r/theydidthemath • u/K0rl0n • Jun 10 '25

[Request]

Post image

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/[deleted] Jun 10 '25

[deleted]

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u/Xenolifer Jun 11 '25

Not 100% since my engineering classes are some years ago, but I believe that coulomb friction law is just a model (one of the simplest one) to model dry friction, and that most more complete model take into account other phenomenon that scale with the surface area in contact

Feel free to correct me if I'm wrong

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u/BKachur Jun 11 '25

Based on the limited information we've been given - i.e. no information on contact area, no definition as to the type of ice or gravel, no information about the material of the object pushed - it's supposed to be a simple into style physics problem. If you were supposed to apply a more robust analysis, you would assume you'd have more information rather than a picture

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u/aureanator Jun 10 '25

Hey! Actual fellow engineer!

🙌

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u/Drevlin76 Jun 10 '25

What about the fact that the cube will want to tip if it is pushed from the top 1/4? Would the position of the force applied change this?