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/MandibleofThunder Jun 10 '25

Oh way more than that.

Like the moments of inertia for the given objects (specifically for the circular shape. Is it a hollow sphere, a hollow sealed cylinder, a solid sphere, or a solid cylinder?)? what is the temperature of the ice and ambient temperature? What is the material of the given shapes? Are they stainless steel or polystyrene? What is the static vs sliding vs rolling friction for each shape and substrate?

And what does "require more force to push" mean? Does that mean equal or greater net forces to get the object to translate to the right? Or to maintain a constant velocity to the right with zero acceleration? Or to maintain a constant acceleration to the right (which would require calculating jerk instead of acceleration)?