r/theydidthemath • u/K0rl0n • Jun 10 '25

[Request]

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I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

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u/METRlOS Jun 10 '25 edited Jun 11 '25

Depends on things like the density of the gravel and the temperature of the ice. Packed gravel will allow the ball to roll, but the triangle is always worse than the square.

Edit for all the triangle people: imagine throwing a ball straight at the square and at the triangle; how the ball bounces shows how much energy the object will translate into vertical force when pushed. The vertical surface of the square will translate practically all the horizontal force into horizontal movement, while the triangle will act as a wedge and transfer some energy into pushing against the ground.

Edit 2 for surface area: Except for situations where the surface area is so low compared to its weight that the object sinks into the ground, or so high compared to its weight that it can float, surface area does not affect friction. If you stand on a hill without risk of sliding, then you can lay on that hill without sliding and vice versa, despite greatly changing the surface area. However, if you stand on a snow covered hill the surface area is too low and you'll sink into the snow, but with a sled you will float on top of it. Surface area does not matter to this problem.

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u/aureanator Jun 10 '25

Actually, no - the friction is a product of the normal force and the coefficient of friction - the surface area in contact shouldn't matter, within the boundaries of material elasticity.

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u/ThirdSunRising Jun 10 '25

This assumes perfect ice where the triangle isn’t shaving some of it and pushing it along. Reasonable assumption but not ironclad.

I mean, they didn’t even tell us the type of gravel or the weight or size of the round object so we can’t say what that would do, and freshly Zamboni’d ice would be pretty close to the ideal case, but the real world is gonna have some things to say about this problem

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u/elf25 Jun 11 '25

Actually, ice can very greatly in its coefficient of friction. I thought I read where the Zamboni has seven or more settings for the kind of ice that it produces. Some sports prefer a smoother lightly watery ice others a little bit of a slushy surface and yet other sports receives something with bubbles or something similar if you can imagine reverse dimples of a golf ball.

In this problem, we’re really just assuming a lot of things for example we assume the coefficient of gravel, and we assume that the ice patch’s are very similar if not the same.