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: **
1, 8.35
7.35 cm.
I obtained the number in the second line by finding how many centimeters the rubber band was from top to bottom. The rubber band was marked with a number 1, and I believe the accuracy to be +-.03 cm.
** The basis for your uncertainty estimate: **
The uncertainty can be attributed to the distortion of the ruler, and also human error. The measurement is so small, it is difficult to determine the exact measure by just looking at it.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
1, 8.35
1, 8.48
1, 8.55
1, 8.25
1, 8.45
1, 8.56
End
7.35, 7.48, 7.55,7.25, 7.45, 7.56
I marked the rubber bands by putting a 1,2,3,4,5, and 6 on the corresponding band. The uncertainty for this is +-.03.
** Distances between ends when supporting 2 dominoes **
7.62, 7.55, 7.65, 7.55, 7.65, 7.72
These results were gained from the weight of two dominoes.
** Lengths when supporting 4, 6, ... dominoes: **
7.84, 7.88, 7.91, 7.68, 7.85, 7.75
4
8.08, 7.98, 8.13, 7.85, 7.92, 7.95
6
8.41, 8.25, 8.55, 8.12, 8.18, 8.25
8
8.78, 8.62, 8.68, 8.45, 8.35, 8.55
10
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.35, 7.48, 7.55,7.25, 7.45, 7.56, .19
7.62, 7.55, 7.65, 7.55, 7.65, 7.72, .38
7.84, 7.88, 7.91, 7.68, 7.85, 7.75, .76
8.08, 7.98, 8.13, 7.85, 7.92, 7.95, 1.14
8.41, 8.25, 8.55, 8.12, 8.18, 8.25, 1.52
8.78, 8.62, 8.68, 8.45, 8.35, 8.55, 1.9
** Describe the graph of your first rubber band **
The first is also described as increasing at a decreasing rate, then increasing at an increasing rate. The second rubber band increased at a fairly constant rate, then at an increasing rate. The third rubber band increased at an increasing rate, and at the very end increased at a decreasing rate. The fourth shape increased at a decreasing rate, then at an increasing rate. The fifth increased at a decreasing rate, then at a constant rate. The sixth increased at a constant rate, then at a decreasing rate.
End
** The tension force in your first rubber band at length 9.8 cm: **
3 N
** The length of your first rubber band when tension is 1.4 N: **
8.2 cm
** 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: **
.19, .38, .76, 1.14, 1.52, 1.9
The curve differs from the actual weight supported because of the weight of the rubber bands and paper clips. Without these weights factored in, the actual weight will not be exact.
** 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: **
7.35, 7.62, 7.84, 8.08, 8.41, 8.78
I am not sure I understand what the second part of this question is asking.
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the values reported in the table. This is true because I measured each one and I know that it is more precise than an estimate. I believe the uncertainty is about +-.03. My evidence for this is that it is difficult to be exact in estimating, especially since the line of the graph does not pass through the points exactly.
** The typical error you estimate when predicting length for a given force from your graphs: **
I believe the uncertainty would be around +-.05. This is true because it is so difficult to see the small measurements and there could be human error. It is difficult to simply eye-ball the measurement.
** **
2 hours!
** **
I was a bit confused by the third to the last question. I thought the measurements corresponding to the forces were the ones I had previously recorded.
Your observations cannot be 100% accurate. Uncertainties are unavoidable. The question is whether your observations, with their unavoidable uncertainties, are more representative of the lengths than the 'smoothed' data of your graph. There is no one correct answer; it depends on the data set. However an answer based on the assumption that the data are completely accurate would not be justified.