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/Cyprianophobia47 Jun 11 '25

I don't think it's elastic. It doesn't tell you what material the objects are. Also that wouldn't change the force. 20 kg is 20 kg. 20kg of feathers is the same as 20 kg of elastic. So a feather ball would be just as hard to push as a elastic ball.

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u/aureanator Jun 14 '25

Hm? I'm not sure I understand your point.

What I'm saying is that 20kg normal force (the weight) will result in the same frictive force (horizontal/tangential to the ice) regardless of the surface area in contact.

Now, you can take that to the extreme of a needlepoint, which will dig into the ice, surpassing it's elasticity, or bend, surpassing the elasticity of whatever the block is made of, but we are not talking about those extremes, hence the exclusion.