Phy 231
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: **
10cm, 22.35 cm
8.23 cm
I placed the singly reduced ruler next to the first rubber band, beginning at the 10 cm mark. The other end of the band went to 22.35 cm. I calculated the actual distance by finding the difference between the end points and then dividing by 1.5, because that is the ratio of cm between the singly reduced ruler and the normal ruler. The top band was marked with a number 1. The measurement is accurate to +/-.05cm.
** #$&* The basis for your uncertainty estimate: **
I used the least distorted part of the singly reduced ruler in an attempt to reduce the uncertainty. Considering that there was uncertainty in the measrement of the length, there was also uncertainty in the calculation because the length had to be converted to the normal centimeters. The measurement shoudl have come within a quarter of a mm of the actual length, which is .025cm and this is doubled because of the conversion, so the uncertainty is +/-.05 cm.
** #$&* Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10, 22.35
10, 22.21
10, 22.09
10, 22.29
10, 22.12
10, 22.25
End
8.23, 8.14, 8.06, 8.19, 8.08, 8.17
They are marked: 1, 2, 3, 4, 5, 6
** #$&* Distances between ends when supporting 2 dominoes **
8.35, 8.15, 8.21, 8.35, 8.27, 8.21
The measurements in cm above are for the weight of 2 dominos.
** #$&* Lengths when supporting 4, 6, ... dominoes: **
8.61, 8.47, 8.43, 8.58, 8.44, 8.47
4
8.79, 8.63, 8.68, 8.70, 8.65, 8.61
6
9.04, 8.93, 8.85, 9.01, 8.98, 8.93
8
9.27, 9.15, 9.02, 9.23, 9.16, 9.15
10
End
I stopped the measurements because I ran out of dominos
** #$&* Your table of force in Newtons vs. length in cm for all rubber bands **
8.23, 8.14, 8.06, 8.19, 8.08, 8.17
.19 N
8.35, 8.15, 8.21, 8.35, 8.27, 8.21
.38 N
8.61, 8.47, 8.43, 8.58, 8.44, 8.47
.76 N
8.79, 8.63, 8.68, 8.70, 8.65, 8.61
1.14 N
9.04, 8.93, 8.85, 9.01, 8.98, 8.93
1.52 N
9.27, 9.15, 9.02, 9.23, 9.16, 9.15
1.9 N
End
The first column of the table contains the length of the stretched rubber band under varying amounts of force. The length is measured in centimeters. The second column of the table contains the abount of downward force exerted on the rubber band. It is measured in newtons. The same data are shown above, except the odd numbered lines are the lengths of each rubber band 1-6 and the even lines are the force exerted by the dominos.
** #$&* Describe the graph of your first rubber band **
The curve for the first rubber band increases at an increasing rate for the main part of the graph, but at the end it begins to increase at a decreasing rate.
The second rubber band curve increases at a decreasing rate and then increases at an increasing rate.
The curve for the third rubber band increases at a constant rate throughout.
The curve for the fourth rubber band increases at an increasing rate throughout.
The fifth rubber band curve increases at a decreasing rate and then increases at an increasing rate at the end of the graph.
The curve for the sixth rubber band increases at an increasing rate for the first part of the graph and then increasis at a decreasing rate at the end.
End
The curves might look different if I had more data points.
** #$&* The tension force in your first rubber band at length 9.8 cm: **
2.2 N
** #$&* The length of your first rubber band when tension is 1.4 N: **
8.98 cm
** #$&* The forces at your observed lengths the 1st rubber band, as given by the curve, and the deviations of those curve-predicted lengths from the observed lengths: **
.18, .31, .76, 1.15, 1.50, 1.95
.-01, -.07, .00, +.01, -.02, +.05
The estimates from the curve were reasonably accurate. Toward the top of the graph, the curve was above the points, so the estimates values were above the actual ones; other than that the numbers were about the same.
** #$&* 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: **
8.25, 8.39, 8.61, 8.78, 8.99, 9.25
+.02, +.04, .00, -.01, -.04, -.02
A lot of the length estimates from the curve near the top were lower than the actual values, while those at the bottom were greater than the actual values.
** #$&* The typical error you estimate when predicting force for a given length from your graphs: **
I would have more faith in the values from the curve because it is a best fit line for the whole data set. It evens out some of the outliers and tends to make the numbers more accurate. There was a bit of uncertainty in the measurements that I ttok, so the best fit curve might help get rid of some of that uncertainty and make the results more accurate.
If I were to estimate a force, the uncertainty would be about .04. The estimates that I ttok from the curve were above and below the actual points by +/- .04 N.
** #$&* The typical error you estimate when predicting length for a given force from your graphs: **
If you were estimating a length from the curve, the uncertainty would be about +/-.03. The estimates from the curve varied from the actual data points by an average of +/- .03 cm.
** **
1 3/4 hours.
** **
Here is one of the length vs. force tables:
Length(cm) Force (N)
8.06 .19
8.21 .38
8.43 .76
8.68 1.14
8.85 1.52
9.02 1.9
&#This looks very good. Let me know if you have any questions. &#