# Homework Help: Determining the uncertainty of the coefficient of friction

1. Jan 31, 2016

### Nick tringali

1. The problem statement, all variables and given/known data

So far i know that the uncertainty of the force of friction is +/- 0.1 and the uncertainty of the force normal is +/- 0.1 also.
2. Relevant equations
Force of friction=(myoo)(force normal)
Myoo= force friction / force normal

3. The attempt at a solution
My data is
Force of friction | myoo | fnormal
0.0 | 0.0 | 0.0
1.4 | 0.264 | 5.3
1.9 | 0.260 | 7.3
3.2 | 0.262 | 12.2
4.1 | 0.272 | 15.1
4.6 | 0.269 | 17.1
Thats my calculated data so first I added 0.1 to1.4 and got 1.5 then I added 0.1 to 5.3 and got 5.4 then divided 1.5/5.4 and got 0.27777 (which is my max myoo value) now to get the min value I subtracted 0.1 from 1.4 and 5.3 and divided again 1.3/5.2 and got .25 for the min myoo value then i subtracter 0.27777 from 0.25 and got my uncertanty to be 0.0277, the problem is i tryed the same prossess with another set of values from my data table and got a different uncertainty. For the last set of numbers with frictonal force of 4.6 i got the uncerntanty to be 0.00855 (i did the same process as before) All of my class mates are doing different ways.

2. Jan 31, 2016

### Simon Bridge

This does not make sense to me ...
You need to be clear about what is being attempted ... myoo is the coefficient of friction I take it?

I cannot tell what you have done -

Let f = ffriction is the friction force, N = fnormal is the normal force, and mu or $\mu$ is myoo is the coefficient of friction. (saves typing)
You would normally want to measure f and N to calculate mu.
You say you have calculated all three for the table ... your problem statement gives uncertainties for f and N, which suggests a measurement for f and N.

OK: assuming you have friction $f\pm\sigma_f$ and normal force $N\pm\sigma_N$ then $\mu = f/N$ - f and N are independant and divided so you propagate the relative errors (percentage errors).

The rule is as for $z=xy$, i.e. $$\left(\frac{\sigma_z}{z}\right)^2=\left(\frac{\sigma_x}{x}\right)^2+\left(\frac{\sigma_y}{y}\right)^2$$

... this you'd do for every line, giving you the uncertainty for each value of mu.

Better: plot a graph of f vs N - the slope will be mu, and you can calculate the uncertainty of the slope.
Also better - find the mean and standard deviation of the mu column of your table ... the value of mu is $\mu = \mu_{ave} \pm \sigma /\sqrt{n}$ where n is the number of entries in the columb.

Note: your table mu value for f=0 is wrong. But I don't know what you actually did: I'm just guessing.

Last edited: Jan 31, 2016
3. Jan 31, 2016

### Nick tringali

Thanks simon, but what do those symbols in the numerator represent?

That is uncertainty right?

Would each value of myoo have there own different uncertainty then, I was looking for the uncertainty for the myoo column as a whole, sorry if im not following you 100%. Should i just use that formula you gave?

I also have a graph like that and the slope too of the line of best fit.

Last edited by a moderator: Feb 1, 2016
4. Feb 1, 2016