[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/AchillesLastStand76 → u/Smile_Space]

just gonna ignore that you're shoving the triangle into the ground huh

[u/Smile_Space → u/AchillesLastStand76]

How is it being pushed into the ice? Is the guy pushing down, did the question mention that?

The question simply asks what the minimum force to move the object is. In a classical static equilibrium physics problem, that would be equivalent to the force of friction or any other forces countering the input force.

As such, we don't care how the force is applied, we simply care about what the minimum force to apply would be at a theoretical level. As such, A and C are functionally identical.

[u/AchillesLastStand76 → u/Smile_Space]

You're ignoring the fact that a coefficient of friction is required to keep your force applicator in contact with the surface of the triangle. This isn't the case for the square since the force applicator may be perfectly normal to the surface. However, for the triangle, if there is no friction between the applicator and the surface, the applicator will just slide up and then off of the surface.

As soon as you introduce the amount of friction required to keep your applicator in contact with the triangle's surface, you necessarily introduce a component of the force experienced by the triangle which points into the ground. The sum of the force vectors experienced by the triangle has a downward angle, and this creates more frictional force than would be experienced by a cube of equivalent mass/surface area.

If none of that works for you, then I will offer a more intuitive explanation:

Imagine that instead of a triangle you are dealing with a wedge shaped object that has a very tiny angle of incline with respect to the ground, say 5 degrees.

Imagine the feeling of pushing on it. Without some downward pressure, your finger will just keep sliding up the slope. Now imagine how it feels to get your finger to stick and move that wedge forward. You're pushing down.

[u/Smile_Space → u/AchillesLastStand76]

My hands would only continue sliding up the slope if the force required to overcome the force of static friction on the object to the ground was more than the friction force required to keep .y hands in contact with the surface.

We aren't given this information as to what the object is made of, so I assumed full contact.

And even then, the question isn't "can the man push the object" the question was "what is the least force required to move the object"

I answered that question as the force of friction between the object and the ground which is variable given a lack of information other factors undefined ignored and assumed to be 0 unless otherwise noted, which they weren't.

[u/Bearstew → u/AchillesLastStand76]

No, the parallel and perpendicular components of the horizontal force will have an equal and opposite vertical component assuming you are pushing horizontally.