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I Physics BB
Extra- credit Discussion Section Problem #5 We‘re gonna try something different this week. This probiem is notkmeaht to be solved alone; you could easily get stuck and not know how to
proceed- We suggest you brainstorm with a small group of other students -- and if your group is
stuck, share ideas with other groups. Your discussion leader will be circulating around to help keep the discussions going. Keep some
written notes on your logic and conclusions to show to her afterwards. You can look things up in your
book if you like, but if you’re spending more than a iittle time searching the book for "the answer", then
you‘re ,missing the Spirit of the whole thing! ' The situation: A number N = 800 people are all milling around a large, square field with side length x: 100 meters.
Assume that each person needs a circular patch of ground of radius R = 20 cm to stand on; when two
people s circles overlap, they bump into each other- For some reason, everyone has their eyes
closed and make no effort to avoid crashing into each other. (And, for that matter, no effort to crash into each other on purpose either) Your gob
Try to come up with a formula for the average distance L that a person can walk before bumping into
someone (in other words, the mean free, path of people on this ﬁeld.) What acthal value do you get
for the mean free path, for the parameters given above (N :: 800 people, x': 100 meters, and H : 20
cm)? Hints: -
You can try to adapt the methods used to prove the expression for a mean free path of gas molecules,
be carefui, Since this field 15 two dimensional rather than three. You might also try to build an equation from sanity checks: How should each of the variables N, x,
and Ft affect the mean free path?
if you come up with an expression, think about the foiiowing questions: What approximations did you have to make in order to simplify yoirr work? is the ”actual" mean free
path likely to be longer or shorter than y'our equation indicates? ; By comparing your calculated value of r. to the other numbers given in the problem, would you say
that the people can be approximated as an "ideai gas"? What did you compare L to in order to
answer this? ...
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- Winter '08