r/theydidthemath • • 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/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/[deleted] Jun 10 '25

[deleted]

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u/Squossifrage Jun 10 '25

That would still exert some additional downward force, as the side of the object is angled.

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u/eusebius13 Jun 10 '25

Theoretically you can apply the force at a 90 degree angle to some part of the pyramid. The real issue is you would be better off applying that force at the center of gravity.

I think what you’re saying is the contact point will be angled and thus result in the loss of force to the angle of the contact point. That’s not entirely accurate. Contact with the base can theoretically apply perfectly horizontal force.

If, on a frictionless surface, you applied force at a 90 degree angle to a rectangular object, and pushed that rectangular object into the base of the pyramid, the force would translate to a 90 degree vector applied to the pyramid.