Coeffiecient of friction question

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SUMMARY

The discussion centers on the calculation of the coefficient of friction for a block on a plane with two ridges affecting the distribution of reaction forces. The user seeks clarification on whether the coefficient of friction, μ, should be calculated as the total frictional force divided by the total reaction force or as the ratio of individual forces. The consensus confirms that both methods yield the same result, allowing for flexibility in calculation depending on the scenario.

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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 [tex]R_{R}\ \mbox{and} \ R_{L}[/tex] 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. [tex]\mu = \frac{F_{L}+F_{R}}{R_{L}+R_{R}}\ \mbox{or} \ \mu = \frac{F_{L}}{R_{L}} = \frac{F_{R}}{R_{R}}[/tex]

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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