Your 'rubber band calibration' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your initial comment (if any): **
** first line ruler markings, distance in actual cm between ends, how obtained: **
97.0,71.0
7.02
These measurements were taken using the triply reduced rulers. This rubber band is marked with a single mark. I believe that the accuracy is +-0.03cm.
** The basis for your uncertainty estimate: **
The length of one triply-reduced millimeter is equal about 0.027cm.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
97.0,71.0
97.9.72.3
98.0,71.3
96.0,69.0
98.0,72.0
99.0,73.0
End
7.02,7.21,7.21,7.29,7.02,7.02
6,5,4,3,2,1
.03cm
** Distances between ends when supporting 2 dominoes **
7.40,7.13,7.24,7.43,7.29,7.18
** Lengths when supporting 4, 6, ... dominoes: **
7.56,7.29,7.43,7.67,7.29,7.29
7.70,7.53,7.56,7.89,7.43,7.48
7.88,7.72,7.70,8.08,7.69,7.69
8.05,7.88,7.88,8.21,7.83,7.77
8.24,8.05,8.02,8.40,8.05,8.02
8.48,8.26,8.26,8.75,8.24,8.24
8.72,8.52,8.51,8.94,8.45,8.45
8.88,8.75,8.75,9.18,8.64,8.61
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.40,7.13,7.24,7.43,7.29,7.18,0.19
7.56,7.29,7.43,7.67,7.29,7.29,0.38
7.70,7.53,7.56,7.89,7.43,7.48,0.76
7.88,7.72,7.70,8.08,7.69,7.69,1.14
8.05,7.88,7.88,8.21,7.83,7.77,1.52
8.24,8.05,8.02,8.40,8.05,8.02,1.90
8.48,8.26,8.26,8.75,8.24,8.24,2.28
8.72,8.52,8.51,8.94,8.45,8.45,2.66
8.88,8.75,8.75,9.18,8.64,8.61,3.04
End
Each line contains the lengths of the rubber bands from 6 to 1 followed by the force exerted by gravity on the dominoes.
** Describe the graph of your first rubber band **
The sixth rubber band seems to be increasing at an increasing rate, increasing at a decreasing rate and then increasing at an increasing rate.
The fifth rubber band seems to be increasing at an increasing rate, increasing at a decreasing rate and then increasing at an increasing rate.
The fourth rubber band seems to be increasing at an increasing rate, then increasing at a decreasing rate.
The third rubber band seems to be increasing at in an increasing rate, increasing at a decreasing rate, and then increasing at an increasing rate.
The second rubber band seems to increase in straight up, then increase at ian increasing rate, increase at a decreasing rate, and then increase at an increasing rate.
The first rubber band seems to increase at an increasing rate, then increase at a decreasing rate, and then increase at an increasing rate.
End
Some of these graphs could appear to be linear in nature while others do not. I do not see a pattern to it, however.
** The tension force in your first rubber band at length 9.8 cm: **
4.2
** The length of your first rubber band when tension is 1.4 N: **
7.5
** The forces at your observed lengths the 1st rubber band, as given by the curve, and the deviations of those curve-predicted lengths from the observed lengths: **
0.18,0.45.0.75,1.45,1.95,2.39,2.7,2.99
The estimate of the curve differs by about .1N
** The lengths predicted for forces .19 N, .38 N, .76 N, 1.14 N, etc. by the curve for your first rubber band; the deviations of your actual observations from these predictions: **
7.02,7.18,7.5,7.62,7.8,8,8.19,8.4,8.65
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the estimated graph because it is more likely to represent the forces as they occur rather than a few data points. I think that the uncertainty would be about +-0.1N because that seems to be how much my data varies from the graph.
** The typical error you estimate when predicting length for a given force from your graphs: **
I think that my estimate for length would be a bit better due to the precision of the measurements, however my estimates from the graph seem to be off by 0.05cm or so most of the time and at others it seems to be about 0.1cm. Maybe on average it is off about +-0.075cm
** **
2 hours
** **
&#Your work looks very good. Let me know if you have any questions. &#