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The science of stepping on a LEGO brick

My curiosity is getting the best of me. I have accidentally stepped on various strategically located bricks throughout my life...most with an outcome that typically includes me hopping around the room, usually in the dark (hence me not seeing it in the first place), while holding my foot and wanting to scream.

So here is the question...what LEGO brick induces the greatest amount of pain when proper force is applied to the underside of the foot?

There are various ways to approach this subject. Clearly one could argue the standard method of calculation using F=ma (force equals mass * acceleration) where my mass of 185 pounds multiplied by my typical walking speed through the home of 2 mph in the dark would equal 370 pounds of focused force on a single brick, assuming that it was a single brick on the floor. With this in mind, one could conclude that a smaller brick would hurt more because of the reduced surface area in which the force is applied. This argument only functions when used in light of hard surfaces such as hard wood floors and instantly becomes a syllogistic fallacy when considering that the majority of overlooked bricks typically occur on carpet rendering the smallest bricks harmless to our sensitive feet.

From another angle, we could also make the argument that because of the relative mass of the smallest bricks compared to the built in shock absorption of our foot structures, that only the bricks above a certain size, beyond what our feet can adequately absorb, would logically be the most painful. Keeping the aforementioned formula in mind, one could logically assume that a 2 x 2 brick (of any color) would be the most painful because no matter whether on carpet or on hard wood, that sucker is going to inflict 370 pounds of force pain due to its ever present corners regardless of orientation relative to gravitational alignment.

Lastly, and possibly the most convincing, would simply be that the most painful brick would be whichever one you just stepped on.

I am thinking that an in-depth research paper is in order.
brickmatic

Comments

  • I think the overriding formula you want is for pressure: P = F/A
    Pressure = Force / Area

    If you step on a flat tile (large surface area), you won't be writhing in agony like you would if you step on the corner of a brick.
  • I'm thinking some experiments are in order. I'll suggest some bricks and you can try stepping on them? :D
  • Good point. F=ma would only come into play when considering the downward acceleration of the foot and would only be fractional of the forward velocity. However, as stated before, one would have to account for the variable of carpet pad which in most cases is approximately .5 inches not accounting for standard wear and tear.
  • I'm thinking some experiments are in order. I'll suggest some bricks and you can try stepping on them? :D
    As much as I would enjoy furthering the cause of science, I find that the destruction of my feet in the quest for answers is probably not the most efficient use of the only two feet that I possess. However, I am sure that there is an undergrad AFOL somewhere willing to sacrifice comfort in exchange for the distinct honor of knowing that their efforts have resulted in a greater understanding of LEGO physics.

  • I'd like to be on the committee for that dissertation defense.
  • I think one could walk through any populated locale where LEGO is sold and randomly query total strangers about their LEGO stepping habits and find that they have fallen victim to the Brick-Pain theorem when LEGO bricks are negligently left to populate traffic areas in the home. It would be difficult to find a non-biased committee. Furthermore, an additional research topic would be to study the various causes of LEGO bricks just happening to appear in those traffic areas...as if quantum tunneling somehow played a role (in which case, I need better storage containers).
  • When I was a kid my brother had a 4x4 baseplate city between our beds. The babysitter came to the door to check if we were in bed, she tripped somehow, and when trying to grab the door, spun around and landed right in the middle on her back.
    That was the first time I heard so many swearwords used in such a short time. She attempted to get up but was obviously a victim of "Lego Accupunture" and had managed to do most of her pressure points.... :/
  • ^Ouch! Did she ever return to your home after that incident? lol.
  • @LegobrandonCP yeah on the condition we packed it away (slid under the bed)
  • That's given me an idea ... a bed of nails made from baseplates and antennas.
  • I'm working with trans clear 1x2 plates at the moment, and boy are they sharp. Are trans pieces made from a harder plastic?
  • ^ Not sure. The trans clear 1x2 bricks require additional strength due to their hollow innards. One could speculate that a stronger plastic blend was required in order to add additional strength to it. It would make sense in that case that all the trans clear parts are from the same plastic blend.
  • I once had a tack stuck in my foot for about 3 hours. I was playing with my Lego city at the time, so I didn't notice or recognize the pinch.
  • ^^^ yes, they are. Polycarbonate, if I recall. I looked into it when wondering why technics was a slightly different colour (it's also made of the same tougher material).
  • As a physicist I have step in and say your physics is atrocious. You're correct in that F=ma. You're mass is not 185 pounds. Pounds is a measure of force, not mass. In US measurement the unit of mass is the slug. But more often the kilogram is used. So you have a mass of 84 kg or 5.7 slugs. Next miles per hour is a measure of velocity, not acceleration. You're 2 mph speed is you're horizontal velocity as you walk forward. The vertical acceleration of your foot fall is should be about the same as acceleration due to gravity, 32 feet per second squared. So if you do that math and convert you'll find the maximum force (all you're mass on one foot) is 185 pounds.

    Now @rocao is correct that pressure in important factor here. It's like a bed of nails. If you take you're weight and spread it out over a large area (like a Lego free floor) it doesn't hurt at all. But start making that area smaller and it becomes an issue.
    brickmatic
  • I guess it's a good thing I am not a physicist. I am merely attempting recall of my physics class from over 20 years ago. Memory is not what it used to be. But thanks for the heads up.
  • As a physicist I have step in and say your physics is atrocious. You're correct in that F=ma. You're mass is not 185 pounds. Pounds is a measure of force, not mass.
    Actually pound is used for weight / mass. Pound when used for force should be called pound-force.

    If you lot over that side of the pond started to use SI units, then confusion would not happen: mass in kg, force in N, etc.

    I agree that some of the calculations above are a bit off though!
  • I don't know about the UK or else where, but in US science pounds are always a measurement of weight (ie force), never mass. In non scientific settings weight and mass used interchangeably. When force is talked about the normally US vernacular is "pounds of force."

    As for the US going to metric, I really have my doubts at this point. There's a number reasons, none of which are very good. I think the closest we came to going metric was in mid 70s. But the driving force behind the change seems to have evaporated.
  • edited March 2012
  • edited March 2012
    whoa...crazy browser behavior - delete please!
  • I would put forth also that if its your Mom who steps on said brick its probably been tossed in the garbage.
  • I'm American. Let me clarify. There are two relevant "pound" references in physics. One is pound force, one is pound mass. A pound in its common usage relates to mass and expresses precisely the same concept of a kilo, as used in LusiferSam's example. It's just that you need 2.2 of them to equate to 1 kilo.

    What was it that Shakespeare said? What's in a name? That which we call a rose. By any other name would smell as sweet.

    Doesn't matter if you express the concept of mass in units of pounds or kilograms or grams or ounces. Or "stone" as you Brits would say! Ha ha ha. Same thing.

  • As a physicist I have step in and say your physics is atrocious. You're correct in that F=ma. You're mass is not 185 pounds. Pounds is a measure of force, not mass.


    Actually pound is used for weight / mass. Pound when used for force should be called pound-force.

    If you lot over that side of the pond started to use SI units, then confusion would not happen: mass in kg, force in N, etc.

    I agree that some of the calculations above are a bit off though!
    The lot on this side of the pond got our crazy ass system from you Brits, don't forget....

    Though the metric system is infinitely easier to use in my opinion.
  • My two cents on the matter is that the most vicious (overall, not necessarily for stepping on) brick is the wing piece from the Droid Starfighters. If I was going to be stranded on a desert island or in a jungle and could only take one brick, that would be it-it would work as a sort of machete.
    Anyway, the 'cutting edge' on that brick would be very hard to step on, so it's probably out of the running.
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