How to draw pulley system diagram to find the relationship between two objects?

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theBEAST
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Homework Statement


Here is the diagram and I need to find a relationship between the acceleration in block A and the acceleration in block B.
http://dl.dropbox.com/u/64325990/HW%20Pictures/datum2.PNG

The Attempt at a Solution


Here is my diagram, which is wrong:
http://dl.dropbox.com/u/64325990/HW%20Pictures/Photo%202012-04-08%209%2039%2025%20PM.jpg

It is wrong in that there shouldn't be a negative sign in front of aB. Instead 3aA=2aB is the correct answer. However I do not know how to derive that answer and where to put my datum. I need help with the diagram, thanks!
 
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Discussion

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ehild said:
If A moves downward B will move to the left and SB will decrease. You supposed aB in the direction of growing sA.ehild

I am still confused... So do you mean that with what I did, I can still get the correct answer? This is really confusing because one object is moving up/down while the other is left/right so I don't know how to set up the signs and how to define the directions.

I forgot to mention in the question that block A accelerates downwards and block B is to the left according to the question. I did the problem with 3a_A=-2a_B and I go the wrong answer. When I used 3a_A=2a_B I got the right answer.
 
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OH I just had an epiphany, so are you saying that the way I drew my diagram would be wrong in that s_B is pointing to the right when it should be pointing to the left since the question tells me a_B is pointing to the left?
 
It depends what you mean on S. If it is the length of a piece of thread, 3SA+2SB =L is right. If it is displacement of a block in the "natural direction of moving) 3SA=2SB.

When the motion goes on along a thread, it can be considered one-dimensional. The actual direction (horizontal, vertical, along a slope... ) is irrelevant. Fit the direction of forces to the supposed direction of the accelerations.

ehild
 
ehild said:
Fit the direction of forces to the supposed direction of the accelerations.

ehild

This is what I am doing now and it has been working great so far! Thanks for your help!