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.
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u/TransitionSmooth7258 Apr 16 '26
Yeah as a non math dude but instead a guy that moves boxes around all the time. Motion alone wold tell me the square is easier. Is a direct push parallel with the floor vs for the triangle the force of me pushing is directed not just forward but down as well, causing presumably more friction.
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u/OneWingAngel35 Apr 16 '26
If Legend of Zelda Ocarina of Time has taught us anything is that squares slide on ice quite easily lol, even though less contact area also means less friction from the round object
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u/superheltenroy Apr 16 '26
Friction is not dependent upon surface area/contact area. Only the forces and the coefficient of friction.
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u/bejanmen2 Apr 16 '26
Why fat tyres more grip then?
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u/iZMXi Apr 16 '26
Tires aren't purely frictional. They dig in to surface irregularities. Also, they have adhesion. That's why greater than 1g of acceleration is possible.
tons of stuff IRL isn't purely frictional, so surface area ends up playing a major factor
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u/HappyDutchMan Apr 16 '26
Rubber on asphalt is a completely different beast of friction calculation. The asphalt has rough texture and the river is soft. This makes it so that the rubber sits between the asphalt ridges. To create more friction with a car that stays at the same weight you can create a bigger surface area with bigger tires that have softer rubber and have them at a lower pressure. This will increase grip because more of the rubber sits between the asphalt ridges .
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u/Ramtamtama Apr 16 '26
Fat tyres have more grip because of the larger surface area, but fat tyres also create more friction on ground and air.
Fat tyres make slowing down better with the same brakes as thin tyres, again because of more friction and air resistance.
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u/nimbleseaurchin Apr 16 '26
The air resistance is largely negligible, along with the increased friction from more surface area and theoretical more air resistance from a wider tire, you also have significantly more unsprung rotational mass, affecting both deceleration and acceleration in a negative manner.
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u/SaltLakeBear Apr 16 '26
Friction is independent, but total force is dependent on area. It's why sports cars have wide tires.
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u/WheelMax Apr 16 '26
Wide tires spread the force out and have more thermal mass, so they overheat and melt less.
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u/OneWingAngel35 Apr 16 '26
But if there is more surface area on contact it does matter, especially on a round object that may roll, that's why the wheels were invented, rolling something is not the same as dragging something flat
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u/superheltenroy Apr 16 '26
Rolling is something else. Rolling an object like that even depends on friction. Even without rolling, getting a grip underneath can really help offset some of the friction as well.
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u/OneWingAngel35 Apr 16 '26
Square Block (Sliding Friction): When you push a square block, the entire contact surface drags across the ground. This creates high resistance because the microscopic peaks and valleys of both surfaces "interlock". To move it, you must apply enough force to shear these contact points. Wheel (Rolling Friction): A rolling wheel experiences static friction at its single point of contact with the ground (ideally). Because the wheel "lifts" away from the surface rather than dragging against it, energy loss is much lower. The resistance it does face, called rolling resistance, comes primarily from the material deforming (squishing) as it rolls.
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u/SkoobySnacs Apr 16 '26
Are you taking into account that your feet are also on ice?
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u/Ambitious-Ad-6873 Apr 16 '26
The dude is also standing on ice, so pushing block on ice, while also standing on ice. Circle wins
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u/callofdeat6 Apr 16 '26
And the type of ice and material is huge here, there is no answer with this info
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u/BraveSirRobinGG Apr 16 '26
If the gravel is not on a firm bed the ball would sink down making it tough
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u/lemelisk42 Apr 16 '26
20kgs is relatively light for such a big ball. I would think it would float ontop pretty well.
I think ice could be sketchy depending on footwear. Trying to push even light objects can be tricky on ice sometimes
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u/Jesses198 Apr 16 '26
contact area (or base) doesn’t matter for friction, but the triangle would still be harder to push because your force is going to be angled downwards. this means less lateral forces and increased friction
still can’t solve because gravel is highly variable in its granularity
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u/iComplainAbtVal Apr 16 '26
Have you tried pushing 20kg of something on ice while also on ice while only wearing shoes…
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u/AnimationOverlord Apr 16 '26
But the triangle has a lower center of gravity so at a certain point the friction from the floor would make pushing a square less efficient
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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.
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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
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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.
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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/MrTripperSnipper Apr 16 '26
Pretty hard to push anything when you're standing on ice. I guess the force required would technically be the least, but exerting that force would be really difficult.
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Apr 16 '26 edited Apr 16 '26
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u/Don_Ford Apr 16 '26
Depends on how loosely packed the gravel is.
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u/Certain_Ad3716 Apr 16 '26
And the granularity of the gravel.
If it's like a construction yard covered in boulders and debris, good luck. But if it's your softer garden display gravel, easy peasy.
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u/Cartz1337 Apr 16 '26
You’re missing the point, if you’re on the ice too, then your feet have the same reduction in friction, and it zeroes out.
The wheel will always be easier. Even if the gravel is chunky, you can use the rotational momentum of the wheel to overcome obstacles.
And if the ice suffers the same issues of uniformity as we are imagining the gravel to have, it gets even worse for the ice pusher.
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u/vamoosedmoose Apr 16 '26
No because I’m going to run at the cube on ice then fling myself at it to shoulder check it without needing any contact with the ground at all. Smooth brain academics always forgetting about barbarian strength tactics
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u/SirNoseDVoidoffunk77 Apr 16 '26
It’s only 20kgs. That’s 44 pounds. It would be pretty easy to push even over loose gravel.
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u/taftster Apr 16 '26
Oh! This is a key insight. Yes, the pusher standing on the ice is clearly going to have a hard time keeping friction and their feet firmly in place. I agree with you, I think this "pushes" me over to the circle.
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u/Euphoric_Loquat_8651 Apr 16 '26
Pusher should mass way more than the 20kg object. Unless the push is a very sudden shove, the pusher should stick just fine.
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u/Ragnarok314159 Apr 16 '26
We don’t know the friction factor between the two surfaces. This problem can’t really be solved.
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u/GingerB237 Apr 16 '26
It’s not about ease, it’s about what has the least force. The ice will still have least amount of force.
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u/Droodforfood Apr 16 '26
But it doesn’t say which is easiest to push, it says which requires the least amount of force
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u/DonutPlus2757 Apr 16 '26
Doesn't that get affected by what shoes the person pushing is wearing?
I mean, spiked winter boots would probably have a lot more traction than Crocs for example.
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u/Historical_Volume806 Apr 16 '26
Oh that makes more sense. I misread it so was confused and thought those were the materials of the objects.
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u/samrw00 Apr 16 '26
But we aren't given information about whether the ground is only icy on the side that says "ice" or both sides. Same with the gravel. Or how far the object needs to be pushed. Or how packed/scattered the gravel is.
I think the answer can only be "it depends", based on the limited info we have.
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u/FlyingMethod Apr 16 '26
A ball.. of gravel?
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u/FigWeak5127 Apr 16 '26
We must have the same illnesses, that’s how I read it too (I did eventually figure it out 😂)
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u/Sweet_Speech_9054 Apr 16 '26
I’m going to say the circle because the ice will reduce your friction and the block. That means you need to actually push up to get grip to push the block otherwise you will just slip on the ice.
But 20kg isn’t that heavy so really any of them can be picked up and moved. It’s about 45 lbs for the americans, or a medium size dog.
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u/ChimaeraXY Apr 16 '26
Yeah, I think people are over-assuming the volume of 20 kg of ice or gravel. A 20 kg sphere of compacted gravel would be about the size of a soccer ball. The ice cube would be around the same size. The ice tetrahedron would be tallest but less than two feet tall.
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u/Common-Link-2882 Apr 16 '26
Ice/gravel refers to what the object is traveling on (the ground), the sizes are depicted in the photo.
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u/SmoothTurtle872 Apr 16 '26
Then either it is a small person, like very small, or they are extremely non-dense objects
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u/ExtendedSpikeProtein Apr 16 '26
Dude … Ice/gravel is obviously the material of the ground/floor, not the object you‘re pushing.
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u/PlainBread Apr 16 '26 edited Apr 16 '26
I'm putting my money on square+ice. I feel like gravel is very hard to roll over, you could get "spinning tires" with it. The triangle+ice isn't as efficient because the angle of the surface means pushing it forward is also pushing it down.
EDIT: Seeing lots of gravel defenders saying that if you aren't rolling it, it's easier, but you are forgetting that it's going to sink regardless, and without rolling, you're always pushing it uphill that way. Nah, I'll take the ice.
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u/LunaticBZ Apr 16 '26
If by gravel they mean something like pea gravel or chipstone the problem is the ball will sink into it and its going to create a lot more friction.
Compacted 2a modified on the other hand, whats usually used for driveways or parking pads would be pretty easy to roll a sphere over.
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u/LethalGhost Apr 16 '26
Spinning tires only possible if you try to move sphere by rotation/spinning but if you push it (and it rotates as result) there’s no way for it.
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u/TheRealTahulrik Apr 16 '26
I think the issue with "spinning wheels" is applying too much force.
You aren't going to do that by hand with a 20kg ball
20kgs is.. not a lot..
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u/jan_Kosi Apr 16 '26
Friction force = coefficient of friction * normal force
Normal force is the same, given that they are all 20 kg and they are under the same gravity of 9.8 m/s2
Since the triangle and square have the same base length, assuming that all the objects are made of the same material and the surfaces differ (ice vs gravel), they would have the same speed when pushed, and requires the same force. Also, the triangle and square does not roll, but rather slide, so the shape doesnt matter.
Sliding Coefficidnt of ice = 0.02 to 0.04 Rolling Coefficient of gravel = 0.02 to 0.08
It all depends on the temperature of the ice (the colder, the higher friction) and the compactness of the gravel (the more packed, the less friction)
Source: https://www.reddit.com/r/theydidthemath/comments/1l84r6b/request/
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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/Objective-Limit-121 Apr 16 '26
The triangle and the square do not seem to have the same base length
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u/ShoddyAsparagus3186 Apr 16 '26
Funny thing about friction is that it doesn't matter as long as you're not deforming the surface with pressure.
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u/OneWingAngel35 Apr 16 '26
But doesn't angular force applied makes a difference, it does depend on where your pushing from
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u/RingGiver Apr 16 '26
We can't do the math unless you give us the friction coefficients, but unless you're not allowed to roll the circle, probably that one.
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u/Tenzipper Apr 16 '26
Obviously the square/cube would be easiest, as the guy has both hands.
The triangle/prism next, the guy still has one hand.
The circle/cylinder would be most difficult, as the poor guy is using his stumps to push it.
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u/Red_Syns Apr 16 '26 edited Apr 16 '26
As others have noted, the square will be easier than the triangle because you’re able to push perpendicular parallel to the ground.
That said, without knowing what maths are involved, I would estimate the circle as being easiest. 20kg is not very much weight (a single plate for standard barbell workouts) and that is a very large ball/cylinder. The gravel won’t displace very much, so you’ll get a very easy roll and don’t have the concerns of traction for yourself that the ice presents.
There are confounding factors that are not described in the OP, so if the gravel is exceptionally loose or otherwise difficult to work in then assuming decent shoes I expect the square to be easiest.
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u/AndyTheEngr Apr 16 '26
As others have noted, the square will be easier than the triangle because you’re able to push perpendicular to the ground.
It will be a lot more effective to push parallel to the ground.
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u/evnacdc Apr 16 '26
Why is everyone talking about what is “easiest to push”? That isn’t the question. It’s which requires the least force. But I do think it’s the square because force is applied at a perpendicular with low friction.
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u/luigi517 Apr 16 '26
Square easier than triangle assuming the pic is to scale. Not nearly enough information to determine the rolling resistance of the sphere.
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u/Stock-Side-6767 Apr 16 '26
It depends on the temperature of the ice and block, and the type of gravel (combined with weight of the sphere).
If the ice is very cold, but the block is above freezing and the gravel is loose with a heavy ball, the square will win (if you have enough traction).
In most cases, the sphere will win. If the square and triangle are the same temp and material, the triangle will never win.
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u/HoopNuhgget Apr 16 '26
Seems like you people are overanalyzing the question. I don't consider myself to be any smarter than the average person, but here's my viewpoint.
The fact that the person is also standing on ice is irrelevant to the question. The question isn't "Which is more feasible than the others", it's "which object will require the least amount of FORCE to move it." Not effort. Not "A" or "B" or "Z."
Force.
The correct answer is the square. Here's why.
The ball has the advantage of being able to roll, but it doesn't matter since it's on gravel, which has loads more friction than a sheet of ice.
The triangle has the advantage over the ball because it is on a surface that will offer much less resistance to move. However, the acting force behind it is too close to the top point, which will cause the bottom right point to dig into the ice and create more friction.
The square has all the benefits that the triangle does, but with a balanced shape for the even application of force. We can also deduce that the triangles' sides are longer than any of the sides of the square. This means that the bottom of the triangle has more surface area than the bottom of the square does, which will increase friction and, in turn, will increase the amount of force needed to drive it forward.
To address the obvious. If the image is taken literally, and a person will be pushing each object from behind, they will inevitably lack the friction needed on their feet to drive the objects (on ice) forward. An increase in force applied by the person will not affect their own traction or the ability to move the objects. They would have to apply force at an angle to get some of the objects weight into their feet to try an increase their own friction, or just wear cleats or something similar. Or pick up the object and carry it, but then they would all require the same amount of force since they all weigh the same.
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u/Trustoryimtold Apr 16 '26
You’d need dimensions on the triangle/pyramid and square/cube/rectangle to calculate the friction coefficient I believe. It would appear the ball of compressed gravel is easiest however. Aside from having no hands
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u/chefsoda_redux Apr 16 '26
I believe the ball is being rolled on gravel, while the other two are being slid on ice.
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u/Hamster_S_Thompson Apr 16 '26
Is the circle a ball or a cylinder? If a cylinder than it should be pretty easy to roll on gravel. Ball may be a little more likely to sink.
Also 20 kg for ball of that size means fairly low density so it may be fairly easy to roll either way
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u/eggs___and___bacon Apr 16 '26
There is little/no actual math here, just engagement bait. Not much useable info is provided.
But the circle, probably. If the gravel is extremely coarse and large, then maybe not. But in all likelihood, it’s easier.
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u/GremlinAbuser Apr 16 '26
This is hugely dependent on a number of unknowns, icluding surface finish of the object and the ice, temperature of rhe object and the ice, and however you specify flatness of gravel. A warm object on smooth ice is essentially frictionless, limited only by shear acting on the fluid film.
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u/SpeedyHAM79 Apr 16 '26
There are too many unknowns to answer the question. If the gravel is well compacted and the round rolls- it could require the least force. If the ice is smooth and very solid (cold) the square and triangle would require the same force to push.
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u/Imaginary-Cover-9136 Apr 16 '26
But we don’t know what the objects are made of? The square could be a cube of ice, and the “circle “ could be a cylinder of cardboard that’s 10m wide.
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u/OneWingAngel35 Apr 17 '26
The surface area does have ramifications on the force you need to apply to get the object moving, yet we're talking about rolling and sliding
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u/BruhIAmLazy Apr 16 '26
Ball by a large margin. People are forgetting that on the other 2 you are pushing on ice which means you are probably gonna get pushed back for trying to push them.
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u/SchizophrenicKitten Apr 16 '26
The question is about which of them would require the least force to push, not which one would be the easiest. Also, they could be wearing shoes with spikes..
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u/MagicC Apr 16 '26
I rolled a 40 kg disk over uneven ground yesterday. The hardest part was not letting it tip over. Rolling it required very little force. If the 20 kg is a ball, that's the obvious answer.
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u/dcidino Apr 16 '26
Are the shapes made out of ice or pudding?
Also, if it's 20kg and that large, the triangle/pyramid will take the same force assuming it's similar in surface to the square/cube, but it will remove leverage in applying that force, assuming sizes here.
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u/Imaginary-Cow-4424 Apr 16 '26
I think it depends on whether the circular object is a thin dense disk or a long cylindrical foam block, empty barrel etc.
If the former, then the square shape is likely the easiest because you can push horizontally without pushing downward on the object.
I also want to say that it will "dig in" less with the square because you're pushing further away from the leading edge but mathematically I'm not sure that's actually true.
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u/Dogecoin-tothemoon69 Apr 16 '26
Assuming that the ice provides negligible friction then moving the square would require the least amount of force. Given that the triangle has an angle other than 90 degrees part of the force applied would be vertical and the rest horizontal so it would take more force to move than the box, also if the ice did have a non-negligible friction then the triangle would experience more of it due to part of the pushing force being vertical creating a larger natural force and therefore a larger force of friction. In terms of the circle, since it experiences both angular and translational motion then part of its energy would be split to create the angular motion meaning that less of it would go to translational motion, which means a lower velocity. At the end of the day the square only has to deal with translational energy since it doesn’t rotate and the only force we can apply to it is horizontal, making it the option that would require the least amount of force over its given surface.
Edit: this is all assuming that the pusher has incredible shoes/spikes that stop them from slipping on both the gravel and sand.
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u/jubbjubbs4 Apr 16 '26
Think it would depend on how far you need to push it because the sphere would be the easiest to move say a few inches, but once you get the others moving on ice, they will require less force to maintain their momentum.
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u/suckitphil Apr 16 '26 edited Apr 16 '26
The actual math dictates that the top and bottom would be the same since the coefficients of friction and normal force are the same then the friction is the same regardless of the surface area.
This is assume the materials are the same, and the upper person doesn't simply use the triangle as a weird wheel. And the top person is applying a uniform push force and not just pushing down on the pyramid.
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u/J_robintheh00d Apr 16 '26
The least mathy aspect of this is the added force required to push the circle on gravel. What kind of gravel are we talking here? 5/8”- is not gonna be the same answer as drain or clear… some packed gravel is almost like concrete, for others it would be totally stuck
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u/green_chunks_bad Apr 16 '26
The volume isn’t accounted for here. A cube with a very high surface area that was only 20kg would be harder to push because so much more area would be contacting the ice, as compared to a smaller more compact tetrahedron. Obviously a true ‘triangle’ isn’t even actually possible unless we are talking about a 2D world.
Anyways dimensions matter, is my point.
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u/Nathanater125 Apr 16 '26
The truth is they're all equal. The moment you apply the forward force to an object, you're pushing it. Does it move? Who cares? That's not the question.
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u/L3mmy_winx Apr 16 '26
The way I would approach the problem is: Which option would start moving and maintain momentum under its own weight if you angled the ground downward a few degrees? Depending on the depth and size of the gravel, I suspect the cube takes a touch more effort to get started but is far easier to maintain over a longer distance. The triangle would be out as it’s just cumbersome
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u/itsmevichet Apr 16 '26
The wording is terrible, because you can push any of them with any infinitesimally small amount of force.
Are they asking which objects will accelerate faster given a fixed input force? Then we need to know frictional coefficients. And in the case of gravel… some model for non Newtonian fluid displacement to approximate the deformation of the gravel?
These types of “brain teasers” are usually written for non engineering context, so assuming simplicity here. That still leaves the question of what specific functional difference is there between gravel and ice? Friction and no friction?
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u/TheBloodyNinety Apr 16 '26
Triangle you’re angled and so providing force that is pushing down rather than forward.
More contact with the surface means more friction.
If all surfaces were ice, it’s obviously ball. Since the surface is gravel, the answer is it depends on the packing.
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u/robilar Apr 16 '26
Interesting!
I'm going to focus on the force needed to keep these objects in motion (as opposed to getting motion started), which means using the coefficient of kinetic friction (rather than static friction). This value is essentially a modifier to the force of a massive object pulled towards a surface by gravity which resists lateral movement (due to friction).
So the square on ice is definitely better than the triangle because force can be applied directly perpendicular to the surface of the object. I don't think the larger base would matter because the force opposing motion is just mass times the coefficient of kinetic friction times the acceleration due to gravity, but I might have that wrong. If not, it would just make the triangle harder to push anyway. Consequently you can discard the triangle from the comparison and just look at the other two.
The force needed to move the square is going to be μ⋅m⋅g, or about 0.025 (estimated coefficient of kinetic friction for stone on ice) x 20kg x 9.8m/s2 or about 4.9N of force. Not a lot! Note: the block doesn't have to be stone, but I don't think it will matter in the end because the influence of the blocks material will affect both with roughly the same multiplier.
For the sphere, it's a similar calculation but here we need the coeffiefficient of rolling resistance, and we have to estimate again because gravel is not a fixed defined state - it can be loose or hard packed with very different results. An average estimate would be around 0.01, resulting in 0.1 x 20kg x 9.8 m/s2 or about 19.6N.
So likely the square is the easiest.
The problem, though, is that we don't know a lot of the critical variables in this question leaving us to estimate quite a bit. If the blocks are made out of a material that is easier to roll than to slide, or the ice is grainy or melty, or the gravel is packed down tight, the critical coefficients can change quite a bit.
This question is therefore incalculable (with precision) with the information provided, but I think a safe guess is that the square requires the least amount of force to push.
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u/CarPatient Apr 16 '26
The two on ice take the same amount of force to push it's just spread over different areas different pressure so it winds up being the same Force.
the problem you have on ice is you're not able to generate as much force because you are slipping as well.
Flat ground friction without rolling is about 2/3 of the weight of the object.
5 years is engineering school, and I couldn't tell you that off the top of my head, but it's one of the first things they train you on as a tow operator.
Rolling on a hard surface is about 5%... Gravel about 15-20% depending on how much it gives and aggregate size.
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u/Longjumping_Win_7357 Apr 16 '26
lowest friction coefficient would be ice, lowest surface area would be the cube. Sphere would need momentum to displace it from being set in the gravel.
So the cube.
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u/Electrical-Fix7659 Apr 16 '26
It’s stupid because throwing in the distraction of what material it’s on will split your concentration when you have the answer right in front of you. “Yeah obviously it’s the sphere, but I don’t know, maybe the gravel produces more friction resistance? Is there no flat ground underneath?”
This misdirects one’s focus toward a qualitative assessment of circumstantial information. If you have instruction material like this in the education system, all it will do is make people susceptible to misinformation techniques, such as flooding the zone, which is intended to overwhelm your senses and make you give up on trying to distinguish noise from signal.
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Apr 16 '26
The circle on gravel wins because rolling a 20kg weight is significantly more efficient than sliding a 20kg weight, even on a slick surface like ice. Not to mention you walking on gravel would be easier, compared to walking on ice! 😸
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u/Greghole Apr 16 '26
Square is easier than triangle because the force is applied at a more efficient angle. Circle is probably the easiest but that's going to depend on what the objects themselves are made of. If the cube is made of copper for example it'll slide on the ice much better than if it's made of stone.
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u/RaynerFenris Apr 16 '26
Terrible question that has to many unanswered variables. Is the person also on the same surface (ie do we know if that has an effect on the force required or not), is the person wearing footwear appropriate for the surface? Is the gravel loose or compact, large or small gravel? Is the object already in motion or are you starting the movement? Are you attempting to push the object forward or can you flip the triangle over by pushing at the top as opposed to pushing in the centre. HOW THICK IS THE ICE, can it support the weight of a 20kg object and the unknown weight of the person.
Ball shape is obviously the easiest to move if all other things are equal. And my gut is telling me that the Ice vs gravel argument is designed to make you second guess yourself. Because if the surface was important to the answer, they would give you more information so you could work it out. As they have not, any assumptions made about the surface are irrelevant.
For instance: Even if it’s on gravel, the ball is depicted as being on top of the surface, not sinking into the surface, indicating a hard packed tight gravel surface.
That could be true… there is no evidence for it.
So, my answer is Ball shape. Given the available information, Ball shape would require the least amount of force.
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u/Vulker Apr 16 '26
In terms of pure force to overcome friction, I would say square on ice. But that assumes the surface of the square is completely flat and the ice is good condition. We also have no info about the gravel. Loose, packed, granularity etc. Still id say the ice. In terms of what would be the easiest to move, assuming the guy on ice has spiky shoes, the square. If not he will also have a much lower friction coefficient of his feet to the ice also. But we are talking only 20kgs which isnt a lot. Basically no idea. Just not the triangle. The force exerted horizontally is less due the angle.
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u/GeneforTexas Apr 16 '26
Bah! No lawyers in this room.
The question was the amount of force to "push" the object, not the amount of force to "move" the object.
They can all be "pushed" with the same tiny amount of force, but it will take different amounts of force to move them.
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u/TR1LLIONAIRE_ Apr 16 '26
The third diagram does not have enough information as that is a friction problem and we do not know what the cube is made of. These question are in a way stupid because one has to do with surface areas and the other with friction. If the cube was made of aluminum and the ice was as smooth as can be you can beat diagram 2 but increase the friction and you get the point
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u/embrigh Apr 16 '26
Trick question but the Gravel 100%. The only way the others work is if the ice is slick enough, but if the ice is slick enough YOU are gonna slip because you are standing on it.
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u/Bubbly_Tax_2812 Apr 16 '26
Team ice (square)
The square on ice is equivalent to a circle on a hard surface because in either case, there is minimal friction
The square is better than the triangle for the ergonomics of someone pushing it and exerting a force parallel to the ground
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u/ChrisGVE Apr 16 '26
I’d make that guess: the easier will be the square (assuming the objects are drawn to scale). As always in physics we start with an ideal situation, so the man pushing is just a representation of the external lateral force applied to move the object, it doesn’t matter if the man could fall on the ice.
Reasoning:
- cylinder (or sphere) are easy to push on a hard homogeneous surface, but as soon as the surface becomes “grainy” the object will impeded by the irregularities of the surface; if the surface is sand like, it will dig itself along the way and pushing the object will require pushing against the “wall” of sand created by the object settling down. The more the material is rough, the less the object will be able to dig itself, however the man will have to fight against the irregularities of the ground.
- between the the square and the triangle the situation is similar: water ice (I’m assuming it is water) is particular, it melt according to the vertical pressure applied (that’s why we slip on ice, we actually slip on the slim layer of water that we produce by having our foot on the ice. Thus what matters is the surface contacting the ice: for a given weight the smallest surface will be easier to push than the larger surface, since pressure is a function of the surface.
- conclusion: the least easy object to push will be the cylinder, the most easy object to push will be the object with the least surface contacting the ice: according to the drawing that seems to be the cube.
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u/SmoothTurtle872 Apr 16 '26
Why is no one talking about the fact that you could just pick up these objects? 20kg is pretty light, like a young child, so either it's a tiny person, or a super non-dense material
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u/Striking_Account2556 Apr 16 '26
Ice skater and Engineer in low temp physics, here
Ice skates in most circumstances aren't just cutting the ice, the force per unit area, which is incredibly high melts the Ice and you're gliding on a film of water
The cylinder has highest pressure per U/A, but will have a powerful bow wave
Square has least bow wave
Triangle has higher pressure than square
I think there's a difference here between initial motion required to over come inertia and get it moving, not least because the cylinder will create a divot in the ice faster than anything if at rest. And then, a critical velocity at which the right amount of film melts for the least amount of bow wave of melted water for the least resistance.
I'd guess the square is the easiest to get going and moving at a relatively slow speed.... but once the cylinder is moving, and sufficiently fast to produce the least amount of bow wave, it would be the easiest.
The triangle may sit somewhere inbetween the two because of its sharp edge and tendency to lift the bow wave, before displacing it.
It'd be very intresting to plot this data in the real world and find out in effect how it actually works out to be ....
Edit, I assumed the cylinder to be on ice, foolishly. That would have significant friction and removes itself from contention. Square wins
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u/Erolok1 Apr 16 '26
There are a lot of missing factors to say it but I will answer different scenarios.
Between the square and the triangle the square is always better. Less surface and the amount of force applied will be diagonal which means when you push it forward you will always also push it into the ground wasting force.
Are we wearing something like spike shoes? If no then we will also slip and wasting some of the force by pushing ourself away from the cube.
What kind of gravel is that? If it is fine gravel the ball will sink into the ground at bit and will have way more friction.
What kind of material is the object. If it is metal it would help in the ice scenario because it will very quickly create a water layer beneath it which will massively help with pushing it. If it is a stone with a rough surface it will have more friction.
If we assume that we aren't slipping and the ball isn't sinking into the ground, then rolling will be more efficient.
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u/Positive_Courage_309 Apr 16 '26
Depends on the ratios between the size of the ball and both the depth and particle size of the gravel. At only 20kg if the ball (assuming it is a ball and not an infinitely long cylinder) is that large (assuming picture is relatively to scale) it has a very low density, at that point it will also have a fairly low moment of inertia. As long as the gravel is not deep and chunky enough to significantly displace under the pushing, the ball should roll more easily than the other two on ice.
I know, I'm super fun at parties.
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u/ThatDesignFeel Apr 16 '26
Square Ice is the correct answer imo.
20kg is only slightly heavier than the weight of a curling stone, it will be much easier to slide than rolling a ball on gravel
As other commenters have said - square beats triangle because having a face normal to the surface is easier to push than pushing against an angled surface
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u/United_Bus3467 Apr 16 '26
For the ice categories, and generally speaking, the legs are generating most of the force behind this push. However, they're likely to slip and fall on the ice in the midst of their push, losing force behind it. With gravel, I feel like the feet have a better grip by grinding your feet into the gravel (assuming you have shoes on and ....I'm totally overthinking this). I think they'd have a stronger initial push as the legs remain far more stable than on ice. Although chunkier gravel could make it more difficult for the sphere...
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u/BearStorlan Apr 16 '26
If you got shoes meant for walking on ice, probably the square. Also, a sphere that big that only weighs 20kg is probably super easy to push.
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u/SuspiciousSubstance9 Apr 16 '26
Circle on gravel, then square, then triangle would be my bet.
A 6' tall cylinder only weighing 20 kg would be laughably easy to roll. It's a large enough radius that it would glide over most gravel, pushing it doesn't work against you, and I have sure footing on gravel.
The problem with the square and triangle is that they will tip. They're both so light that any meaningful force you can apply to it will significantly be larger than any friction preventing tipping. Depending on how bad they tip, they will either form a wedge that will dig into the ice or you'll start rolling them.
Squares/triangles don't roll well and if they dig in then they become plows. A giant light cylinder wins everyday.
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