Phy 231
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): **
I found the ramp in the lab materials that I asked about on the last lab. Sorry about that! :) The hotwheels ramp worked fine though. Do I need to redo it?
** first line ruler markings, distance in actual cm between ends, how obtained: **
10, 27.9 cm
7.46 cm
I used the doubly-reduced ruler and got a measurement between 10 and 27.9, so 27.9 - 10 cm = 17.9 cm, and since 2.4 cm corresponds to one actual cm, 17.9 cm/2.4 cm = 7.46 cm. The rubber band is marked 1. Since the greatest measurement marked is millimeters, we can tell to within +-.5mL or +-.05cm.
** The basis for your uncertainty estimate: **
Well, the uncertainty would be +- half of the smallest marker (which is the millimeter line), and since we haven't done any calculations with them yet, it remains +-.05cm.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10, 27.6
10, 27.4
10, 26.9
10, 27.6
10, 27.6
End
7.33, 7.25, 7.04, 7.33, 7.33
1, 2, 3, 4, 5, 6
+-.05cm
** Distances between ends when supporting 2 dominoes **
7.5, 7.38, 7.38, 7.21, 7.38, 7.5
These results were from the weight of two dominoes.
** Lengths when supporting 4, 6, ... dominoes: **
7.71, 7.42, 7.63, 7.49, 7.46, 7.79
8.04, 7.71, 7.88, 7.63, 7.71, 7.92
8.25, 8.04, 8.17, 7.71, 8.13, 8.21
8.42, 8.13, 8.25, 7.96, 8.17, 8.42
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.46, 7.33, 7.25, 7.04, 7.33, 7.33, .19
7.5, 7.38, 7.38, 7.21, 7.38, 7.5, .38
7.71, 7.42, 7.63, 7.50, 7.46, 7.79, .76
8.04, 7.71, 7.88, 7.63, 7.71, 7.92, 1.14
8.25, 8.04, 8.17, 7.71, 8.13, 8.21, 1.42
8.42, 8.13, 8.25, 7.96, 8.17, 8.42, 1.8
End
These are the lengths of bands 1-6 for 1 domino, 2 dom, 4 dom, 6 dom, 8 dom, 10 dom, followed by the force for each respective pile of dominos. The units are in cm.
** Describe the graph of your first rubber band **
The first graph is increasing at an increasing rate and then increasing at a decreasing rate.
The second graph is increasing at an increasing rate, and then increasing at a decreasing rate, and then increasing at an increasing rate.
The third graph is increasing fairly constantly, and then increasing at an increasing rate at the end.
The fourth graph is increasing at an increasing rate, and then increasing at a decreasing rate.
The fifth graph is increasing at an increasing rate, increasing at a decreasing rate, and then increasing at an increasing rate again.
The sixth graph is increasing at an increasing rate, increasing at a decreasing rate, then increasing at an increasing rate again, but it's more slight than the other graphs.
End
** The tension force in your first rubber band at length 9.8 cm: **
That would be way off my graph at about 5 or 6 N.
** The length of your first rubber band when tension is 1.4 N: **
8.19
** 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: **
.25, .30, .71, 1.2, 1.44, 1.76
It differs, respectively, by .06, .08, .05, .06, .02, and .04 N
** 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: **
7.38, 7.56, 7.8, 7.98, 8.23, 8.48
0.08, 0.06, 0.05, 0.06, 0.02, 0.06 cm
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the curve because it averages out all the values.
Well, I use the cm marks on a ruler to construct my graph on paper since my graphing calculator is shot, and since the mm tick marks on the ruler correspond to an actual mm (I began the graph at 7 cm and ended it at 9), I could technically have been accurate to +-.05cm, but since I didn't mark those mm, and only marked cm and half cm, then I'd be accurate to about +-.25 cm (since the closest tick marks are in .5cm intervals).
I did the same thing for the N marks. Using my ruler I marked off N in half N (every cm was a half N, and I only ticked on the integer cm), so since the smallest tick mark is .5 N, I'd be accurate to +-.25 N. Although, had I marked off the mm marks from the ruler or the .05 N marks, I would have been accurate to +-.025 N.
** The typical error you estimate when predicting length for a given force from your graphs: **
Again, since I measured the cm in .5 cm marks, I'd have +-.25 cm uncertainty since 0.5cm/2 = .25, and we aren't calculating anything else with that uncertainty, so it doesn't compound.
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3 hours
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&#This looks very good. Let me know if you have any questions. &#