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: **
4.0, 11.5
7.50 cm
The number in the second line was just obtained by finding the distance from the two points in the first line.
** The basis for your uncertainty estimate: **
Measuring to the 0.01 cm mark makes the measurement more precise and accurate. In the above box 7.50 cm can be +0.01 or -0.01 of the 7.50 cm mark.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
1.0, 12.6
1.0, 14.2
1.0, 12.8
1.0, 13.0
1.0, 12.1
1.0, 12.8
End
11.60, 13.20, 11.80, 12.00, 11.10, 11.80
1, 2, 3, 4, 5, 6
+/-0.01
** Distances between ends when supporting 2 dominoes **
12.40, 13.30, 12.00, 12.50, 11.00, 12.30
These results were from the weight of two dominoes.
** Lengths when supporting 4, 6, ... dominoes: **
12.00, 13.70, 12.80, 12.60, 10.90, 11.60
4
12.00, 13.70, 11.90, 12.70, 11.70, 11.60
6
13.00, 14.80, 12.80, 15.30, 12.40, 13.50
8
13.10, 15.10, 12.90, 15.80, 13.00, 14.20
10
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
11.60, 13.20, 11.80, 12.00, 11.10, 11.80 ; 2.204, 2.508, 2.242, 2.280, 2.109, 2.242
1
12.40, 13.30, 12.00, 12.50, 11.00, 12.30 ; 2.356, 2.527, 2.280, 2.375, 2.09, 2.337
2
12.00, 13.70, 12.80, 12.60, 10.90, 11.60 ; 2.280, 2.603, 2.432, 2.394, 2.071, 2.204
4
12.00, 13.70, 11.90, 12.70, 11.70, 11.60 ; 2.280, 2.603, 2.261, 2.413, 2.223, 2.204
6
13.00, 14.80, 12.80, 15.30, 12.40, 13.50 ; 2.470, 2.812, 2.432, 2.907, 2.356, 2.565
8
13.10, 15.10, 12.90, 15.80, 13.00, 14.20 ; 2.489, 2.869, 2.451, 3.002, 2.470, 2.698
10
End
** Describe the graph of your first rubber band **
Rubberbands 1-6 all increased at relatively constant rate. My points were extremely close together it was hard to tell the variance in the distance.
End
Each is listed from 1 to 10 dominoes which is what it took for one rubberband to be stretched 33%
Rubber Band 1
L(cm) F(N)
11.6 2.204
12.4 2.356
11.5 2.185
12 2.28
13 2.47
12 2.28
12.9 2.451
13 2.47
13.3 2.527
13.1 2.489
Rubberband 2
L(cm) F(N)
13.2 2.508
13.3 2.527
13.5 2.565
13.7 2.603
14 2.66
13.7 2.603
14.5 2.755
14.8 2.812
15.2 2.888
15.1 2.869
Rubberband 3
L(cm) F(N)
11.8 2.242
12 2.28
11.5 2.185
12.8 2.432
12.2 2.318
11.9 2.261
12.7 2.413
12.8 2.432
13.1 2.489
12.9 2.451
Rubberband 4
L(cm) F(N)
12 2.28
12.5 2.375
12.4 2.356
12.6 2.394
12.5 2.375
12.7 2.13
13.6 2.584
15.3 2.907
15.5 2.945
15.8 3.002
Rubberband 5
L(cm) F(N)
11.1 2.109
11 2.09
12.5 2.375
10.9 2.074
11.4 2.166
11.7 2.223
11.1 2.109
12.4 2.356
11.2 2.128
13 2.47
Rubberband 6
L(cm) F(N)
11.8 2.242
12.3 2.337
11.9 2.261
11.6 2.204
13 2.47
11.6 2.204
13.1 2.489
13.5 2.565
13.8 2.622
14.2 2.698
** The tension force in your first rubber band at length 9.8 cm: **
1.8 N
** The length of your first rubber band when tension is 1.4 N: **
7.8 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: **
2.200, 2.350, 2.280, 2.280, 2.48
It is roughly the same.
** 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: **
2.204, 4.712, 9.12. 13.68
I multiplied 0.19 by each length so they differ a lot.
** The typical error you estimate when predicting force for a given length from your graphs: **
The values that I reported in the table are more accurate.
Each force was multiplied by 0.19 N and then I would allow a variance of +/- 0.05 N.
** The typical error you estimate when predicting length for a given force from your graphs: **
+/- 0.05
It is easy to be off by 5 hundredths of a centimeter. It is easiest to estimate by 0.05 cm.
** **
3 hours
** **
You appear to have excellent data.
The lengths of the rubber bands are a bit greater than those generally reported. Did you measure these with standard centimeters or with one of the reduced rulers? No problem either way, as long as you specify which was used and use the same rulers for subsequent experiments with rubber bands. If you used one ruler for calibration then later measured distances with another ruler, your graphs would give you incorrect forces.