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/