Lab
Experimental Radius
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This activity simulates an experiment in particle physics where a target material would be bombarded by high speed particles and conclusions are drawn from the results of the collisions. It will give you a chance to use a "Monte Carlo" statistics technique.
Problem:
To indirectly determine the radius of a single target circle using probability and the value of
.
Procedure:
Tape a page of circles on the floor and loosely cover it with a sheet of carbon paper placed "inky-side" down. Working in pairs, drop a marble from waist height so that the marble hits the carbon paper. Your partner must catch the marble after its first bounce. Repeat this a minimum of 100 times. Care should be taken to distribute the hits as randomly as possible over the entire target area. When you are done, you will count the total number of "target hits." It is "OK" to miss the paper from time to time. Those points will naturally be excluded form the data set. All measurements are to be in centimeters to two-decimal places.
Refer to the following information for the next eleven questions.
Data and Analysis
1. What is the total area of the rectangular area outlined on your target paper in cm
^{2}
?
2. How many circles are printed in the rectangular area from question #1?
3. How many total hits did the marble make within the rectangular target area outlined on the paper?
4. How many of the hits fell
completely within
the circles? Do not count hits that struck a circle's perimeter.
5. What percent of your total hits (question #3) fell within the circles?
6. Based on this percentage and the total area of the rectangular target area, how much of the rectangular target area was covered by circles?
7. Based on your answer to question #6 and the total number of circles on your page, what is the experimental area of one circle?
8. Using the formula for the area of a circle, A =
r
^{2}
, what is experimental radius of one circle?
9. Now, to obtain the actual diameter of a circle, measure the diameters of three circles and report your average value below. Remember to label these three measurements on your target papers.
10. According to your average diameter (question #9), what is actual radius of the circles?
11. What is the percent error of your experimental radius?
Adapted from:
Fermilab
Topics in Modern Physics, May 1990
Catching the Sun, 1992
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