Does the Coefficient of Static Friction Remain Constant Regardless of Mass?

[jamesyboy1990]

Homework Statement

hi, i am almost done my lab on the coefficient of friction on an inclined plane. I was attempting to prove that the coefficient of static friction would be the same no matter the weight of the mass that was static on the incline. However, i plotted a coefficient versus mass graph, and the line wasn't horizontal (the coefficient changed). My quick question was whether i still need to find the equation for finding the coefficient based on my results, or if i could just conclude that in my case, the coefficient didn't stay constant, and then move to my conclusion

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

How did you calculate the coefficient of friction for your results?

 

[jamesyboy1990]

i had an incline, measured the weight of the mass, and changed the angle such that if i increased the angle by a little bit, the mass would slide. I did this for several different masses and recorded the angle. I then used a freebody diagram and the equation for static friciton (u = Fmax/R)

 

[Hootenanny]

And how did you calculate the normal reaction force?

 

[jamesyboy1990]

R = mg cosx
F = mg sinx

so in essence, the coefficient was tanx

 

[jamesyboy1990]

technically, all i need to know is whether i would have to process the graph to find a relation between weight and the coefficient (although i know that technicallly the coefficient is independent of mass) if all i wanted to prove in the lab was that the coefficient was independent of mass (and in my case, my experimental data didn't prove it)

 

[Hootenanny]

Your not actually plotting $\mu$ vs. $m$ what your actually plotting is $\tan\theta$ vs. m since;

$$\mu = \frac{F}{R} = \frac{mg\sin\theta}{mg\cos\theta} = \tan\theta$$

 

[jamesyboy1990]

but since tanx = u, so why should it matter whether you plot u vs. m or tanx vs m?

 

[Hootenanny]

but since tanx = u, so why should it matter whether you plot u vs. m or tanx vs m?

Indeed, $\tan\theta = \mu$, but are you keeping the angle constant?

 

[jamesyboy1990]

no, because the greater mass wouldn't stay static at the certain angle, so it would decrease.

if i am trying to prove that the coefficient should stay the same, and it doesn't in my experiment, do i have to do more, or can i just stop once the graph shows that the coefficient changed?

 

[david1701]

i thought that: Frict max=mu R
so for your experiments to prove mu is irrespective of mass the particle has to be on the point of slipping
that may be too simple i am only doing as physics and you guys might be talking about something higher tho from mechanics mu is >= to R/Frict max
(sorry about symbols ect)

 

[jamesyboy1990]

honestly, the only question i wanted answered was in respect to the set up to the lab. Once you process enough data to prove/disprove the purpose of the lab, do you have to do any more processing, or can you just go straight to conclusion/evaluation?