How Do You Calculate Friction Force in a Two-Mass System?

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AI Thread Summary
To calculate the friction force (fk) in a two-mass system, the equation derived is fk = m(a + g) - Ma, where m is the mass of the hanging block and M is the mass on the plane. The discussion highlights the importance of correctly defining the positive and negative directions for acceleration (a) to ensure accurate results. There is a suggestion that the expression for tension (T) may be incorrect, potentially due to misinterpretation of direction conventions. Clarifying the direction of acceleration is crucial for solving the problem accurately. Understanding these dynamics is essential for correctly applying Newton's laws in this context.
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Homework Statement



http://img406.imageshack.us/img406/6092/testdd5.th.jpg http://g.imageshack.us/thpix.php


find the fk in terms of M,m,a

Homework Equations





The Attempt at a Solution



So what I got in the end result after decomposing the forces on each object and then do a substitution is :

fk = m(a+g) - Ma,

where m is the mass of the hanging block and M is the mass of the object in the plane. Is this wrong?
 
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I think your expression for T is incorrect. It may have to do with defining + and - directions.

In your +/- convention: if "a" is positive, do the blocks accelerate to the left & up, or to the right & down?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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