Why are my heavier objects sliding on a smaller incline than lighter objects? Coefficient of Static Friction

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.

• 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. Sep 18, 2023 at 18:07
• Do you get the different weights by using different blocks, or by adding weight to the same block? Sep 18, 2023 at 18:14
• 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. Sep 18, 2023 at 22:54

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.

• 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? Sep 18, 2023 at 22:47
• 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 Sep 19, 2023 at 2:33
• 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. Sep 19, 2023 at 12:30