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: **
10.00, 27.50
7.29
The number in the second line was found by taking the measurement of 27.50-10= 17.50 cm on the double-reduced ruler and then dividing this by the 2.4 cm(on double reduced ruler) per actual cm.
The rubber band is marked with 1 line on the inside of it made by a permenat marker.
I believe that these results are accurate to +-0.08 cm.
** The basis for your uncertainty estimate: **
As far as human error goes I believe that we could be off by up to 2 mm on the reduced ruler which would be 0.08 actual cm. Which would be 1% of the total measurement.
There is going to be some error in trying to hold the ruler in place while you get both readings. After you get the first you try to align your head so that you are looking straight at the ruler and there is a good chance that it could move a little as you do this.
Also you are trying to not touch the chain to keep from affecting the length adversly one way or the other.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10.00, 27.50
10.00, 27.75
10.00, 27.30
10.00, 27.80
10.00, 26.90
10.00, 41.90
END
7.29, 7.40, 7.21, 7.42, 7.04, 7.04
The first rubber band has 1 mark made across it sideways, the second has to and so on up to the 6th rubber band that has 6 marks made across it sidways about .5 cm apart.
I believe that these results are accurate to +-0.08 cm.
** Distances between ends when supporting 2 dominoes **
7.46, 7.52, 7.37, 7.48, 7.33, 7.26
These measurements are for each rubber band in cm starting with #1,#2,ets. for 2 Dominoes.
** Lengths when supporting 4, 6, ... dominoes: **
7.50, 7.62, 7.48, 7.75, 7.48, 7.44
4
7.69, 7.79, 7.52, 7.87, 7.62, 7.69
6
7.83, 7.92, 7.79, 7.96, 7.73, 7.77
8
7.94, 7.98, 7.87, 8.27, 8.27, 7.90
10
END
All measurements are in cm.
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.29, 7.40, 7.21, 7.42, 7.04, 7.04, 0.19
7.46, 7.52, 7.37, 7.48, 7.33, 7.26, 0.38
7.50, 7.62, 7.48, 7.75, 7.48, 7.44, 0.76
7.69, 7.79, 7.52, 7.87, 7.62, 7.69, 1.14
7.83, 7.92, 7.79, 7.96, 7.73, 7.77, 1.52
7.94, 7.98, 7.87, 8.27, 8.27, 7.90, 1.90
** Describe the graph of your first rubber band **
The graph of the first rubber band is increasing at an increassing rate over the first three readins then it continues to increase but at a more constant rate. I believe that the second point on this graph has a large error.I believe that I could fit one line very close to all points but the second.
The points from the second rubber band increase at an increasing rate over the first 3 points and then continues to increase at an increasing rate but not as steep. I believe the 3rd point in this graph has some error. I could fit one curve increasing at an increasing rate to all the points except the third.
I don't understand it, but there seems to be a pattern here. With the third rubber band the forth point in this set is the one that seems to be out of line with the other points. This graph is increasing at an increasing rate, then increasing at a decreasing rate and then increasing at an increasing rate againe.
The forth rubber band seems to have 2 waves in the graph. It increases at and increasing rate, increases at a decreasing rate, increases at an incresing rate, and then increases at a decreasing rate againe. It looks a lot different from the other rubber bands.
The 5th rubber band increases at an increasing rate over the first 2 points, then increases at a constant rate untile the last point where it increases at a decreasing rate.
The sixth rubber band increases at an increasing rate except around the last point which seems to increase at a decreasing rate.
ENd
Your results are good and except for the anomalies you noted above are very consistent with what would be expected.
** The tension force in your first rubber band at length 9.8 cm: **
14.8 newtons.
I don't believe thatthis is an accurate reading. None of my points stretched any where close to 9.8 cm and with the line increasing at an increasing rate it throws the reading off by a great deal.
** The length of your first rubber band when tension is 1.4 N: **
7.86 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: **
0.19, 0.43, 0.67, 1.16, 1.61, 1.83
0, 0.05, -0.09, 0.02, 0.09, -0.07
In this example I used the numbers from rubber band #4 and fitted a line that is increasing at an increasing rate over the entire graph.
** 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: **
7.40, 7.50, 7.65, 7.78, 7.90, 8.00
0, -0.02, 0.03, -0.01, -0.02, 0.02
Againe I used the data from rubber band number 4.
** The typical error you estimate when predicting force for a given length from your graphs: **
I believe that the data from the estimated curve is closer to the values for the length. The varience in the numbers all seem to be within +- 0.02.
I believe that any force that we calculate beyond a lengh of 8.3 is going to have an increasing uncertainty.
I believe that the uncertaninty of any of the estimates under a length of 8.3 will be with in +-0.05 N. I determined this by taking the average of the absolute value of the differences between estimated and calculated force.
** The typical error you estimate when predicting length for a given force from your graphs: **
I believe that any estimated measurement againe below 8.3 cm is going to be with in +-0.02. This againe is the average of the absolute value of the differences between the estimated and the calculated length.
** **
3.5 hours.
** **
You appear to have excellent results.