Three boxes on different inclines

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AI Thread Summary
The discussion focuses on a physics problem involving three boxes on inclines and their interactions through pulleys. Box A weighs 8.0 kg on a 110-degree incline, box B weighs 2.0 kg on a flat surface, and box C weighs 9.0 kg on a 130-degree incline. Initially, an incorrect acceleration of 1.57 m/s was calculated, but after correcting the direction of the gravitational components, the acceleration was revised to 0.57 m/s². The participants are also tasked with calculating the coefficient of static friction and the tension in the strings, but they are hesitant to proceed without confirming the initial calculations. Accurate component analysis is crucial for solving the problem correctly.
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Homework Statement


There are three boxes, box B weighs 2.0kg, and is sitting on a flat surface. To the left is box A, tied to box B. Box A weighs 8.0kg and is sitting on an incline 110 degrees from the horizontal (or 70 depending on the location of the measurement). To the right of box B is box C, sitting on an angle 130* from the horizontal, tied to box B. It weighs 9.0kg. All ropes are supported by pulleys.
a)assuming no friction, calculate acceleration of the system
b) calculate coefficient of static friction to remain motionless
c) coefficient of kinetic friction is 0.050, calculate acceleration and tension in both strings


Homework Equations


fnet = ma


The Attempt at a Solution


I managed to get an acceleration of 1.57m/s to the right, but I feel like it's wrong, I can't seem to get the components of gravity to work out right, I think I'm doing something wrong there.
I haven't got to B or C because I don't want to go through the entire thing with incorrect numbers.
 
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Update : turns out I had cosine and sine reversed so my components were in the wrong direction, I got an acceleration of 0.57 m/s/s which is much more reasonable.
 
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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