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:
5.0, 12.1
7.1 cm
The numbers on the first line were the cm markings on the ruler at the top and bottom of the rubberband. Subtracting the first from the second number, gave the actual length in cm of the rubberband, which is given on the second line. The accuracy is + or - .1 cm. This length was measured with an actual ruler, becuase my reduced rulers seemed distorted.
The basis for your uncertainty estimate:
The uncertainty was based on the face that the ruler is only precise to + or - 0.1 cm.
Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:
5.0, 12.1
5.0, 12.0
5.0, 12.0
5.0, 12.1
5.0, 12.1
End
7.10, 7.00, 7.00 cm, 7.10 cm, 7.10 cm
1, 2, 3, 4, 5
+ or - 0.1 uncertainty
Distances between ends when supporting 2 dominoes
7.20, 7.30, 7.20, 7.40, 7.30
The numbers above are measurements in cm, + or - 0.1 cm, of 5 rubberbands in a chain with the weight of 2 dominos pulling down on the chain
Lengths when supporting 4, 6, ... dominoes:
7.6, 7.5, 7.5, 7.7, 7.5
4
7.8, 7.6, 7.6, 7.9, 7.7
6
7.9, 7.8, 7.8, 8.1, 7.9,
8
8.1, 8.1, 8.1, 8.3, 8.1
10
End
Your table of force in Newtons vs. length in cm for all rubber bands
7.10, 7.00, 7.00, 7.10, 7.10, 0.19N
7.20, 7.30, 7.20, 7.40, 7.30, 0.38N
7.60, 7.50, 7.50, 7.70, 7.50, 0.76N
7.80, 7.60, 7.60, 7.90, 7.70, 1.1N
7.90, 7.80, 7.80, 8.10, 7.90, 1.5N
8.10, 8.10, 8.10, 8.30, 8.10, 1.9N
End
Each row in the data listed above represents the stretch of a chain of rubber bands when pulled downward with the force of a certain number of dominos. The First 5 columns represent the length in cm of 5 different rubber bands. The 6th column represents the force in N exerted by gravity on the dominos pulling the chain of rubber bands in that row.
Describe the graph of your first rubber band
The graph of the frist rubber band was increasing at a decreasing rate, then increasing at a constant rate.
The graph of the second rubber band was increasing at an increasin rate and then increasing at a decreasing rate.
The graph of the third rubber band was increasing at a relatively constant rate.
The graph of the 4th rubber band was increasing at an increasing rate and then increasing at a constant rate.
The graph of the 5th rubber band was increasing at an increasing rate and then increasing at a constant rate.
The tension force in your first rubber band at length 9.8 cm:
6.4 N
The length of your first rubber band when tension is 1.4 N:
78 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:
.10, .30, .80, 1.3, 1.6, 2.0
-.09, -.08, .04, .2, .1, .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:
7.15, 7.25, 7.55, 7.70, 7.90, 8.17
.05, .05, -.05, -1.0, 0, .07
The typical error you estimate when predicting force for a given length from your graphs:
I have more faith in my numbers than the curve beacuse I don't know if I drew the curve to best represent the data.
The uncertainty would be about +- 0.2 because this was the greatest distance between the actual numbers and the curve when I previously estimated force for a given length.
The typical error you estimate when predicting length for a given force from your graphs:
The uncertainty would be about +- 1.0 because this was the greatest distance between the actual numbers and the curve when I previously estimated length for a given force.
2.5 hrs
I didn't have enough dominos to actually stretch my rubber bands to near 30% of their original length. Also, you ask us to do a lot of things but there are no boxes to fill in our answers. Ex: In the box below describe the shapes of all six rubber bands, repeating in the first line the description just given for the first, then giving your description for the second rubber band in the second line, etc.. Follow by a line containing the word 'End'. You may if you wish add comments starting on the next line, Describe your curve and describe your thinking about how to construct the curve.
Thanks for pointing out the missing box.
Your work is excellent.