Sunday, October 25

There were Real Physicists!

Physics is in one word REAL. Its also broad, varying, growing, and most importantly…INSANE. Lets begin.

“You are invited to develop a theory of bottle washing. Assume that you have a large volume W of clean water and a bottle of volume B which contains a small volume D of dirt. W>>B>>D. When water is put into the bottle the dirt dissolves immediately, and when the bottle is emptied a small residue R of solution remains. How do you get the bottle as clean as possible using all the water?”

quoted from Thinking Like a Physicist: Physics Problems for Undergraduates written by the staff of the Physics Department of the University of Bristol, and edited by N Thompson. Problem 15.

That is a REAL problem on a REAL test at the REAL University of Bristol, although I think by Raymond’s definition the professor that gave it wouldn’t be a REAL physicist no matter what research or degrees they have earned.

Lets begin again.

“You are invited to develop a theory of bottle washing. YES!!!! I SCORED AN INVITE TO THE PARTY OF THE WEEK! Assume that you have a large volume W of clean water Delicious! and a bottle of volume B is that B-Awesome or Super-B? which contains a small volume D of dirt. time to get dirty! W>>B>>D. Gotta love the much greater than signs. When water is put into the bottle the dirt dissolves immediately, That's convenient, and when the bottle is emptied through direct drinking by yours truly (after being poured through a Brita *commercial plug*) a small residue R of solution remains Bummer . How do you get the bottle as clean as possible using all the water?”

I’m thinking…

A: tear off the bottom of the bottle by magic, sylar’s cutting ability, brute force, or whatever other device you prefer. then begin a continuous pouring of water through one end and emptying through the other.

2: Fill up the bottle, empty it. Repeat until W=0. Note that the bottle will never be 100 percent clean but D will approach an asymptote = 0.

III: Quit while you’re ahead. throw away the bottle and keep whatever container W is initially contained in instead.

Clover: new version of A. Note anytime the dirt comes into contact with water it dissolves instantly but some solution always remains. So what you really want to do is dilute that solution as much as possible. Maybe theres an equation for this or along the lines of but I haven’t taken fluids yet so.. what i will say is that the more number of times you fill and empty the better off you are. So maybe instead of filling the bottle up all the way, you should fill it some optimal fraction so that you fill and empty the bottle more times. Perhaps you should even change the fraction, slowly increasing or decreasing. My best guess is decreasing. This is assuming that the amount of solution that remains behind is always a constant. Note i’m also betting that in the official answer they probably set N= number of times the bottle is filled and emptied and S= amount of solution left behind each time.

Lets Continue.

“It is clear that nothing is to be gained, at any stage, by re-using the rinsings from an earlier stage, since this would only serve to increase the concentration of the residue. If a volume of water knR (kn is a numerical factor to be determined) is added during the nth cycle of operations, the amount of dirt remaining is reduced according to Dn= Dn-1R/(R+knR). Thus after p operations,

Dp/D0=II 1/(1+kn)

if kn is kept at a constant value, k, then the number of operations to use all the water is W/kR and so

D/D0 = (1+ k)^(-W/(kR))

thus

ln (D/D0) = –W/R ln(1+k)/k

The largest value of the right-hand side (=W/R) occurs when k=0, and thus the smallest value of D is given by D=D0^(-W/R) and is obtained yb using as little water as possible for each operation. It is clear from this result that no improvement results from trying any procedure other than keeping kn constant.”

-same citation.

To paraphrase the “I’m on a boat” song..

This is as Real as it gets!

So…I’m going to say that out of 50 points we probably would have gotten …

A: if the teacher has a sense of humor: 45/50, if not: 0/50

2: 4/50

III: Kicked out of the University of Bristol

Clover: 35/50

Please appreciate the fact that I wrote out my answers before looking at the book’s answer and did not go back and change a word despite the grand temptation p.s.

Your turn

Problem 60: You have no mackintosh or umbrella, and have to make a journey ton foot in steadily falling rain. FI you run, the journey will not take so long, but you may intercept more rain. Taking as your criterion the necessity to minimize the number of rain drops that strike you and assuming that the rain falls steadily and vertically at 10 m/s construct a theory that enables you to decide the best speed at which to run. Mention any short comings of the theory which occur to you.

I’ll post the answer after receiving 4 ideas from you my beloved audience.

Need more insanity?

http://www.physics.harvard.edu/academics/undergrad/problems.html

A professor, David Morin, at Harvard used to post one physics problem each week. They’re all still up with the solutions but the last one was posted May 31 2004. Happy Hunting.

Oh and this post is dedicated to Dr. Rassoul for recommending the book to me when I came to FIT to visit before applying. (7 PREPOSITIONS in one sentence!) and of course props to Raymond for welcoming us to reality.

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