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: **
1.00, 8.71
7.71
The second line is actual length of the rubber band in cm (Actual length = final length - starting length). The error is estimated to be within +- .03 cm
** The basis for your uncertainty estimate: **
I think that my eyes are probably good enough to be able to discriminate a mm into about three pieces.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
1.0, 8.71
1.0, 8.75
1.0, 8.67
1.0, 8.65
1.0, 8.58
1.0, 8.55
End
7.71, 7.75, 7.67, 7.65, 7.58, 7.55
Uncertainty of all measurements is +- .03cm
** Distances between ends when supporting 2 dominoes **
7.91, 7.85, 7.91, 7.85, 7.90, 7.75
Lengths in cm for all 6 rubber bands while using two dominoes as weight.
** Lengths when supporting 4, 6, ... dominoes: **
8.18, 8.20, 8.03, 8.08, 7.97, 7.99
4
8.30, 8.34, 8.28, 8.40, 8.29, 8.22
6
8.50, 8.50, 8.41, 8.48, 8.40, 8.43
8
8.51, 8.58, 8.49, 8.60, 8.53, 8.47
9
End
All values are for lengths of rubber bands in cm to +- .03 cm.
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.71, 7.75, 7.67, 7.65, 7.58, 7.55, .19
7.91, 7.85, 7.91, 7.85, 7.90, 7.75, .38
8.18, 8.20, 8.03, 8.08, 7.97, 7.99, .76
8.30, 8.34, 8.28, 8.40, 8.29, 8.22, 1.14
8.50, 8.50, 8.41, 8.48, 8.40, 8.43, 1.52
8.51, 8.58, 8.49, 8.60, 8.53, 8.47, 1.71
End
Lengths of rubber bands with various forces applied. First 6 columns correspond to particular bands, 7th column equals force in newtons applied to each.
** Describe the graph of your first rubber band **
The first rubber band has a curve that increases at a gently increasing rate with a sharp increase at the end.
The second rubber band has a graph that is increasing in a mostly linear fashion.
The third rubber band has a graph that is increasing at an increasing rate, slowly at first, then faster for a while, then in a roughly linear fashion.
The fourth rubber band has a graph that is increasing slowly at first and then at a greatly increasing rate towards the end.
The fifth rubber band has a graph that is increasing. It increases at a linear rate, then increases quickly, then at a linear rate, and then quickly again.
the sixth rubber band increases at a smooth and slightly increasing rate.
End
** The tension force in your first rubber band at length 9.8 cm: **
2.5 Newtons
** The length of your first rubber band when tension is 1.4 N: **
8.4
** 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: **
.2, .35, .85, 1.15, 1.5, 1.7
.01, .03, .09, .01, .02, .01
** 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: **
.18N, .36N, .77N, 1.10 N, 1.50N, 1.70N
.01N, .02N, .01N, .04 N, .02N, .01N
** The typical error you estimate when predicting force for a given length from your graphs: **
I would tend to have more faith in the points that I measured... call me old fashioned I guess. However I measured these values, and I would tend to to rely on them more than the curve. I would rather take more measurments and average them than try to use a curve to infer an average across such a small data set. I would say +-.04 N is a reasonable estimate for uncertainty, none of my numbers show a much larger gap than that.
** The typical error you estimate when predicting length for a given force from your graphs: **
Again, I think that +- .04 is a reasonable number. I had an average around four, with most being lower, and then one number being about .09, but that was the only aberrent data point.
** **
2 hours 44 minutes
** **
Very good work. Be sure to hang onto the rubber bands and their calibrations for upcoming experiments.