Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Physics Answer to a Question...



[For some reason the following message which I sent yesterday seems not to
have made it to the list. I debated reposting not only because some of
the analysis has now already appeared (although my results are a little
different) but also out of concern for prolonging this repugnant thread!
Obviously I suffer neither from discretion nor valor, so ...]

***********************************

The answer to this ludicrous but frighteningly typical textbook
problem depends critically (as David points out) on the unstated
information about how the water is administered to this demented
soul as he coasts along on his impossibly slick chair glides.

Case 1) If he receives the water from assistants moving with him
who are careful to simply drop 1 gram of water into his mouth
after each "shot," then your answer (10,000 shots) is exactly
correct although your derivation is unsatisfactory since it does
not specifically make the assumption about delivery method or
explain how it is taken into account.

Case 2) If he receives the water (after each shot) from
stationary assistants then one must take into account the fact
that the received water is a retarding influence. His net
velocity change after each drop is then given by

delta v = (spit mass/50kg) (5 m/s - current v)

Taking "spit mass" to be an infinitesimal quantity the above can
easily be integrated. The result is that he needs to produce
11,158 times. (A spreadsheet calculation based on a finite spit
mass of 1 g gives the same result.)

Case 3) He doesn't replenish (i.e., the rocket problem). Of
course, this is ruled out by the problem statement but it is nice
to compare this case with the other two. Here, each successive
shot is more effective because of the smaller remaining mass.
Assuming the mass of each shot is small enough to be considered
infinitesimal, the standard result applies and gives

change in mass = initial mass *
(1 - exp-(final velocity/relative shot velocity))

which gives 9,064 big ones as the result.

In any event, I hope this disgusts you as much as the fact that I
enjoyed working this all out disgusts me. Frankly, I'd find a
different problem.

John
----------------------------------------------------------------
A. John Mallinckrodt email: mallinckrodt@csupomona.edu
Professor of Physics voice: 909-869-4054
Cal Poly Pomona fax: 909-869-5090
Pomona, CA 91768 office: Building 8, Room 223
web: http://www.sci.csupomona.edu/~mallinckrodt/