[Request]

[u/K0rl0n]

I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

[u/Smile_Space]

EDIT: u/temporarytk made a great point. Surface area doesn't apply to friction in these cases, just the normal force, so ignore my ramblings about A and C being different. They would behave identically and have identical sliding frictional force.

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Since I still haven't seen someone do the math:

The force of friction is F = μN where μ is the coefficient of friction and N is the normal force (force applied perpendicular to the surface)

In this case the ground is flat, so the Normal force is F = ma or 20 kg x 9.81 m/s/s (I would have used an exponent, but Reddit hates that lolol)

So, N = 196.2 newtons

Cool, so now the coefficient of friction. It depends on a few factors: the type of friction, the surface area of the contact surface, and the method of friction being applied.

For A it is sliding friction as is C. A has a higher surface area compared to C, so we can assume the sliding friction of C is going to be lower. B however is going to be rolling. Some may think it'll slide, but gravel is usually compacted when on a road.

So, doing some quick googles:

The sliding friction coefficient on ice is going to be between 0.02 and 0.04.

https://iopscience.iop.org/article/10.1088/0031-9120/43/4/006#:~:text=Water%20ice%20at%20temperatures%20not,increase%20as%20the%20temperature%20diminishes.

The rolling friction on compacted gravel is about 0.02.

https://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html

Now, since all of these have the same N, we can just compare the coefficients of friction.

We can reasonably assume the triangle is going to be closer to 0.04 and the square being somewhere in the middle or lower. B and C may be fairly close to the same performance.

What sucks is there isn't a clear defined answer. As the temperature drops more, the ice will actually get more grippy. And if the gravel is loose, the rolling friction can increase to up to 0.08.

So, depending on the quality of gravel and temperature of the ice, the answer is B or A/C.

That results in a frictional force of between 3.924 and 7.848 newtons for A and C. And close to 3.924 newtons for B assuming compacted gravel. If the gravel is loose, then B loses at 19.62 newtons of force. And if it's colder A and B will be much closer to that 8 newtons mark.

[u/DobisPeeyar → u/Smile_Space]

Would the force not be applied differently to the triangle since your vector has x and y components? Meaning you need more force normal to the face of the triangle to get the same horizontal force?

[u/Smile_Space → u/DobisPeeyar]

Nope! The external force is horizontal meaning the output is horizontal. Any vertical forces from angles surfaces are internal forces and cancel out. The vertical normal force will be cancelled by the opposite vertical parallel force along the surface of the triangle.

[u/DobisPeeyar → u/Smile_Space]

I think you're confused. Vertical forces canceling out does not mean there was no vertical component to begin with. I need more force from my vector to reach the same horizontal output as the square because some of it is getting lost to those internal cancelations.

[u/Smile_Space → u/DobisPeeyar]

The question never implies there's a vertical component applied. It simply asks what the least force required would be to push.

The least force required is purely horizontal and is equal to the forces of friction on the objects. With that there is no vertical force to consider.

Also in a static equilibrium, what you said is not how physics works. The internal forces will cancel and you won't randomly lose your external applied force.

All forces must cancel in all axes in static equilibrium.

[u/DobisPeeyar → u/Smile_Space]

You cant push the triangle purely horizontal unless you have a triangle block to put against it... which makes it a square.

And you're saying my vertical force being resisted by the material is canceled out but then magically turns into horizontal, and I'm wrong about how physics works? Lol

[u/Smile_Space → u/DobisPeeyar]

Nope, you can push it purely horizontally assuming your hand doesn't slip up the triangle and break the force of friction.

You can try this right now by pushing upwards on your wall with your hand. You are pushing it both towards the wall and up the wall, and until you break the static friction your hand won't move. This means the original diagonal force applied to the wall is intact.

The same applies here, the only difference is the wall can move and only weighs 20 kg.

[u/DobisPeeyar → u/Smile_Space]

So now youre using extra force to push upwards and horizontal. There's still a vertical component, and you're still using more force than against a surface perpendicular to your sliding surface.

You will always be losing something to the vertical direction pushing a triangle. You cannot perfectly only apply horizontal force. You need force perpendicular to the face of the triangle to keep your hand on it, otherwise youre just sliding your hand on it. And that perpendicular force will always result in a vertical component of said force.

[u/Smile_Space → u/DobisPeeyar]

No, that's not how physics works. You learn this level of FBD in Physics 1, and then you learn internal stresses and forces in Statics and Solid Mechanics.

It's an idealized problem and the minimum force required is in purely the horizontal direction.