Weighted Coin Project
Date: 02/01/97 at 14:44:07 From: Anonymous Subject: Weighted Coin - Science Project My 5th grade son and I have done a simple science fair project. We flipped a "true coin" (a quarter) 100 times. Amazingly the result was exactly 50 H and 50 T. We then created a weighted coin by gluing a dime eccentrically to the heads side of the quarter and repeated the experiment. This time we got 68 tails up (noweighted side up) and 32 heads up (weighted side up). Question: In the analysis section, I proposed that due to gravity the time spent in revolution is different for the 2 sides of the weighted coin and therefore, a difference in H and T could be expected. Do you have any more info on this? Thanks, Scot J. Spivak, MD
Date: 02/02/97 at 06:23:51 From: Doctor Mitteldorf Subject: Re: Weighted Coin - Science Project Dear Dr. Spivak, You and your son have picked an interesting problem. If you have more time to spend with it, I'd say there are two directions you might go. One is to think more about the physics of the situation. How does a symmetric object spin? How does an asymmetric object spin? Any object will rotate about its center of gravity (c.o.g.). The easiest objects to analyze consist of two weights on a stick: if the weights are equal, the c.o.g. is half way between them, but if one weight is greater, then the c.o.g. is closer to that one. You can read about this in a high school physics text. Surprisingly, perhaps gravity has nothing to do with it! What you learn might apply in a general way to the situation of two coins glued together, but it will not be easy to find the center of gravity for the object you have created. The second thing you might do is to think about means and standard deviations. For your true quarter, 50 heads is the most probable answer, but most of the time you'll get another number - 51 or 47. This seeming paradox is because there are so many numbers "near 50" and there's only one 50. If you have the time and the patience, it would make an excellent 5th grade project to repeat the 100 tosses twenty or thirty times, and make a bar graph: How many times did you get a number of heads between 48 and 52? How many times between 53 and 57? etc. You should see a bell-shaped curve emerging. If you feel it's appropriate, you might introduce to your son the notion of "standard deviation". Roughly, that's a measure of how far from 50 (in either direction) you expect the number of heads to be. The answer, in this circumstance and in many others, is the square root of 50, or about 7. You can read about all this together in an elementary text in probability and statistics. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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