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: **
10.0,17.3
8.20,8.30,7.10,7.60,7.70
The numbers above are the distances between each rubber band from the top down; respectively: #4, #2, #1, #3, #5, #6. The measurements are believed to be accurate within .05 cm.
** The basis for your uncertainty estimate: **
Considering the lighting in this room, and the fact that double checking my measurements often resulted in a change of .05 cm.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10.00,17.30
10.00,17.40
10.00,17.40
10.00,17.40
10.00,17.35
10.00,17.35
end
8.20,8.30,7.10,7.60,7.70
4,2,1,3,5,6 are the numbers of the rubber bands from top to bottom.
Uncertainty is + or - 0.05 cm
** Distances between ends when supporting 2 dominoes **
7.45,7.55,7.60,7.60,7.50,7.50
The above are the lengths of the rubber bands from the weigt of two dominos.
** Lengths when supporting 4, 6, ... dominoes: **
7.70,7.75,7.80,7.80,7.75,7.80
4
7.90,8.00,8.10,8.05,8.00,7.95
6
8.10,8.20,8.30,8.30,8.25,8.10
8
8.45,8.55,8.65,8.70,8.60,8.35
10
8.85,9.00,9.05,9.05,9.10,8.75
12
9.20,9.30,9.45,9.55,9.55,9.20
14
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.30,7.40,7.40,7.40,7.35,7.35, .19 Newtons
7.45,7.55,7.60,7.60,7.50,7.50, .38 Newtons
7.70,7.75,7.80,7.80,7.75,7.80, .76 Newtons
7.90,8.00,8.10,8.05,8.00,7.95, 1.14 Newtons
8.10,8.20,8.30,8.30,8.25,8.10, 1.52 Newtons
8.45,8.55,8.65,8.70,8.60,8.35, 1.90 Newtons
8.85,9.00,9.05,9.05,9.10,8.75, 2.28 Newtons
9.20,9.30,9.45,9.55,9.55,9.20, 2.66 Newtons
End
Each column represent the measurements in cm of one rubber band with each subsequent addition of dominos. The last column represents the downward force exerted by gravity on the donimos.
** Describe the graph of your first rubber band **
The shape of the (force vs. length) curve fitting the behavior of the first rubber band can be descrived as increasing at an increasing rate up to the point were 8 dominos were added. The behavior of the graph then can be described as increasing at a constant rate. The rubber bands are all oval in shape.
End
** The tension force in your first rubber band at length 9.8 cm: **
3.3 Newtons
** The length of your first rubber band when tension is 1.4 N: **
8.0 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: **
.19,.40,.77,1.20,1.45,1.90,2.30,2.60
.07 Newtons is the maximun deviation.
** 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: **
7.3,7.42,7.67,7.89,8.15,8.45,8.82,9.22
0,-.03,-.03,-.01,.05,0,-.03,.02
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the values from the table, because they are the actual values reported for each respective weight. The uncertainty of the graph has proven to deviate by as much as .07 Newtons from an actual value.
This is a valid conclusion provided your measurements are sufficiently accurate; otherwise the smoothed trend of the graph is more likely to be accurate.
** The typical error you estimate when predicting length for a given force from your graphs: **
+-.05 cm
To help account for parallax and systematic errors, I used the maximun deviation for uncertainty.
** **
Probably 7 hrs., but maybe could have been done in 4.
** **
To keep the time to a minimum, I would eliminate all but one rubber band. Six rubber bands is uneccessary, especially for the limited educational purposes of this experiment.
We're not done with the rubber bands yet--this experiment is only the beginning. For example, if you integrate the force vs. length function you get a stored-energy function. And you'll need at least 4 of the rubber bands is subsequent experiments. Rubber bands also have significant and interesting thermodynamical behaviors. Once you understand rubber bands, you easily can deal with ideal spring and you're prepared to handle real springs.
However the intent here was 1-2 hours, not seven. Typical reported times range from 1.5 hours to 3.5 hours; the experiment therefore does tend to run a bit longer than intended.