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6b_ec5 - our I Physics BB Extra credit Discussion Section...

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Unformatted text preview: / ' . our 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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