When Galileo did the experiment, he performed an initial trial and based on the data he got, made predictions for other trials. Galileo made his calculations based on the theory that "the squares of the speeds acquired in vertical fall to the table top are proportional to the distances fallen from rest ... Since all distances were traversed in the same time ... they are proportional to the speeds acquired in the initial fall ..." [1]. From this, if D is the horizontal distance and S is the vertical fall from rest, the relationship is that the ratio of the squares of the D's is equal to the ratio of the S's. After finding an inital point, one S and one D, given another S, the value for D corresponding to the second S could be predicted. Galileo's initial point was the smallest vertical fall from rest and its corresponding horizontal distance. By this method, he made fairly accurate predictions. Based on Galileo's data as reproduced in Drake's article in Isis the largest percent error between the predicted and the observed was [(observed-predicted)/observed*100] 3.50%. [1]
Using the same method as Galileo, the results we obtained are:
TRIAL ONE (angle 13.4 degrees) 4 ft
roll dist | fall dist | horz dist(avg) | pred dist | % diff |
---|---|---|---|---|
1 ft | 0.232 ft | 1.163 ft | 1.163 ft | initial point |
2 ft | 0.464 ft | 1.649 ft | 1.645 ft | 0.227 |
0.927 ft | 2.305 ft | 2.327 ft | 0.951 | |
6 ft | 1.391 ft | 2.783 ft | 2.850 ft | 2.423 |
TRIAL TWO (angle 6.7 degrees)
roll dist | fall dist | horz dist(avg) | pred dist | % diff |
---|---|---|---|---|
1 ft | 0.117 ft | 0.891 ft | 0.891 ft | initial point |
2 ft | 0.233 ft | 1.211 ft | 1.260 ft | 4.026 |
4 ft | 0.467 ft | 1.720 ft | 1.782 ft | 3.576 |
6 ft | 0.700 ft | 2.130 ft | 2.182 ft | 2.430 |
8 ft | 0.933 ft | 2.458 ft | 2.519 ft | 2.519 |
written by: Sharmaine Jennings
email address: vanese@owlnet.rice.edu
last revised: April 17, 1995