Phy 201
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 cm, 22.30 cm
12.30 cm
I obtained the number on the second line by subtracting the two numbers on the first line. The number on the second line indicates the overall length of the topmost rubber band. I believe the number to be accurate to .1 cm, using the single-reduced ruler.
** #$&* The basis for your uncertainty estimate: **
My estimate of uncertainty, allows for any distortion and any measurement inaccuracy that may occur.
** #$&* Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10.00 cm, 21.30 cm
10.00 cm, 17.00 cm
10.00 cm, 17.10 cm
10.00 cm, 19.40 cm
10.00 cm, 19.60 cm
10.00 cm, 18.40 cm
End
11.30 cm, 7.00 cm, 7.10 cm, 9.40 cm, 9.60 cm, 8.40 cm
1, 2, 3, 4, 5, 6
+ or - .1 cm
** #$&* Distances between ends when supporting 2 dominoes **
11.90 cm, 7.10 cm, 7.30 cm, 9.50 cm, 9.70 cm, 8.50 cm
These are the lengths of the rubber bands under the weight of 2 dominoes.
** #$&* Lengths when supporting 4, 6, ... dominoes: **
12.50 cm, 7.70 cm, 7.80 cm, 9.80 cm, 9.90 cm, 8.80 cm
The previous numbers are lengths of the rubber bands supporting 4 dominoes.
13.10 cm, 8.20 cm, 8.00 cm, 9.90 cm, 10.40 cm, 9.50 cm
The previous numbers are lengths of the rubber bands supporting 6 dominoes.
13.60 cm, 8.30 cm, 8.10 cm, 10.10 cm, 10.50 cm, 9.60 cm
The previous numbers are lengths of the rubber bands supporting 8 dominoes.
14.90 cm, 8.50 cm, 8.20 cm, 11.00 cm, 11.10 cm, 9.90 cm
The previous numbers are lengths of the rubber bands supporting 10 dominoes.
** #$&* Your table of force in Newtons vs. length in cm for all rubber bands **
11.30 cm, 7.00 cm, 7.10 cm, 9.40 cm, 9.60 cm, 8.40 cm, .19 N
11.90 cm, 7.10 cm, 7.30 cm, 9.50 cm, 9.70 cm, 8.50 cm, .38 N
12.50 cm, 7.70 cm, 7.80 cm, 9.80 cm, 9.90 cm, 8.80 cm, .76 N
13.10 cm, 8.20 cm, 8.00 cm, 9.90 cm, 10.40 cm, 9.50 cm, 1.14 N
13.60 cm, 8.30 cm, 8.10 cm, 10.10 cm, 10.50 cm, 9.60 cm, 1.52 N
14.90 cm, 8.50 cm, 8.20 cm, 11.00 cm, 11.10 cm, 9.90 cm, 1.9 N
End
The first 6 columns of the table indicate the lengths of the 6 rubber bands, measured in cm. The seventh column, is the force exerted on the rubber bands, measured in Newtons.
** #$&* Describe the graph of your first rubber band **
The first graph, indicates force vs. length for rubber band #1. It is increasing at an increasing rate, then increasing at a decreasing rate.
The second graph, indicates force vs. length for rubber band #2. It is increasing at an increasing rate throughout.
The third graph, indicates force vs. length for rubber band #3. It is increasing at an increasing rate throughout.
The fourth graph, indicates force vs. length for rubber band #4. It is increasing at an increasing rate, then increasing at a decreasing rate.
The fifth graph, indicates force vs. length for rubber band #5. It is increasing at a decreasing rate throughout.
The sixth graph, indicates force vs. length for rubber band #6. It is increasing at an increasing rate, then increasing at a decreasing rate.
End
** #$&* The tension force in your first rubber band at length 9.8 cm: **
This force does not exist, because the length of the rubber band is over 9.8 cm with no force applied.
** #$&* The length of your first rubber band when tension is 1.4 N: **
I would estimate the length of rubber band #1 to be about 13.40 cm.
** #$&* The forces at your observed lengths the 1st rubber band, as given by the curve, and the deviations of those curve-predicted lengths from the observed lengths: **
.185 N, .375 N, .80 N, 1.10 N, 1.40 N, 2.0 N
.005 N, .005 N, .04 N, .04 N, .12 N, .10 N
** #$&* 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: **
11.20 cm, 11.80 cm, 12.40 cm, 13.00 cm, 13.75 cm, 14.50 cm
.10 cm, .10 cm, .10 cm, .10 cm, .15 cm, .40 cm
** #$&* The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the numbers reported in the table, because the curve of best fit is an estimate, whereas the table numbers were actually taken.
I believe my uncertainty for the force to have an uncertainty of + or - .15 N, because some of the estimates for the first graph were coming close to this in variance.
** #$&* The typical error you estimate when predicting length for a given force from your graphs: **
+ or - .5 cm. The estimating for the curve of best fit, gave variance numbers coming close to this, so this would be my conservative estimate.
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2 hours 30 minutes
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&#Very good responses. Let me know if you have questions. &#