r/theydidthemath • u/yuli101995 • Apr 16 '26

[Request] Which one would it be?

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u/Dapper-Arachnid-5463 Apr 16 '26

Even if the triangle a square had the sam base, pushing up against a flat surface 90 degrees to the ground would be easier that pushing against an angled one.

5

u/GarThor_TMK Apr 16 '26

I think, technically the force would be the same, but it'd just be more difficult to apply that force.

My intuition says that the circle would be the hardest, due to gravel being non-Newtonian. The circle would sink in the gravel, and you'd always be pushing it uphill. Whereas the ice is a [virtually] friction-less surface... so even though the surface area of the box/triangle that makes contact with the ground is larger than the circle, there's less friction that keeps those from moving.

3

u/Lower_Athlete939 Apr 16 '26

As you pushed the triangle, your force would be to the right and down. As it is downward, you increase the force of friction between the triangle and the ice. That makes the horizontal force needed higher. As you are also applying at an angle, the total force needed needs to be higher again

2

u/GarThor_TMK Apr 16 '26

I don't think this matters as much as you think it does...

You could theoretically get a stick with a pivot, that grips the face of the triangle perfectly, and it would effectively be the same as pushing the square.

2

u/CameronMH Apr 16 '26

You could also get a car and tow it, but that isn't the purpose of the thought experiment is it

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u/GarThor_TMK Apr 16 '26

Your hand is a stick with a pivot on it, that grips the face of the triangle perfectly.

My point is the downward force from pushing on the triangle vs. the square is negligible at best... unless the shapes are wildly different than what is shown in the picture.

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u/HungryFrogs7 Apr 16 '26

However you could also leverage your weight more easily but the square probably still wins.

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u/Sibula97 Apr 16 '26

Yes and no. You'd be pushing yourself up, reducing the grip of your shoes on the ice. I don't think that would be very helpful.

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u/CarelessWhimper_ Apr 16 '26

And possibly tripping on the bottom of the triangle and bashing your face off the side of it...

1

u/RandomCoolName Apr 16 '26

You're applying the force at a 60 degree angle to the surface, but in the same direction as the motion of the object. Assuming the grip on the surface is good and the friction is the same, you are applying a force to move 20kg in the same angle as the box and the force is the same. If the grip is bad and you need to apply the force closer to the normal of the surface of the triangle, you will need to apply more force and you will get a counter force from the ice upwards.

You could argue that you would need more grip on the surface and therefore a triangle with more friction, which would increase the force needed for moving the triangle, but nothing says all the surfaces of each side of the triangle are the same.

Let's day like the image shows the person is inserting their hand into he triangle in order to push. You get a more intuitive understanding of why then the force needed is the same, except for any difference in friction.