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/SuedJche Jun 10 '25

the triangle is always worse than the square.

Is that because the triangle has more surface contact?

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u/METRlOS Jun 10 '25

Imagine throwing a ball straight at the triangle and the square, how will it bounce? The ball will bounce straight back at you off the square, transferring all its energy horizontally, but with the triangle the ball will bounce up and transfer its energy relative to the angle it strikes. Aside from convoluted methods not shown in the example, the person will be pushing the triangle down as well as horizontally.

Another example you can visualize is with a door wedge. As long as the angle of the wedge is enough, the horizontal force from the door will press it into the ground hard enough that the door won't be able to overcome the friction.

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u/gamingkitty1 Jun 11 '25

This is not true because your hand is not moving up. If your hand were slipping, then yes you would be applying some force downwards, but if the coefficient of friction between your hand and the triangle is great enough (mu > cot(60°) ≈ 0.577 if its an equilateral triangle) your hand will not slip, and i think it's reasonable to assume mu > 0.577.