Why is it so difficult to complete the milk crate challenge?
In: Physics
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The crates are light so they shake and move a lot, add to that the fact that you’re 2 meters up and you have a recipe for disaster
ELI5: roughly speaking every time you go up 1 milk crate, after the first, you increase the potential energy proportional to the number of crates. At the top of the crates, you have the potential to hit the ground with more force than needed to break any single bone in your body. assuming you fall directly on that bone with all your weight/energy.
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For more in depth explanation:
Explaining in terms of algebra based physics.
Standing on the ground your potential energy is PE =m*G*h
PE is roughly how hard of a fall you take as it turned into kinetic energy when you lose your footing
PE= m(mass in kg)*G(gravity=9.8m/s^2)*h(height in m)
(0 on the ground, because h = 0)
Standing on top of a stack of X number of milk crates it is now
PE=m*G*(X*h0(height of 1 milk crate=11inches=0.2794m))
Just standing on 1 milk crate increases your potential energy by m*G*0.2794
and that goes up X times for every crate you climb.
I’ll assume an average 62kg for mass, and use that as an example
1 milk crate = PE = (62kg)*(9.8m/s^2)*(1 * 0.2794)= 169.76344 joules of energy
3 milk crates = PE = (62kg)*(9.8m/s^2)*(3 * 0.2794)= 509.2903 joules of energy
highest i’ve seen is 7 milk crates = PE = (62kg)*(9.8m/s^2)*(7 * 0.2794)= 1188.34408 joules of energy
Now this is the energy you have at the top, which translates into force in 2 ways; a fall; force going into the crates as you descend and disperse your potential energy you gained climbing the crates
ASSUMING FALL FROM THE TOP OF 7 CRATES
POTENTIAL ENERGY is now your KINETIC ENERGY
KE = 1/2*m*v^2 = PE = 1188.34408 joules of energy
1/2*(62kg)*(v^2) = 1188.34408 joules
velocity you hit the ground with will be 6.1914m/s = 13.8498miles per hour
Force hitting the ground = m*g*h/s where s is the distance the force is being applied
62kg*9.8m/s^2 *1.9558m / 0.01m (very small part of you hitting the ground) is equal to
118834.408Newtons
it only takes 4000Newtons to break a femur. this is 29.708602 or about 30 times the force needed to break the strongest bone in your body.
This is better explained with the aid of a couple of drawings, but hopefully you can imagine it based on the descriptions. You can think of the stack of crates (or a single crate) as a lever that is pivoting on the bottom edge of the crate where it meets the ground. The length of the lever is the height of the stack. If the force of you standing on the top is going straight down, it helps you stay balanced. Any sideways force tries to make it tilt. If the tilt force is greater than the down force, you start to tip.
For the sake of simplicity, we will assume the crate is a perfect 2 foot wide square that is 1 foot tall (even though a milk crate is not. This is way more stable than a standard milk crate). If you stand with weight centered, that means that your weight is 1 foot from the edge, and every crate adds 1 foot to the stack. This makes the math easier because the weight is always multiplied by one when you’re looking at the way your weight helps to keep you stable.
Let’s say we have a 100 lb person. If they are perfectly centered and still, then 100 lbs of force is straight down, and they have no trouble balancing. The force (pounds) is multiplied by the distance from the edge (feet) to get “foot-pounds”. There is 100 foot-pounds keeping the stack from tipping. I’m gonna call this 100 foot-pounds of “stability”.
The 100 lb person is doing a pretty good job staying balanced, but when they wobble, their weight is 80% (80 lbs) straight down, 20% (20 lbs) directly sideways. I’m gonna refer to the effects of the 20 lbs sideways force as “tilt”. Tilt gets multiplied by the height of the stack. Let’s see how that works with 1-6 boxes:
1 box: (80×1) foot-pounds stability vs (20×1) ft-lbs of tilt. (80 is more than 20, stays balanced.)
2 boxes: 80 ft-lbs vs (20×2) ft-lbs (80>40, stays balanced)
3: 80>60, balanced
4: 80=80, barely balanced. any worse and you tip over.
5: 80<100, you’re tipping over
6: 80<120, you’re even further off balance.
Every time you add to the stack, you increase the multiplier of the tilt, but the stability force stays the same.
let’s say the same 100 lb person practices a lot and improves their balance. Now when they wobble, their weight is at worst 90% down and 10% sideways.
1 box: 90 ft-lbs vs 10
2 boxes: 90>20
3: 90>30
4: 90>40
5: 90>50
6: 90>60 (they should easily be able to balance on the 6-box stack and complete the challenge)
A real milk crate is closer to 1 foot tall and 1 foot wide so the effect would be worse. Your weight would be centered 6 inches (0.5 feet) from the edge, so essentially the corrective force would be half as strong.
TL;DR: It becomes easier and easier to tilt the stack of boxes as it gets taller, but the force that keeps the stack stable stays the same. Eventually, when the stack gets to a certain height, even a very small wobble will cause it to tip over. 6 boxes is enough to be a difficult challenge for most people.
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