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):
first line ruler markings, distance in actual cm between ends, how obtained:
99.00, 67.15
8.61 cm
I obtained the numbers in the first line using my triply reduced ruler copy and stated my starting point (a=99.00) and finishing point (b=67.15) of the rubber band. I obtained the second line in actual centimeters by determining the distance between the two points (a-b) and dividing that number by 3.7 cm, since the conversion formula I obtained when measuring out the triply reduced ruler copy was 1 cm/3.7 cm. This rubber band is marked #1 and I believe the measurements to be +-.05 cm.
The basis for your uncertainty estimate:
I've read the text's discussion on uncertainty over and over and I still don't understand how to calculate for it. I used the uncertainty above on the basis of any optical errors in reading the ruler.
You estimated the uncertainty based on the estimated accuracy of your measuring device and on your experience with doing the measurements. This is a good basis for this estimate.
Other things that might be taken into consideration in this experiment when estimating uncertainties might include
the limits of resolution of your measuring device
the consistency of separate independent measurements of the same quantity
the deviations of points on a graph from the estimated 'ideal' curve
Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino:
99.00, 67.15
99.00, 65.70
99.00, 66.45
99.00, 67.50
99.00, 65.35
End
8.61 cm, 9.00 cm, 8.80 cm, 8.51 cm, 9.09 cm
1, 2, 3, 4, 5
+-.05 cm
Distances between ends when supporting 2 dominoes
8.78 cm, 9.15 cm, 9.18, cm, 8.85 cm, 9.11 cm
Lengths when supporting 4, 6, ... dominoes:
8.92 cm, 9.56 cm, 9.32 cm, 9.34 cm, 9.65 cm
9.50 cm, 9.92 cm, 9.66 cm, 9.46 cm, 9.92 cm
9.82 cm, 10.41 cm, 10.09 cm, 9.89 cm, 10.22 cm
10.35 cm, 11.01 cm, 10.66 cm, 10.35 cm, 11.03 cm
End
Your table of force in Newtons vs. length in cm for all rubber bands
8.61 cm, 9.00 cm, 8.80 cm, 8.51 cm, 9.09 cm, .19 N
8.78 cm, 9.15 cm, 9.18 cm, 8.85 cm, 9.11 cm, .38 N
8.92 cm, 9.56 cm, 9.32 cm, 9.34 cm, 9.65 cm, .76 N
9.50 cm, 9.92 cm, 9.66 cm, 9.46 cm, 9.92 cm, 1.14 N
9.82 cm, 10.41 cm, 10.09 cm, 9.89 cm, 10.22 cm, 1.52 N
10.35 cm, 11.01 cm, 10.66 cm, 10.35 cm, 11.03 cm, 1.90 N
End
The first column of my table is length measured in centimeters and the second column is force measured in Newtons. The quantity measured is the number of dominoes.
Describe the graph of your first rubber band
Graph 1 started out increasing at an increasing rate and then began increasing at a decreasing rate.
The tension force in your first rubber band at length 9.8 cm:
1.5
The length of your first rubber band when tension is 1.4 N:
9.7
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, .4, .65, 1.3, 1.55, 1.92
0, +.02, -.11, +.16, +.03, +.02
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:
8.61 cm, 8.70 cm, 9.00 cm, 9.45 cm, 9.79 cm, 10.30 cm
0, -.04, +.08, -.05, -.03, -.05
The typical error you estimate when predicting force for a given length from your graphs:
I have more faith in the curve because the curve would average out normal errors. I still don't understand calculating for uncertainty. I would only guess +-.05 N.
The typical error you estimate when predicting length for a given force from your graphs:
I do not understand calculating for uncertainty.
For example, using your third graph, if you estimate the length of the rubber band for a force of 1.5 Newtons, what is your estimate?
If you then suspended 1.50 Newtons from the rubber band, how close to your estimate do you think the actual length would be?
For a typical length estimate for a typical force with a typical rubber band, how close do you think your estimates would be?
Your answers should be based on your experience of the system, and the results you have obtained here.
Other than making reasonable estimates and connecting them with your experience, and perhaps expressing your estimates as approximate percent errors, nothing else is required at this point.
In other labs, we will consider how the uncertainty in one or more measurement affects the results of calculations and predictions based on these measurements.
Your report has been received. We will be discussing this work as a group, after the due date.