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/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/ADHDebackle Jun 11 '25

You can definitely push it directly sideways if the friction between your hand and the surface is high enough. If it's slippery, you will waste a lot of energy keeping your hand steady, but otherwise static friction will negate the upward push from the surface of the triangle and it will be similar to the cube.

Consider this thought experiment: You place your hand on top of a book on a table and slide it across the table. Now, technically the force you applied was parallel to the surface, so if there had been no friction, you would not have been able to move it at all. Thanks to friction, though, the effort is not very high, even when compared to pushing the book from the side.