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: **
2.000, 10.00
8.00 cm
To obtain these numbers I followed the instructions and used my ruler at 10 cm for the bottom of the 1st rubberband and measured to the top. The rubberband stretched from 7.50 cm to 8.00 cm. I think it is accurate withing 0.05 cm. My rubberband is marked with a pen, because I did not recieve the marked rubberbands in my standard kit.
** The basis for your uncertainty estimate: **
I based this on the fact my initial rubberband was 7.50 cm. After adding one domino it appeared as though it gained .50 cm exactly. However I know this is not true, due to human error when viewing, so I gave myself .05 cm both ways on my judgement.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
2.000, 10.00
2.000, 10.00
2.000, 10.00
2.000, 10.00
2.000, 10.00
2.000, 10.00
end
They were all 8.00 cm, thus they all stretched 0.50 cm.
I marked each rubberband w / a pen that displayed a number so I could distinguish them.
The uncertainity will be on the 0.01 decimal. This is because the ruler I used only showed cm and .1 of cm.
** Distances between ends when supporting 2 dominoes **
8.25, 8.25, 8.25, 8.25, 8.25, 8.25
results of 2 dominos.
** Lengths when supporting 4, 6, ... dominoes: **
8.50, 8.50, 8.50, 8.50, 8.50, 8.50
4
8.75, 8.75, 8.75, 8.75, 8.75, 8.75
6
9.00, 9.00, 9.00, 9.00, 9.00, 9.00
8
9.50, 9.50, 9.50, 9.50, 9.50, 9.50
10
Your results are completely uniform for all six rubber bands. The chances of the rubber bands being that uniform at to the nearest millimeter are practically zero. There will be significant variations in the lengths of the individual rubber bands when the chain supports these loads.
** Your table of force in Newtons vs. length in cm for all rubber bands **
8.00, 0.19
8.25, 0.38
8.50, 0.76
8.75, 1.14
9.00, 1.52
9.50, 1.90
end
The first column contains the distance, this is measured in cm. The second column contains the force being exerted by the dominos in the bag, this unit is Newtons.
** Describe the graph of your first rubber band **
It is a straight line that I drew to try to cover all of the points with an equal distance.
Increasing at a decreasing rate then at an increasing rate. The first few dots were really close together as far as length vs. force goes, but with each one they spreaded out even further. They force really begins to play a factor, and so does gravity (9.8 m/s)
end
** The tension force in your first rubber band at length 9.8 cm: **
2.1 F
** The length of your first rubber band when tension is 1.4 N: **
8.90 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: **
1.10, 1.50, 1.75, 2.4, 2.7
.10, .30, .25, .65, .8
** 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, 8.33, 8.50, 8.75, 9.25, 9.75
0, .08, 0, .25, .25, .25
** The typical error you estimate when predicting force for a given length from your graphs: **
Values reported in table, because once I created my lines, I felt that if there was any miscalculations they could be accounted for when I drew my best fit line.
if it was at the begining of the graph I would say +-0.3 N, if it was at the end I would say +-.12 N. Simply because at the begining the graph was increasing at a decreasing rate, and at the end it was increasing at an increasing rate.
** The typical error you estimate when predicting length for a given force from your graphs: **
+-.25. Simply because the way the graph is positioned, especially at the end where it is increasing at an increasing rate.
** **
3 hrs, had some of it previously completed.
** **
It does not appear that you have data for all six rubber bands. You need to have six well-calibrated rubber bands, six different graphs.
A single calibration applied to different rubber bands will lead to large errors in any subsequent experiments that use these rubber bands.