Coeffiecient of friction question

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The discussion revolves around the correct application of the coefficient of friction in a scenario involving a block on a plane with two ridges. The user seeks clarification on whether the coefficient of friction should be calculated using the total frictional force divided by the total reaction force or by using the individual forces on each side. They initially believed the latter was correct but are curious if combining the forces simplifies the problem. The conclusion drawn is that both methods yield the same result, affirming the user's understanding of the concept. This clarification helps in solving the posed homework question effectively.
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[SOLVED] Coeffiecient of friction question

I'm probably being stupid here, but I just want to check I'm using the coefficient of friction right.

Homework Statement


A block on a plane, in equilibrium for the moment, the block has two ridges on the bottom, so reaction forces are split into R_{R}\ \mbox{and} \ R_{L} and the same for friction.

Is the coefficient of friction the whole of the frictional force on the block divided by the whole of the reaction force, of equal to the ratios of left and right forces?

i.e. \mu = \frac{F_{L}+F_{R}}{R_{L}+R_{R}}\ \mbox{or} \ \mu = \frac{F_{L}}{R_{L}} = \frac{F_{R}}{R_{R}}

I originally was certain that it was the latter, but if you could combine them like the former, it would make my impossible question quite simple.
 
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Both are the same. I hope you know enough elementary algebra to prove it.
 
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