# Do I force the intercept to zero when determining the coefficient of friction?

I have made these measurements of kinetic friction force vs normal force:

I want to measure the coefficient of friction as the slope of the line. Unfortunately the line does not pass through $$(0,0)$$. If I force the intercept to zero I get a quite different coefficient of friction ($$0.6$$). I wonder if I should:

1. Just use the slope and ignore that the line doesn't go through $$(0,0)$$
2. Force the line through $$(0,0)$$
3. Remove the two outer points since they are the most problematic.
4. Remove the two outer points and force the line through $$(0,0)$$

I have no opportunity to redo the experiment so I have to work with what I got. What would be the correct approach?

EDIT: This is a school project and I'm the teacher.

• One simple, somewhat canonical approach is to put error bars on your points, then fit with a line with intercept. This will give you error bars on the intercept yourself, and you only have to worry if zero lies way outside the error bars. – knzhou Feb 28 '19 at 12:03
• However it looks like you don’t have error bars and that this is a high school or intro college lab. Since it’s not a “real” experiment you should just do whatever your teacher approves of. If you don’t know, any of your 4 options is good enough. – knzhou Feb 28 '19 at 12:05
• Yes it is a school project, but I am the teacher, so I have to know what to tell the students. I think error bars might be too advanced right now. – bgst Feb 28 '19 at 12:10
• And also a discussion of curvefits -- is linear a good model in this case, do other curves fit better, does something like "quadratic" friction exist and so on. Which could include something about the dangers of blindly fitting things as demonstrated by Anscombe's quartet. – tpg2114 Feb 28 '19 at 12:30
• By eye, it looks like you do get a pretty good fit to a line through the origin, except for the last point where there is a significant jump in load. Maybe you measured that point badly, or maybe the friction coefficient isn't independent of load for big enough loads. Don't forget that Coulomb's so-called "law" of friction has little if any physical basis, and for many materials it isn't even approximately true. – alephzero Feb 28 '19 at 13:21

I've taught high school physics in the past, and I would tell the students that the slope of the line represents the kinetic friction coefficient. I would also tell them that since $$F_k=μ_kmgcos(θ)$$, the surface that the experiment is performed on must be PERFECTLY level, other measurements must be perfectly accurate, and the physics must conform EXACTLY to the chosen mathematical model if we are to see the intercept go exactly through zero. Obviously, all of these conditions were not perfectly met in this experiment.

Regarding the forcing of the plot through (0,0), the answer would be "no", as one or more of the possible sources of error listed above have no doubt affected the measurements. In addition, as you noted, forcing the intercept to be (0,0) will greatly affect the calculated slope of the line, which is the friction coefficient that you are trying to estimate.

• Yeah this is what I tell my college physics classes, they sometimes get strange answers even if I've been through their set-up and diagnosed no problems...I just say the data is what they get at that point and they aren't being penalized for bad data necessarily as they would be for bad analysis. – Triatticus Feb 28 '19 at 20:58

You basically never force the origin. The closest you come is including the origin in your data if you measure it.

The reason for that is that experimental effects can (and do!) render invalid various assumption you make that lead to expecting the origin to be included. David White's provides one example of such an effect for a dynamic friction measurement, but there are others effect that might also contribute. What is one surface or the other has a film of polar material (like skin oils...)?

An example of "measuring the origin" comes from a Ohm's law that I supervised the other day. The instructions to the students includes things like

1. Turn on a multi-meter and set it to it's most sensitive voltage measuring setting. If it has a calibration screw turn this to get zero while disconnected. If not record the value while disconnected for later subtraction.

2. Wire up a simple circuit consisting of DC power supply and resister.

3. Measure the voltage drop across the resister while the power supply is turned off.

4. Turn on the power supply and measure the voltage drop as various currents (also measured) but those details don't matter here.

Step (3) is an explicit measurement of the origin, so you include that point in the data. Even that doesn't force the origin, but it will certainly pull the intercept in.