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my poor attempt @ FBD...enter image description here

I did the FBD, and I found too many variables which are not eliminating...Moreover, I believe this question is based on kinetic and static friction. But, $\mu$ here is ambiguously defined...How Do I get the integral value?

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What is $N$? At first, normal force came to mind. But if N is the normal force, and $\mu$ is the coefficient of friction and thus dimension-less, how can $N=10\mu$? –  artistoex May 16 '13 at 10:46
    
It is written If WE Define, so maybe, N is just a variable...but my guess is as good as urs.. –  Saurabh Raje May 16 '13 at 10:49
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For pushing it up, we have to overcome friction(act downwards) as well as the $mg\sin\theta$. So, $$3N=f+mg\sin\theta$$

Now the block is just slipping , so friction is acting upwards, and so does the force applied externally.So, $$N+f=mg\sin\theta$$

Eliminate $N$ and use $f=\mu mg\cos\theta$.

Solve for $\mu$ you get your answer.

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