Your work on rubber band calibration 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:
10.6, 10.6
7.57, 7.57
I obtained the numbers in the second line by dividing the ruler markings by 1.4 because I used the singly reduced ruler to measure. I believe the units are accurate to +-.03.
The basis for your uncertainty estimate:
The measurements may not be exact because of distirtion and optical uncertainties but they should be accurate to the .03.
Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:
10.6, 10.6
10.0, 10.5
10.6, 10.6
10.4, 10.4
10.2, 10.2
End
7.57, 7.14, 7.57, 7.43, 7.29
1, 2, 3, 4, 5
Uncertainty is +-.03
Distances between ends when supporting 2 dominoes
7.68, 7.22, 7.63, 7.49, 7.63
These results correspond to the weight of two dominos.
Lengths when supporting 4, 6, ... dominoes:
7.72, 7.51, 7.95, 7.63, 7.60
4
8.13, 7.60, 8.05, 7.90, 7.75
6
8.25, 7.93, 8.30, 8.10, 7.95
8
8.62, 8.10, 8.50, 8.30, 8.15
10
End
Your table of force in Newtons vs. length in cm for all rubber bands
7.57, 7.14, 7.57, 7.43, 7.29, .19
7.68, 7.22, 7.63, 7.49, 7.43, .38
7.72, 7.51, 7.95, 7.63, 7.60, .76
8.13, 7.60, 8.05, 7.90, 7.75, 1.14
8.25, 7.93, 8.30, 8.10, 7.95, 1.52
8.62, 8.10, 8.50, 8.30, 8.15, 1.9
End
In each line, the first five numbers represent lengths in cm. The last number in each line corresponds to the downward force exerted by gravity in Newtons.
Describe the graph of your first rubber band
The shape is a relatively straight line that is increasing. The graph is increasing at a constant rate.
The tension force in your first rubber band at length 9.8 cm:
This is not possible because I did not have any lengths to graph up to 9.8cm.
The length of your first rubber band when tension is 1.4 N:
7.7
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:
.1, .3, .4, .8, 1.2, 1.7
I believe that the estimate of the curve differs by about .1 to the actual weight supported. It is hard to remain precise when there are so many calcluations involved that already contain uncertanties.
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:
7.55, 7.70, 8.00, 8.20, 8.50, 8.70
.02, .02, .08, .07, .25, .08
I have more faith in the curve.
The typical error you estimate when predicting force for a given length from your graphs:
+-.1
Oce all of the uncertainty factors are taken into consideration, the graphs cannot be any more accurate than .1.
The typical error you estimate when predicting length for a given force from your graphs:
+-.1cm
With all of the factors of uncertainty taken into consideration, the graphs cannot ne any more accurate than .1.
Good work. We will be discussing this further after the due date.