rubber band calibration

Your work on rubber band calibration 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):

My rubber bands were not marked.

first line ruler markings, distance in actual cm between ends, how obtained:

2.0, 11.1

9.15 cm

I obtained the end points by starting the top of the band at the 2cm mark on my ruler and the bottom stopped at the 10.7cm mark. I double checked by using the singly-reduced copy of a ruler. This showed that my measuremet was correct. MY RUBBER BANDS ARE NOT MARKED. I believe that my measurement was accurate to the +-0.1.

The basis for your uncertainty estimate:

I think the uncertainty is +-0.1 because the smallest unit on the rulers was the millimeter which is 1/10 of a centimeter.

Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:

2.0, 11.1

2.0, 10.9

2.1, 10.9

2.0, 10.8

2.1, 11.0

END

9.10, 8.90, 8.80, 8.80, 8.90

MY BANDS HAVE NO MARKINGS

The uncertainty for this reading is the same as the uncertainty for the last which was +-0.1 cm.

Distances between ends when supporting 2 dominoes

9.59, 9.16, 9.19, 9.11, 9.20

The results of adding a domino to the bag made the bag heavier and put more tension on the rubber bands. The top band tends to stretch the most.

Lengths when supporting 4, 6, ... dominoes:

10.22, 10.03, 10.12, 9.91, 10.05

11.49, 11.15, 11.15, 10.78, 11.19

12.15, 11.70, 11.65, 11.30, 11.65

Throughout the entire experiment, the uppermost band maintained the longest stretch.

Your table of force in Newtons vs. length in cm for all rubber bands

9.1, 8.8, 8.9, 8.7, 9.0, 0.19

9.59, 9.16, 9.19, 9.11, 9.2, 0.38

10.22, 10.03, 10.12, 9.91, 10.05, 0.76

11.49, 11.15, 11.14, 10.78, 11.19, 1.14

12.15, 11.7, 11.65, 11.3, 11.65, 1.33

END

Each line represents the lengths of the rubber bands at a certain force as a result of tension from a certain number of dominoes. The first 5 numbers on each line are the lengths of each rubber band, 1 through 5. The last number in the series is the force exerted on the bands. The first line is for 1 domino, the second for 2, the third line for 4, the fourth line for 6, and the last line for 7 dominoes. The bands are measured in centimeters and force is measured in Newtons.

Describe the graph of your first rubber band

The graph for my data was increasing at a decreasing rate. To double check this information, I did a graph for each rubber band. Each band's graph was increasing at a decreasing rate. The third point for each band seemed to increase more. After that point, however, the graphs were still increasing but at a slower rate.

The tension force in your first rubber band at length 9.8 cm:

0.527 Newtons

The length of your first rubber band when tension is 1.4 N:

12.65 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:

0.20, 0.40, 0.75, 1.18, 1.35

Actual values of force for the first band are 0.17, 0.42, 0.71, 1.16, 1.32. This means my estimates were off by +0.03, -0.02, +0.04, +0.02, +0.03.

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:

9.3, 9.7, 10.2, 11.8, 12.2

Actual values of force for the first band are 9.1, 9.59, 10.22, 11.49, 12.15. This means my estimates were off by +0.2, +0.11, -0.02, +0.31, +0.05.

The typical error you estimate when predicting force for a given length from your graphs:

I have more faith in the points because they give an actual measured and precise value. The curve is less precise because it is basically an average from all of the points. The concept of uncertainty is new for me and we have not had any experience with it yet. I think that the uncertainty would be +-0.01 because the smallest unit of Newtons is in the 0.01 place.

The typical error you estimate when predicting length for a given force from your graphs:

I would think the uncertainty would be +-0.1 because most of my measurements' smallest units were in the 0.1 place. This is because the smallest unit on my ruler was the millimeter which is 1/10 of a centimeter.