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): **
this was really challenging for me. I was unclear about some of the instructions that are contained in the lab, so my answers will probably reflect that. Thanks
** first line ruler markings, distance in actual cm between ends, how obtained: **
10, 22.2
12.20
I used one of the paper rulers, presumably the actual-size paper ruler to determine my measurements. The distance measured represents the length of the rubber band with force of one domino pulling down on it. The accuracy of the measurement is, in my estimate, +/- .02 cm.
** The basis for your uncertainty estimate: **
the force of one domino was not quite sufficient enough to stretch the rubber band taught, therefore making it somewhat difficult to accurately measure the length
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10, 22.2
10, 23.5
10, 23.5
10, 23.0
10, 22.2
10, 22.5
END
12.20, 13.50, 13.50, 13.00, 22.20, 22.50
1, 2, 3, 4, 5, 6
The accuracy of the measurement is, in my estimate, +/- .02 cm.
** Distances between ends when supporting 2 dominoes **
12.50, 13.90, 13.60, 13.40, 12.50, 12.90
the data provided here is from the weight of two dominoes
** Lengths when supporting 4, 6, ... dominoes: **
13.00, 14.10, 13.70, 13.50, 12.90, 13.20
4
13.30, 14.30, 13.90, 13.80, 13.00, 13.40
6
13.40, 14.50, 14.10, 13.90, 13.30, 13.70
8
13.50, 14.50, 14.30, 14.10, 13.50, 13.80
10
** Your table of force in Newtons vs. length in cm for all rubber bands **
12.20, 13.50, 13.50, 13.00, .19
12.50, 13.90, 13.60, 13.40, .38
13.00, 14.10, 13.70, 13.50, .76
13.30, 14.30, 13.90, 13.80, 1.14
13.40, 14.50, 14.10, 13.90, 1.52
13.50, 14.50, 14.30, 14.10, 1.90
END
columns 1 through 4 are the lengths of each rubber band with the given weight attached. the last column is the weight that is suspended from the chain.
the unit of measure for the lengths is the cm, the quantity in Newtons
** Describe the graph of your first rubber band **
the shape of the curve for the first rubber band appeared to be increasing at an increasing rate, as a matter-of-fact, it appeared that nearly all of the rubber bands seemed to mirror each other. I'm starting to wonder if I did something wrong with my graph. What do you think?
** The tension force in your first rubber band at length 9.8 cm: **
I feel that the curve for a rubber band will be a sharp curve upwards as the weight increase.
The force appears to be about 1.8 N
According to your data, none of the rubber bands exerts a significant force at lengths much shorter than 12 cm.
However I suspect that you used a singly-reduce ruler rather than a full-sized ruler.
** The length of your first rubber band when tension is 1.4 N: **
9.2 cm
None of the lengths you report is in the vicinity of 9.2 cm. A 1.4 N force would be between the 1.14 N force and the 1.52 N force you report, so the length would be somewhere in the range of 13 or 14 N or so.
** 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: **
.22, .41, .78, 1.16, 1.54, 1.93
in each case it appears that the estimate differs from the actual weight by at the most.03 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: **
12.20, 12.50, 13.00, 13.30, 13.40, 13.50
.03, .03, .02, .02, .02, .03
** The typical error you estimate when predicting force for a given length from your graphs: **
At this point I don't have much faith in any of my calculations concerning this lab. As with everything else I've done previously, I think my estimates would be +/- .03 N
** The typical error you estimate when predicting length for a given force from your graphs: **
I not sure. Possibly +/- .04 cm
** **
3 hours
** **
See my notes. I suspect your measurements were made using a singly-reduced ruler, or perhaps the doubly-reduced. As a result some of your answers don't manage your data. However, you appear to otherwise have done a good job on the experiment.
It is possible that you used the wrong rubber bands, but I think the thinner rubber bands would stretch more than you report when subjected to these forces. In any case please clarify.
You will need good calibration data for subsequent experiments. If you simply measure the ruler you used with a standard ruler you should be able to figure out how to easily convert your data to standard centimeters. Your graphs would not have to be redone; all that would be required would be to change the labeling of the horizontal axis.
Send me a copy of your modified calibration results and let me know if you need help in the process of relabeling your graphs.
The lines that need to be modified are the ones below; first four numbers in each line should probably be in the neighborhood of 7.5 - 9 cm or so.
12.20, 13.50, 13.50, 13.00, .19
12.50, 13.90, 13.60, 13.40, .38
13.00, 14.10, 13.70, 13.50, .76
13.30, 14.30, 13.90, 13.80, 1.14
13.40, 14.50, 14.10, 13.90, 1.52
13.50, 14.50, 14.30, 14.10, 1.90
For reference, the following won't apply directly to your rubber bands but here is a set of data reported by another student; your rubber bands won't be identical to his, but the lengths should be in the same general range.
7.61, 7.6, 7.75, 7.15, 7.2, 7.3
.19
7.75, 7.7, 7.9, 7.78, 7.88, 7.93
.39
8, 7.9, 7.6, 7.5, 7.6, 7.77
.76
8.25, 8.1, 7.75, 7.7, 7.8, 7.9
1.14
8.5, 8.3, 8, 7.95, 7.97, 8.15
1.52
8.85, 8.55, 8.2, 8.15, 8.12, 8.3
1.9