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, 17.6cm
7.6cm
I held the top of the chain with my left hand and measured the length of the first rubber band with my right hand. The first number is the measurement on the ruler where the rubber band started. The second number is the end of the rubber band. 7.6 cm is the length of the rubber band. I think this is accurate to .05 cm because it is hard to tell with just looking at it in comparison to a ruler.
** The basis for your uncertainty estimate: **
The basis for the uncertainty is human error. While holding the rubber band chain, I could not be entirely steady which could cause uncertainty. Also, trying to calculate to the nearest .05 cm is difficult when just using eyesight.
** Positions of the ends of each rubber band, actual lengths of each when the chain supports 1 domino: **
10, 17.6
10, 18
10, 17.9
10, 17.6
10, 18
10, 16.8
End
7.6, 8, 7.9, 7.6, 8, 6.8
1, 2, 3, 4, 5, 6
The uncertainty could be because of not being steady while measuring, difficult seeing the marks on the ruler, or the ruler itself being inaccurate.
** Distances between ends when supporting 2 dominoes **
7.6, 7.4, 7.2, 7.5, 7.6, 7
Results of 2 domino bag.
** Lengths when supporting 4, 6, ... dominoes: **
7.9, 7.5, 7.4, 7.5, 7.8, 7.4
4
8, 7.7, 7.7, 7.7, 8, 7.8
6
8.3, 8.2, 7.9, 8, 8.6, 8
8
9, 8.3, 8.1, 8.1, 8.8, 8.2
10
End
** Your table of force in Newtons vs. length in cm for all rubber bands **
7.6, 8, 7.9, 7.6, 8, 6.8 ( 1 domino / 0.19 N )
7.6, 7.4, 7.2, 7.5, 7.6, 7 ( 2 dominoes / .38N )
7.9, 7.5, 7.4, 7.5, 7.8, 7.4 ( 4 dominoes / 0.76N )
8, 7.7, 7.7, 7.7, 8, 7.8 ( 6 dominoes / 1.14 N )
8.3, 8.2, 7.9, 8, 8.6, 8 ( 8 dominoes / 1.52 N )
9, 8.3, 8.1, 8.1, 8.8, 8.2 ( 10 dominoes / 1.9N )
End
Each column represents the length of the first rubber band for each force. The units of measurement are in centimeters. There were 6 rubber bands for each force.
NOTE: The above instructions to list the information for the table were confusing.I just listed them in a way which I can recognize.
** Describe the graph of your first rubber band **
In a rubber band length vs force graph, each rubber band grew in length as the force grew. I would call it increasing at a constant rate. The information is too close together to really tell if the slopes are increasing at an increasing/decreasing rate. Also, the data is not linear enough to really see if this is happening either. The data tends to jump around a lot which I think is a cause of the uncertainty in measuring.
** The tension force in your first rubber band at length 9.8 cm: **
2.28 N
** The length of your first rubber band when tension is 1.4 N: **
7.95 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: **
0.19, 0.19, .22, .23, .25, 3
The estimate differs greatly because, even though the force grew at a constant rate (adding dominoes), the lengths of the rubber bands did not grow at an equal rate.
** 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: **
7.6, 7.6, 7.9, 8, 8.3, 9
I'm not sure what curve estimate they're referring to. Since the forces given were the actual forces recorded (0.19, 0.38...) there were no estimates for these points. This is because there were already actual data values at these points. Therefore there is no difference in length from what I observed to what I recorded.
** The typical error you estimate when predicting force for a given length from your graphs: **
I have more faith in the values from the table because those were actually recorded instead of estimated by a curve. If I were to estimate a given force, there would be great uncertainty because of the randomness of the points and the inaccuracy of the curve.
** The typical error you estimate when predicting length for a given force from your graphs: **
There would also be uncertainty in estimating the length because of the randomness of these measurements too. Since we dealt with such a small change in weight, the lengths changed only slightly. Because of this slight change in length, our measurements were more vulnerable to uncertainty. This helped make the data very random and made it hard to predict the trend of length vs force.
** **
1 hour
** **
&#Your work looks very good. Let me know if you have any questions. &#