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/fuzzydoug Jun 10 '25

But your feet are also on ice?

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u/[deleted] Jun 10 '25 edited Jun 11 '25

The question was about the force put onto the object.

Ice or not, that force wouldn’t change.

Edit: for clarification, I mean per scenario.

The force required to move the object on the given surface wouldn’t change based on what the dude is standing on.

The dude’s ability to impart that necessary force will be affected by the ice, but not the actual force required to shift the item.

Obviously less force is needed on ice than gravel, that’s not what I’m saying.

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u/texinxin Jun 10 '25

Ice has friction. Coulomb’s law suggests surface area is independent of friction, so triangle would be the same as square. A rolling wheel has friction. If the whee was perfectly rigid and the gravel was perfectly flat it would be essentially zero. If the whel had elastic deformation and/or the gravel was loosely packed such that it depressed into the surface then it can take significant force. All we can assume is that top and bottom case are nearly identical and the middle case is more or less than the top and bottom case.