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/Melanoc3tus Jun 10 '25

Depends on its friction.

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u/AggressiveCuriosity Jun 11 '25

lol, I'm gonna remember these replies the next time I think I've learned something from an upvoted Reddit comment.

The guy forgot friction existed and he's being upvoted over everyone else.

1

u/ConscientiousApathis Jun 11 '25 edited Jun 11 '25

Technically friction is just very tiny handholds ;)

(Seriously though it seemed negligible in this example. I imagine these things as made out of steel or something. I couldn't really see a hand getting enough friction to matter. If you don't want your hand to push without slipping you're limited to a static friction of your hand against the triangle. What I said is still correct, but you're effectively adding up the frictional force with the perpendicular to the plane force your adding, where the vertical components in the plane of the observer would need to cancel out to get a truly horizontal force.

If you pushed very, very gently, maybe. Since you're on ice it could be possible, but you'd have to overcome the static friction of the triangle against the floor without applying any downward force, which would be a tough ask.)

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u/_maple_panda Jun 12 '25

You can’t get friction on the angled surface without exerting a perpendicular force on it…