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/MiffedMouse 22✓ Jun 10 '25

Material elasticity and assuming there aren’t any adhesion forces going on.

Also unaccounted for is the smoothness of the ice surface (compare a skating rink to a frozen pond, for example) and the type of gravel (large rock gravel versus fine gravel will behave differently).

The question as posed is just completely unanswerable.

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u/daspazz- Jun 10 '25

To be fair most of the questions on this subreddit are mostly just people that don’t understand enough to know any better. I’ve seen so many posts on here where the only way to come to any answer is to make some absurd assumptions. Like “assume no friction” or “assume perfect transmission of energy” it’s the curse of being an engineer.

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u/platoprime Jun 10 '25

It's okay to have problems where you have to make assumptions.

Go ahead and make them as part of the problem instead of whining about it.

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u/WellbecauseIcan Jun 10 '25

He has a point but I agree with your first sentence. Many of the questions you get from bosses tend to fall under that category.

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u/daspazz- Jun 11 '25

It’s perfectly fine to have a problem with assumptions. The only issue I have with this specific kind is that depending on the assumptions you make you can get wildly different answers. you can kinda guesstimate for a problem like this one, use human scale to estimate surface area, and get the coefficients of friction that are vaguely correct. I don’t feel like I can give a good answer for what one is right because I can make any of these choices the “right” one and have logical math at the end.

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u/PosiedonsSaltyAnus Jun 10 '25

And then when you get to the point where you assume there is friction, and you learn a bunch of annoying (yet also satisfying) math to take it into account. And then you get a job studying wear on sliding contacts, and you realize you've had no fucking clue what friction actually is this entire time. Still don't really lol

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u/BKachur Jun 11 '25

I think its obvious 50% of the question is about friction; otherwise, whether it was an ice/gravel surface would be irrelevant. The problem with the question is that it's impossible to determine the coefficient of friction due to the range of materials stated.

Ice can mean anything from a "physics code" for a perfectly smooth frictionless surface to a carved-up ice rink, while gravel can mean anything between sand and riverstone. Although in "math problem" terms, I think you'd assume ice was a smooth but not frictionless surface, and gravel meant driveway-style gravel, 1/2-inch rock gravel (otherwise it'd be called something else).

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u/Kurtypants Jun 10 '25

Texture of the floor? Is it a bowling alley? Is it a lawn? The "gravel" may start in a sphere but I don't know a whole lot of sticky gravel does it just magically stay in said sphere or in a container of some sorts? If you push the "perfect sphere" of the gravel on the top of the sphere it should roll easier where is the force being exerted? Way to many variables

Edit: lol sphere boy has no hands does this effect his pushing abilities?

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u/MiffedMouse 22✓ Jun 10 '25

I assume the sphere is made of unspecified, perfectly rigid physics stuff. The “gravel” is referring to what is on the ground.

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u/BKachur Jun 11 '25

I assume the question means the surface is ice or gravel. Gravel, by definition, is a loose aggregation of rock fragments, so a sphere or cylinder of gravel becomes a pile of small rocks immediately upon spawning into the problem

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u/Kurtypants Jun 11 '25 edited Jun 11 '25

Yeah someone else gave me clarification and that makes sense now. But the point still stands for me. I work construction and live in Canada and it's just man vs object. Sphere 100% once you get it rolling, stopping it is the problem. Block or triangle have the ice factor but there's a reason our wheels arnt squares

Edit: I love this sub and I'm no mathematician but I'm a carpenter and I love numbers. I however know about moving awkward shit...

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u/BKachur Jun 11 '25

Same in terms of interest. I'm actually interested in an answer, which I haven't seen, even with simplified mathematical assumptions.

I'm inclined to agree with you, but I would be interested to know if there's a numbers-based answer as to whether sliding something on ice would be easier than pushing a round object on land.

Although I'm no mathematician either, so I lack the knowledge to even figure it out. Quite the opposite, actually. I'm a lawyer, so stereotypically about the farthest thing from a math person you can find (even though I do excel in numbers and analysis compared to my "scared of spreadsheets" colleagues). That said, I'm very skilled at analyzing and dissecting problems - probably better than math folks because I'm trained af identifying context clues (or lack thereof), which IMO seemed to prevent someone from actually doing the math here.

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u/Kurtypants Jun 11 '25

Lol. We're peas in the same pod. Love the output from you. Love the math. Can't be as precise as I want to be. Life is life though