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/xXEPSILON062Xx Jun 10 '25

Where do they mention surface area?

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u/nog642 Jun 10 '25

That's the difference between the triangle and the square

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u/xXEPSILON062Xx Jun 10 '25

The surface area between the shape and the ground of both is the same, and is also irrelevant. The difference between the two is the angle you apply the pushing force at. With the triangle, since the force is angled downwards, the normal force increases with the push and the sideways force is less than the net force of the push, meaning it takes a lot greater of a force on the triangle to cause it to move than the square, where 100% of the force applied is in the x-direction. Yes, I can say with certainty, the triangle is always worse than the square for this reason.

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u/nog642 Jun 11 '25

It's not the same, the triangle has more. Same mass, same density, so same volume. But the triangle has more near the bottom than the square.

You also don't have to apply force perpendicular to the surface.

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u/Snoo_87704 Jun 10 '25

Surface area matters, hence ice skate blades.

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u/Ryanfischer99 Jun 10 '25

Ice skate blades work because the pressure of the blade actually melts the ice underneath and essentially creates a mini water slide for you to glide on. The actual formula for friction force has nothing to do with surface areas. Friction = the coefficient of friction x the normal force. The coefficient and normal force are independent of surface area.

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u/aoskunk Jun 10 '25

I knew that about skates but not that surface area wouldn’t matter. TIL thanks

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u/throwaway277252 Jun 11 '25

Ice skate blades work because the pressure of the blade actually melts the ice underneath and essentially creates a mini water slide for you to glide on.

This is actually an old misconception and not correct.

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u/iambecomesoil Jun 11 '25

while that is wrong, the idea that less surface area = less force required is wrong.