In the wake of Sheryl Crow's announcement that we can all do our part to save the earth if we only use one square of toilet paper per potty break, I have decided to let my inner nerd run amuck. For those of you that don't know me, I am an engineer. So, I have decided to see if it would be actually possible from an engineering perspective, for one to actually get away with using only one 4.5" x 4.5" square of toilet paper. No, I am not enough of an empiricalist to rush home to try it out. I have chosen (for the sake of sanitation) to crunch the numbers.
Before we start plugging in numbers, we must first acknowledge the premise that we want to avoid having our hands come into direct contact with...well, you know. For the purposes of applying Newtonian physics, the "body in motion" is a square of toilet paper. The forces at work are the "wiping force" (Fwipe), a force perpendicular to one's posterior (Nbottom), and the force required to overcome the friction between one's backside and the toilet paper (f). In order to use the toilet paper without the paper breaking, the sum of the forces must be less than or equal to the tensile strength of the paper. Since forces are vector quantities (i.e. they have direction and magnitude), one can't just add up the numbers; one must also consider the direction of the force. A Google search revealed that the tensile strength of wet 2-ply toilet paper is 0.8 lb/inch and that 0.033 is the coefficient of friction (the Greek letter mu) of a toilet paper manufactured by Proctor & Gamble. However, the provided mu is only between skin and the toilet paper, not "substances" and toilet paper. Assuming a significant degree of adhesion, we can say that our assumed mu is actually 0.33.
For the average person, let's say that Fwipe is 0.5 lb along the surface and Nbottom is 2 lb against the surface. I realize that this varies with situation and individual, but an analysis of technique would be far too exhaustive for this particular entry. The friction force "f" is mu times Nbottom. This means that f is 0.825 lb in the same direction as Fwipe. The sum of the forces is 1.325 lb. The tensile strength of the toilet paper would not be 0.8 lb/inch*4.5 inches because the full 4.5 inches is not in contact with the surface. The "contact" length would be 1.5 inches, which gives a tensile strength of 1.2 lb. Because the tensile strength is less than the sum of the forces, the toilet paper will tear and you'll have a horrible mess on your hands (yes, the pun was intended). Said mess will then cause you to use even more toilet paper, as well the additional water and soap you will no doubt use to clean up after yourself.
There are a few things that I find interesting in the "nature Nazis" targeting of toilet paper. The first being that quite a few granolas that I know personally are germaphobic. Despite this, they are targeting one of the major sanitary developments of the 20th century. Materials previously used for this function are too bulky to fit through the plumbing of today's bathroom. The other interesting observation is that the enviro-wackos had previously targeted "inefficient" toilets, making it impossible to purchase a toilet that can actually take care of business in one flush. One must now use two flushes to adequately remove refuse, and in the process use more water than before the 1.7 gallon flush.
We have troops in Iraq and Afghanistan, fighting to preserve our way of life and share that way of life with others. There are complete nutcases running North Korea, Iran, and Venezuela. Nutcases who have the wealth (and weaponry) of entire nations at their disposal if they so wish to attack us. It is entirely possible that terrorist organizations are able to enter our country through woefully inadequate border security. All of this, and with what are we supposed to be concerned? According to Sheryl, we are supposed to be worried about conserving our most precious resource: toilet paper. Maybe it's so we can clean up all the crap we are going to be in if we as a nation don't start paying attention to more important matters.
Links to this Post: Confessions of a Crazy Schoolmarm
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3 comments:
LOL.
Now we know why the left has no sense of environmental humor! Hysterical laughter might lead to more toilet paper use.
Which, as you note, would seriously confound certain specimens of modern California plumbing.
A certain Astrophysics major I know asked me to pass along his two cents:
also you may want a more detailed analysis of the angle at which the force on the toilet paper is acting and you will need two coeficients of friction (one for motion, one for static)
finally a rough aproximation of the geometry of the anal region would yield greater accuracy
of course, in science you can (usually) only do so much theoretical arm waving, the final test of your model is if course the actual experiment
heheh, a pretty good first approximation though
Naturally, the appeal of an actual experiment is diminished by the outcome of the theoretical model.
Hmm. That would be an interesting analysis, considering that the angle at which the force is applied changes along the path of the wipe. Also, where would one even begin to look for static and kinetic coefficients of friction for, ahem, "substances"? And don't even get me started on potential issues resulting in various viscocities.
Hehe, I had better stop now before I really step in it.
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