# Homework Help: Proof that COF depends only on asperities

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1. Jan 25, 2016

### ashym

1. The problem statement, all variables and given/known data
I am trying to craft a hypothesis regarding factors that affect the coefficient of friction. I know that it is determined by the triboforces and asperity interactions at the interface between the materials (among other factors, but right now I'm just gonna focus on this), but how do I prove it?

2. Relevant equations
I know F=µFn, and the whole proof that µ=tan theta. One step there goes: µ=ffk/fn = mgsinθ/mgcosθ = sinθ/cosθ=tanθ...does the cancelling of mg that occurs at least prove that mass does not influence COF? Because the only way I can think of proving that COF is independent of everything but the materials in question is via deduction - i.e. by proving that other system variables also have no effect, although I'm not sure if the basic proof above even does that and whether such an approach is possible with other variables. How do I go about this? Do I explain it all conceptually, or is it possible to mathematically support?

3. The attempt at a solution
BTW, the experiment I conducted just involved using ramps made of different materials and elevating it until the object began to slide, at which point I measured the angle of inclination. After taking tan of those values I'll find that the COF varies obviously, but all that proves is that the angle affects the force of friction and I wonder whether the design is even appropriate for what I'm seeking...Everyone conducted their experiments like that and I don't know how the info derived even pertains to the question at hand...do you see anything wrong with this or am I not understanding how to apply it?

2. Jan 25, 2016

### Dr. Courtney

Think about what experiment is needed to disprove (or support) a given hypothesis.

Proving things with equations is math.

Science is disproving hypotheses with experiments (falsifiability).