by dy. Write out the energy balance for that and cancel the dy's.

 

[CWatters]

Is the equation in the image part of the solution provided by your teacher or your attempt at the solution?