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I gave my students a lab on the coefficient of friction in 2D. I use a wooden plank and sandpaper as my IV. I have done this experiment in a few different ways, but the normal consensus was still the same. It requires a larger incline for heavier objects to slide (as long as the material was the same). Well, this year, I used small frisbees as my "material" to which I add weight to. For some reason, the heavier weights are now sliding at smaller inclines than the lighter objects.

I tried to take into account that the sandpaper added grooves to the frisbees, but then...wouldn't the mass still make the normal force greater?

I feel as though the solution is more simple than I am thinking, but right now, I cannot find the answer.

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  • $\begingroup$ frisbee is a general term, and I expect from the icons i see in wikipedia that the bottom is curved, so they might only touch on a point , friction playing little role. but gravitational attraction would be higher for higher mass. so I voted to close for lack of clarity. $\endgroup$
    – anna v
    Commented Sep 18, 2023 at 18:07
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    $\begingroup$ Do you get the different weights by using different blocks, or by adding weight to the same block? $\endgroup$
    – Bob D
    Commented Sep 18, 2023 at 18:14
  • $\begingroup$ I added weights to the frisbee disk. The students place the weights in the center (there is a small groove that the weight can sit on). Plastic disk against plywood and sandpaper with added weight on top. $\endgroup$
    – Physics Disciple
    Commented Sep 18, 2023 at 22:54

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I have written similar things in other answers. But getting this message out depends on repeating it to some extent.

John Yeager, a well-respected rock mechanics expert, has a famous quote that goes something like this: "There are two things you need to know about [the coefficient of] friction. It is always 0.6 and it will always make a monkey out of you."

There are (at least) three different levels of "laws" that we learn in physics and engineering. The first level of laws are things like $\Sigma \textbf{F} = m \textbf{a}$ and its angular counterpart. These laws are extremely accurate (say, maybe one part in a million) for everyday objects that move much slower than the speed of light.

The next level of laws are called "constitutive" that describe material behavior. Laws of this sort would include $\bf \sigma = E \epsilon$. They are also quite accurate, on the order of maybe 1% or better under controlled experimental conditions.

The last and least accurate set of physical laws, including friction effect $F = \mu N $, coefficient of restitution, etc. are rough approximations. Calling them "laws" is probably a misnomer. Although they are convenient for teaching concepts, they can give you a +/- 20% estimate at best, but should not be treated as "laws" in the same sense of constitutive laws or Newton-Euler laws. Slightly different conditions will lead to different measurements and answers, as any tribologist (friction scientist) will tell you. It is an unfortunate feature of many physics and engineering courses that they fail to point out the fundamental differences in the accuracy of these laws. So students are left thinking that they are all as valid as the other.

So, the answer to your question is, basically, "it's complicated." I suspect that there is some effect from contact PRESSURE which takes the surface area into account. But that is just a guess. One way, maybe, to get an improvement in your results would be to use more slippery surfaces. The weirdness gets a bit better when things are smooth and/or oiled.

Credit for these observations goes to my teacher and advisor Andy Ruina from Cornell University. If you want to read his version of the above and extended commentary, I recommend his book "Introduction to Statics and Dynamics," co-authored with Rudra Pratap.

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I think the reason is to do with indentation. If you place a heavy object of a soft surface for a while the object sinks into the surface and leaves an indentation or impression of the object when it is removed. This indentation has a sharp edge or lip and moving the object requires the object to rise over this lip or crush material in front of it in order to make progress. On a hard surface this indentation effect is microscopic but still there. This is one reason sledges or skis have a curved leading edge to prevent 'digging in'. Your frisbees provide a curved leading edge and this helps prevent the digging in effect. Normally we say static friction is independent of the surface area of the contact area of the sliding object. This is an approximation and when the contact area is very small the contact area can make a difference due to the indentation effect.

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I have done this experiment in a few different ways, but the normal consensus was still the same. It requires a larger incline for heavier objects to slide (as long as the material was the same).

If the contacting surfaces of the block and incline truly have the same coefficient of static friction, $\mu_{s}$,, then theoretically the mass (weight) of the block should have no effect on the angle $\theta$ upon which sliding begins, since that angle theoretically depends only on the coefficient of static friction. That relationship between the angle and coefficient of static friction where sliding begins is

$$\tan\theta=\mu_{s}$$

The equation arises from the fact that the force acting down and parallel to the incline due to its weight is $mg\sin\theta$ while the maximum possible static friction force acting upward is $\mu_{s}mg\cos\theta$. Impending motion occurs when the two forces are equal.

Hope this helps.

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  • $\begingroup$ This is what I gathered as well, when I completed the work. The "mg" from both components cancel. If this is the case, I suppose another question is to why we see a change at all. I had them complete 5 trials with three different weights. I saw data that supported heavier weights = steeper incline and now vice versa....I suppose we could treat it similar to free-fall, but the problem I have is the difference in angles can be between 7-10 degrees in light objects vs heavy objects. Perhaps its how some of the grooves touch the ramp? $\endgroup$
    – Physics Disciple
    Commented Sep 18, 2023 at 22:47
  • $\begingroup$ I’m not sure what you mean by “three different weights”. If they’re 3 different objects with different weights then the coefficients of static friction might not have been the same for the different objects. To eliminate that possibility I would use the same object but put different weights on it. That’s what you did with the frisbees but it appears there are questions about the uniformity of their contact surfaces $\endgroup$
    – Bob D
    Commented Sep 19, 2023 at 2:33
  • $\begingroup$ My apologies. The frisbee had three different weights placed on top of it to increase the load. They tested with one of the weights on top, then another, etc. Example: A Frisbee + 1.5 N load place on top; tested for five trials. $\endgroup$
    – Physics Disciple
    Commented Sep 19, 2023 at 12:30

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