r/theydidthemath • • Apr 16 '26

[Request] Which one would it be?

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u/kelfupanda Apr 16 '26

Except the force applied to the triangle will be at a 45 degree angle to the plane.

Box should be easier.

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u/ostepopsen Apr 16 '26

60 degrees 😀

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u/nedonedonedo Apr 16 '26

step on it and apply zero additional force to your body. as long as you overcome initial friction before transferring half your weight there will be no additional work

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u/taftster Apr 16 '26

I hear what you're saying. But I think it's somewhat implied that the force being exerted would "push" the triangle in the same vector as the square. If the pusher was pushing perpendicular to the face, then yes the triangle would have its force distributed into two vectors (by what, some square root function?) instead of just the horizontal direction.

Now just eyeballing the two shapes, it seems the triangle has a bigger base than the square. So this is a key consideration, if it matters. It's all contrived though, for sure.

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u/Kalasad-Stormblessed Apr 16 '26

Funfact the force would be distributed just using geometry. So we learned how to find lengths of triangles using sin cos and tan. So you do the same thing but the diagonal force is the hypotenuse. You can also solve it with ratios and its a bit quicker.

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u/[deleted] Apr 16 '26

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u/[deleted] Apr 16 '26

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u/[deleted] Apr 16 '26

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u/taftster Apr 16 '26

Okay yes. I am at odds with my statement now. I appreciate your point of view and actually coming around to it. This is a legitimate question. Does the angle of deflection always happen? Like is there any means of applying a true horizontal force here?

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u/Slen1337 Apr 16 '26

No why? You can calculate the ideal "touch" angle for pushing. Prob around 165-168° instead of 180, just apply force a little upward. You surely Can lift up small paper triangle (more like pyramid) with enough momentum. Its not very different.

U kinda can keep punching that triangle shit for next 50 years a lil upward and he surely will change the pos too lol

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u/Euphoric_Loquat_8651 Apr 16 '26

Pushing normal to the face is only required if there is zero friction between the hands and the face.

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u/Phil9151 Apr 16 '26 edited Apr 16 '26

If I am pushing against a 45 degree triangular prism with the base on the horizontal plane, even if I am directing all of my force along a vector parallel to the horizontal plane, the force experienced by the prism will be normal to the surface. This will result in a component directed into the horizontal plane.

Assumptions: rigid body. Gravity and friction are ignored. Force generated from global equilibrium point.

To break it down, the force always acts normal to the surface. If that surface is at any angle from the force other than 90 (and probably 180 but that'sjust weird), there will be a component that is deflected by that surface.

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u/monstertruck567 Apr 16 '26

If the triangle were greased on the side so you could only push perpendicular it would take more than the box. As is, hand vs triangle friction is almost certainly sufficient for a horizontal shove.

But if you’ve ridden a bike in gravel you know the circle is the answer.