Coeffiecient of friction question

[paneity]

[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.

 

[Shooting Star]

Both are the same. I hope you know enough elementary algebra to prove it.

 

[ogb p]

The coefficient of friction is a measure of the resistance to motion between two surfaces in contact. It is typically denoted by the symbol μ and is defined as the ratio of the frictional force to the normal force between the two surfaces.

In the case of the block on the plane, the coefficient of friction would be the ratio of the combined frictional forces on the block (from both ridges) to the combined reaction forces (from both ridges). Therefore, the correct expression for the coefficient of friction in this scenario would be: μ = (F_L + F_R) / (R_L + R_R).

It is important to note that the individual frictional forces (F_L and F_R) and reaction forces (R_L and R_R) cannot be combined in this case, as they are acting in different directions and cannot be added together.

In summary, the coefficient of friction is the ratio of the total frictional force to the total normal force between two surfaces, and it cannot be simplified by combining individual forces. I hope this clarifies any confusion.