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:
20.0cm, 28.91cm
8.91cm
The first number is the beginning of the rubber band and the second number is the end of the rubber band. The number in the second line is the difference of those two numbers, or the length of the rubber band. I believe that the number is within +-.01cm since it is almost on the line for 8.90 cm. It is not far form this.
The basis for your uncertainty estimate:
I believe the uncertainty of the length has to be 0.01 since that is the level where human estimation comes into play. The human eye has to decide the fraction of the millimeter. The lines on the ruler help and can be relied upon, but only to a certain point.
Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:
20.0cm, 28.9cm
20.0cm, 29.29cm
20.0cm,28.93cm
20.0cm,28.98cm
20.0cm,28.67cm
END
8.91cm,9.29cm,8.93cm,8.98cm,8.67cm
I,II,III,IIII,IIIII
The uncertainty in these measurements I would say is more like +-.03 since the values are more spaced between the millimeter markings. That is the amount that I believe could be a discrepancy between the human value and the true value.
Distances between ends when supporting 2 dominoes
9.19cm,9.33cm,9.02cm,9.08cm,8.87cm
These are from the weight of two dominoes.
Lengths when supporting 4, 6, ... dominoes:
9.41cm,9.81cm,9.42cm,9.39cm,9.12cm
4
9.86cm,10.19cm,9.88cm,9.92cm,9.4cm
6
10.12cm,10.61cm,10.13cm,10.29cm,10.03cm
8
10.63cm,11.24cm,10.72cm,10.74cm,10.46cm
10
End
Your table of force in Newtons vs. length in cm for all rubber bands
8.91cm,9.29cm,8.93cm,8.98cm,8.67cm, .19Newtons
9.19cm,9.33cm,9.02cm,9.08cm,8.87cm, .38Newtons
9.41cm,9.81cm,9.42cm,9.39cm,9.12cm, .76Newtons
9.86cm,10.19cm,9.88cm,9.92cm,9.4cm, 1.14Newtons
10.12cm,10.61cm,10.13cm,10.29cm,10.03cm, 1.52Newtons
10.63cm,11.24cm,10.72cm,10.74cm,10.46cm, 1.90Newtons
End
The measurements are in cm and measure the lengths of five rubber bands supporting the weight of 1, 2, 4, 6, 8, or 10 dominoes, respectfully.
Describe the graph of your first rubber band
The graph appears to be increasing at an increasing rate, then increasing at a decreasing rate. It is in general approximately linear.
Bands III and IIII had nearly identical graphs that increase decreasingly, increasingly and then finally decreasingly. Band 5 and 2 were similar graphs that increase increasingly then decreasingly.
End
The tension force in your first rubber band at length 9.8 cm:
1.2 Newtons
The length of your first rubber band when tension is 1.4 N:
10.1 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,.5,.75,1.4,1.5,1.8
.01,.12,.01,.26,.02,.1
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:
8.8cm,9.2cm,9.45cm,9.8cm,10.1cm,10.6cm
.11,.01,.04,.06,.02,.03
The typical error you estimate when predicting force for a given length from your graphs:
I have more faith in my curve than my table since the curve allows for averages and changes. THe table is a clear cut square set of data that may or may not be right.
The uncertainty would be +-.01Newtons since the Newtons seem to hold more constant when the curve is compared to the data table. There was not much more of a discrepancy than the hundredths place for the Newtons.
The typical error you estimate when predicting length for a given force from your graphs:
I would say the uncertainty of the length would be more like +-0.1cm since the length has a higher difference between the data table values and the curve. The uncertainty is higher in this factor since it is more based on human error.
Good work. We may discuss this further in an online discussion.