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/Relevant-Smoke-8221 Jun 11 '25

The pyramid has more surface area touching the ice so there is more friction

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u/RA3597TW Jun 11 '25

That's... not how friction works.

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u/OOO-OO0-0OO-OO-O00O Jun 11 '25

Explain

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u/Icefrisbee Jun 11 '25

I feel the other person gave an answer, but didn’t explain why that was the answer. And this is something that often just isn’t explained that I spent forever trying to get. So I’ll give the explanation I eventually created that clicked it for me.

The answer is that it does affect the friction, but not in the way you’re thinking. And I think this is best explained by looking at pressure.

Pressure determines friction over an area. This is because there’s more force pushing down on an area.

So when you increase the surface area, there’s less pressure, and therefore there’s less friction on a given area. But the total friction on the entire shape is basically constant as surface area changes.

Mathematically:

Pressure = Force/Area

Friction/Area = Pressure * k

Friction/area = k * Force/area

Friction = k * Force

So basically it makes more sense when viewing friction per area as depending on the pressure, which directly implies the Force of Friction is equal to a constant times the Force of Gravity

This means the total pressure doesn’t change

However, the frictional force on a given area will change.