I was taking a poop this afternoon and was revisited by an old problem. You are seated on a crapper with a constant anal sphincter to water-line distance D. The greater the length (L) of poop extruded before sphincter-executed release, the lesser the distance (D-L) for acceleration but the greater the mass of poop available for making a splash. What is the poop length L at which maximum splash is achieved?
Larger poop momentum (MV) will result in more splash. Find L for maximum MV.
D = Distance from anal sphincter to water-line
L = Length of poop column
A = Cross-sectional density of poop
M = AL = mass of poop
V = Velocity of poop hitting water
From newton's equations
V^2 = U^2 + 2A(D-L) (where U = 0 and A = 10)
V^2 = 20(D-L)
V = Sqrt[20(D-L)]
MV = AL * Sqrt[20(D-L)]
dMV/dL = -10AL*(20D-20L)^(-1/2) + A(20D-20L)^(1/2)
If dMV/dL = 0,
L = 2/3 D
Conclusion: To maximize splash, release poop two-thirds of the way to the water-line.
4 comments:
most intriguing post ever..
I will have to remember it next time I poop.
Just tried.
But the question is Do we want the splash or not..
ummm...
I don't think I like the feeling of water hitting my hole...
Just for you Hee Jung, I have followed up with the relevant MV vs L plot on the next post.
Thank you for putting that so succinctly HeeJ :)
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