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:
5.00 cm,16.97cm
7.76 cm
I used the middle ruler of the singly-reduced rulers. When measuring the distortion of that ruler, I found that each cm on the paper ruler corresponded to an average of 1.543 cm/ cm on my full sized ruler. I subtracted the initial position measurement from the endpoint measurement to obtain a 11.97 cm interval. I divided the 11.97 cm by 1.543 cm/cm to obtain 7.76 cm +- .03cm.
This is rubber band #1.
The basis for your uncertainty estimate:
I am measuring with markings that indicate .01 cm - .09 cm, and I am certain about whether or not the endpoint falls beyond the halfway point. The uncertainty is between .01 cm and .04 cm or between .06 cm and .09 cm. This results in an estimation range of .03 cm.
Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:
5 cm,16.97 cm
10 cm,21.52 cm
20 cm, 32.01 cm
10 cm, 21.42 cm
10 cm,21.38 cm
10 cm,21.41 cm
end
7.76 cm, 7.47 cm,7.78 cm,7.40 cm, 7.38 cm, 7.39 cm
1,2,3,4,5,6
+- .03 cm
Distances between ends when supporting 2 dominoes
7.92 cm, 7.56 cm, 8.27 cm, 7.59 cm, 7.62 cm,7.53 cm
This is a list of rubber band length when weighted with 2 dominoes.
Lengths when supporting 4, 6, ... dominoes:
8.12 cm, 7.76 cm, 8.11 cm, 7.76 cm, 7.74 cm, 7.73 cm
4
8.34 cm, 7.98 cm, 8.32 cm, 8.04 cm, 8.01 cm, 7.97 cm
6
8.61 cm, 8.14 cm, 8.61 cm, 8.25 cm, 8.11 cm, 8.16 cm
8
8.82 cm, 8.41 cm, 8.87 cm, 8.54 cm, 8.55 cm, 8.48 cm
10
end
Your table of force in Newtons vs. length in cm for all rubber bands
7.76 cm, 7.47 cm,7.78 cm,7.40 cm, 7.38 cm, 7.39 cm
.19
7.92 cm, 7.56 cm, 8.27 cm, 7.59 cm, 7.62 cm,7.53 cm
.38
8.12 cm, 7.76 cm, 8.11 cm, 7.76 cm, 7.74 cm, 7.73 cm
.76
8.34 cm, 7.98 cm, 8.32 cm, 8.04 cm, 8.01 cm, 7.97 cm
1.14
8.61 cm, 8.14 cm, 8.61 cm, 8.25 cm, 8.11 cm, 8.16 cm
1.52
8.82 cm, 8.41 cm, 8.87 cm, 8.54 cm, 8.55 cm, 8.48 cm
1.9
end
This is a list of the lengths of each of six rubber bands supporting an increasing load, alternating with the force in Newtons that the load is exerting on the bands.
Describe the graph of your first rubber band
increasing at a decreasing rate
increasing at a decreasing rate
increasing at a decreasing rate
increasing at a decreasing rate
increasing at a decreasing rate
increasing at a decreasins rate
end
Some of the graphs look closer to levelling off than others, though I didn't get close to 30% stretch for any of them
The tension force in your first rubber band at length 9.8 cm:
2.5
The length of your first rubber band when tension is 1.4 N:
8.43
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:
1.9,.39,.76,1.16,1.59,1.8
0,.01,0,.02,.07,.10
The first four points for the first band fit a smooth curve. The curves of the other bands had more estimation.
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:
7.76,7.89,8.12,8.30,8.51,8.87
0,.03,0,.04,.1,.05
The typical error you estimate when predicting force for a given length from your graphs:
I have more faith in the curve, because the forces we are measuring act in a way that is represented by a smooth curve.
The uncertainty in estimating length from my graphs is about .08, because I used an increment of .15 or .20. The uncertainty in estimating force is about .05 because I used an increment of .19. For both of these quantities, the uncertainty is within half the increment.
The typical error you estimate when predicting length for a given force from your graphs:
Your data here look very good.
Your report has been received. We will be discussing this work as a group, after the due date.