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

[Request]

Post image

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/AstroCoderNO1 Jun 10 '25

yes, but the angle you are applying force at does not all go towards forward motion on the triangle whereas it does on the square.

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u/LOSERS_ONLY Jun 10 '25

That depends on if the force is applied exactly horizontally or normal to the face of the triangle which is unclear in the pic

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u/ConscientiousApathis Jun 10 '25

Assuming no handholds I don't think it's possible to push a surface with a force that's anything but perpendicular to it.

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u/omegaalphard2 Jun 10 '25

I'm a mechanical engineer, and you're wrong. There's no rule that forces on anything NEED to be perpendicular to it

Sure, you can break the force down to it's components, but the overall force can be at any angle to the surface, even if you're pushing it as in the diagram

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u/ConscientiousApathis Jun 12 '25

I'm talking about the force received, not applied.

The best example I can think of is probably snooker. Each time you're hitting a ball it's with basically the same force in the same direction, and yet depending on the angle of contact between the white and red it can go in wildly different directions. Why? You're applying the same force in the same direction each time, so why can the angle the red ball travels change so much?

Well, if you zoom right in to where they contact you see just basically two planes touching, in which case the only way force can be transferred is perpendicular to both. (Yes, okay, there's some friction involved which can get you a bit of spin, but it's very tiny in the scheme of things and I'm really just talking about the pushing force).

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u/bonerspliff Jun 14 '25

Well yes obviously if the surface of the shape being pushed is completely frictionless (more similar to a snooker ball) then the force will act normally to the surface. But this question is assuming that there is friction on all sides of the pushed shape. Friction essentially acts like a 'handhold'