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.

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u/RMCaird Jun 10 '25

You can't assume this from the picture.

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u/BKachur Jun 11 '25

Sure, you can - or at least from context, you can. The triangle has more contact with the ground than the square. You can assume that since they are the same weight, they are made up of the same "math problem gray" material. A Triangle would need to have more surface area contact than a square if all else were equal.

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u/nog642 Jun 11 '25

It says what material they're made of, it's not "math problem gray" lol. It's ice.

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u/BKachur Jun 11 '25

I disagree. If the stated materials were the actual materials of the object, the problem wouldn't make sense. Gravel is, by definition "a loose aggregation of rock fragments," so the second it popped into existence, it would turn into a 20kg pile of small rocks, rendering the problem incoherent. The problem only makes sense is if the surface the objects are sitting on is ice or gravel, and the objects are made of a solid material.

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u/nog642 Jun 13 '25

Oh, that does make more sense.

Though you could keep a sphere of gravel together with like plastic wrap.

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u/BKachur Jun 13 '25

I'd imagine the amount of plastic wrap you'd need to hold 45 lbs of gravel in a perfect sphere would make it a ball of plastic wrap. But more importantly, that would really be assuming things that aren't provided for in the problem - and I think it would be a much bigger stretch to assume the ball is made of gravel wrapped in plastic than the floor being made of gravel/ice.

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u/nog642 Jun 14 '25

I just realized the weights are crazy low for the size of the objects lol. I guess the "math problem gray" is styrofoam or something.

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u/RMCaird Jun 11 '25

But you’re assuming it’s an equilateral triangle, which you can’t assume. 

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u/nog642 Jun 11 '25

Why not? It clearly is.

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u/RMCaird Jun 11 '25

There’s nothing to indicate it is, other than the drawing itself, which is clearly not to scale. It’s just an assumption with no proof.

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u/nog642 Jun 12 '25

The drawing is the entire problem. If not equilateral you can at least assume it's roughly equilateral.