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Biker
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Homework Statement
I have an incline with a degree of Alpha and it is with friction that is equal to (Us = tan theta)
It is accelerating to the right. Prove that this equation if it is true then the block will slide.
a > g tan(Theta - Alpha)
The Attempt at a Solution
That was my thought of forces.So I figured out that if I want them to stick together then it should have the same acceleration and orientation.
So the Net of forces should be ma and has the same orientation as (a)
I have encountered a problem before with 2 stacked objects and found that the static force keeps the blocks together by giving it the same acceleration ( Correct me if I am wrong, I kinda get confused on how that happens) and also I can't find any force that could be acting that way so it produces the same acceleration and orientation. Anyway as a result, I came up with these equations.
Friction - mg sin alpha = ma cos alpha (1)
mg cos alpha - N = ma sin alpha (2)
Friction = Us N
Then by putting 2 in 1
Us (mg cos alpha - ma sin alpha) - mg sin alpha = ma cos alpha
Us as mentioned is equal to tan theta
Tan theta mg cos alpha - tan theta ma sin alpha - mg sin alpha = ma cos alpha
Divide all of it by cos alpha and m
Tan theta g - tan theta a tan alpha - g tan alpha = a
Do some math and you will come up with this
g(tan theta - g tan alpha) = a ( 1 + tan theta tan alpha)
a = g (tan theta - g tan alpha) / ( 1 + tan theta tan alpha)
a = g tan( theta - alpha)
If I want it to slide then a bit more acceleration will make it slide then a > g tan(tehta - alpha)
I highly doubt that the solution is right but I hope so. (Ehhhh worth trying right??) My conflict is with the static friction how it makes things move because that what I understood from this problem.
http://www.uwgb.edu/fenclh/problems/dynamics/multi/1/
He put a value of f and saw if that value of f equals to the static friction or no. I hope someone clear this misconception for me.
Thanks. [/B]
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