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: **
10mm, 80mm
7cm
The numbers in the second line was obtained by subtracting 10mm from 80mm and converting to cm's. The rubber band was marked with 1 black stripe. I think I'm within + or - 1mm.
** The basis for your uncertainty estimate: **
Some of my uncertainty may come from visual perspective and the bands hanging from a fixture and swinging slightly.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10mm, 80mm
10mm, 80mm
10mm. 83mm
10mm, 80mm
10mm, 81mm
10mm, 82mm
End
** Distances between ends when supporting 2 dominoes **
7.2cm, 7.2cm, 7.5cm, 7.2cm, 7.3cm, 7.4cm
These lengths are using 2 dominoes.
** Lengths when supporting 4, 6, ... dominoes: **
7.4cm, 7.4cm, 7.7cm, 7.4cm, 7.5cm, 7.6cm
4 dominoes
7.6cm, 7.6cm, 7.9cm, 7.6cm, 7.7cm, 7.8cm
6 dominoes
7.8cm, 7.7cm, 8.0cm, 7.8cm, 7.8cm, 8.0cm
8 dominoes
8.0cm, 7.9cm, 8.2cm, 8.0cm, 8.0cm, 8.2cm
10 dominoes
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.0cm, 7.0cm, 7.3cm, 7.0cm, 7.1cm, 7.2cm, .19 Newtons0
7.2cm, 7.2cm, 7.5cm, 7.2cm, 7.3cm, 7.4cm, .38 Newtons
7.4cm, 7.4cm, 7.7cm, 7.4cm, 7.5cm, 7.6cm, .76 Newtons
7.6cm, 7.6cm, 7.9cm, 7.6cm, 7.7cm, 7.8cm, 1.14 Newtons
End
Each column is identified with a numbered rubber band and the last column is the force being exerted on the specific row of rubber bands.
** Describe the graph of your first rubber band **
All of the bands appeared to be increasing at an increasing rate throughout.
The rubber band shapes appeared to straighten out and stretch as more dominoes were added.
End
** The tension force in your first rubber band at length 9.8 cm: **
5.32 Newtons
** The length of your first rubber band when tension is 1.4 N: **
1.4 Newtons
7.75cm
** 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, .38, .76, 1.14, 1.52
These don't vary any because my measurements using the dominoes were the basis for my graph.
If you fit the best possible smooth curve to the data, there is no expectation that the curve will actually pass through any of the data points. If there is a 1 mm uncertainty in measurements, this will certainly cause the curve to 'miss' at least some of your data points. If the curve goes out of its way to hit the data points, then it's not smooth.
Typical deviations reported by students are in the range from .01 N to .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: **
7cm, 7.2cm, 7.4cm, 7.6cm
These don't vary any because my measurements using the dominoes were the basis for my graph.
Data points are the basis for your smooth curve, and your predictions here should completely ignore the data points and use values given by the smooth curve.
The effect of the smooth curve is to 'smooth out' the uncertainties inherent in the measurement process. This curve is more likely to represent the actual trend of the data than the data points. It is more likely to represent the actual behavior of the system.
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the tables because you can extrapolate the values you are looking for.
The uncertainty would probably be around plus or minus .12 Newtons using my graphs
** The typical error you estimate when predicting length for a given force from your graphs: **
I think my uncertainty on the length would be plus or minus .05cm because of the measuring scale I was using plus the graphing divisions I used on the graph.
** **
It took me 3 hours and 30 minutes.
** **
I guess I can always count on taking the longest estimate for completing these assignments. I got somewhat confused because there wasn't a benchmark for the Newtons versus distance other than what information that was gathered in the lab. Without a benchmark comparison all I can do is compare my figures to my own figures which leaves me wondering if I'm right or not.
The benchmark I gave you in the lab about the weight of the dominoes (which for this experiment is the force standard) is good to within a couple percent (the dominoes themselves vary by a couple percent). The rubber bands themselves can reliably measure forces to within +-5%, so the uncertainty in the system itself is greater than the uncertainty in the force standard.
You appear to have very good data, which will allow you to determine with good accuracy the tension in a rubber band of given length. You will be using that information in subsequent experiments.
You might well be more meticulous with your measurements than many students. There are patterns that very few students could anticipate that should emerge in carefully taken data, and those patterns are more clearly present in your work than in most.
Times reported this semester on this experiment run from 1.5 hours to 3.5 hours (yours wasn't the only one at this end of the range), with the strongest concentration around 2.5 hours. On this experiment, how much of the 3.5 hours do you think were required to take and record the measurements, and how many to do the analysis and answer the questions?