Phy 231
Your 'energy conversion 1' 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 optional message or comment: **
** How far and through what angle did the block displace on a single trial, with rubber band tension equal to the weight of two dominoes? **
1.2 cm, about 15 degrees
Pulling the dominoes back about .15 cm, they move about 1.2cm, and only rotate about 15 degrees.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of two dominoes: **
1.5 cm, 20 deg
1.4 cm, 0 deg
1.2 cm, 15 deg
1.7 cm, 45 deg
1.2 cm, 5 deg
These are the values obtained from pulling back .15 cm
** Rubber band lengths resulting in 5 cm, 10 cm and 15 cm slides: **
8 cm
8.8 cm
9.1 cm
The 8 cm gave a 5.5 cm ds, the 8.8 gave 9.8 cm, and the 9.1 cm gave 11.7 cm, but I didn't want to chance it and stretch it any further.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of four dominoes: **
3.5 cm
2.5 cm
3.6 cm
3.1 cm
3.4 cm
These are the ds values that the domino block slid when pulled back .24 cm.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of six dominoes: **
5.5 cm
6 cm
4.9 cm
5.4 cm
5.7 cm
These are the ds values when pulled back .56 cm.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of eight dominoes: **
6.4 cm
6.5 cm
6.2 cm
6.7 cm
6.8 cm
When pulled back .8cm, these are the results.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of ten dominoes: **
10.4 cm
10.3 cm
10.5 cm
9.5 cm
10.1 cm
When pulled back about 1 cm these are the results.
** Rubber band length, the number of dominoes supported at this length, the mean and the standard deviation of the sliding distance in cm, and the energy associated with the stretch, for each set of 5 trials: **
7.5, 2, 1.4, .2121, .00015J
7.7, 4, 3.22, .4438, .00175J
8.04, 6, 5.5, .4062, .00555J
8.25, 8, 6.52, .2387, .00855J
8.42, 10, 10.16, .3975, .011651
Since, relatively, the energy associated with each interval (0-2, 2-4, etc.) was .00015 J, .0016 J, .0038 J, .003 J, and .0031 J, I just added appropriate intervals. So the energy at 4 dominoes would be the 0-2 interval + the 2-4 interval for energy.
** Slope and vertical intercept of straight-line approximation to sliding distance vs. energy, units of slope and vertical intercept, description of the graph and closeness to line, any indication of curvature: **
693.43, 1.5253
cm/J, J
I did the graph in excel and the points are fairly close to the line except for the 2nd and 4th points, but since they were over and then under, it averaged out on the best-fit line, and it didn't appear to curve.
** Lengths of first and second rubber band for (first-band) tensions supporting 2, 4, 6, 8 and 10 dominoes: **
661.26, 3.1384
cm/J, J
They're very close to the best-fit line, except for the second and fourth point again (above and under). It looks (generally) like a straight-line relationship to me from this graph.
** Mean sliding distance and std dev for each set of 5 trials, using 2 rubber bands in series: **
7.5 cm, 7.6 cm
7.71 cm, 7.8 cm
8.04 cm, 8.15 cm
8.25 cm, 8.35 cm
8.42 cm, 8.5 cm
** Slope and vertical intercept of straight-line approximation to sliding distance vs. energy, units of slope and vertical intercept, description of the graph and closeness to line, any indication of curvature: **
2.73 cm, .3162
6.6 cm, .8426
10.15 cm, .7047
13.68 cm, .8884
19.1 cm, .5944
** 1-band sliding distance and 2-band sliding distance for each tension: **
1.4, 2.73
3.22, 6.6
5.5, 10.15
6.52, 13.68
10.16, 19.1
** Slope and vertical intercept of straight-line approximation to 2-band sliding distance vs. 1-band sliding distance, units of slope and vertical intercept, description of the graph and closeness to line, any indication of curvature: **
1.88, 0.3677
no units (cm/cm), cm
Points 3 and 4 are slightly off the line (under and then over), but not by a really significant amount. It's not really curved.
** Discussion of two hypotheses: 1. The sliding distance is directly proportional to the amount of energy required to stretch the rubber band. 2. If two rubber bands are used the sliding distance is determined by the total amount of energy required to stretch them. **
I think it supports that hypothesis pretty well. The graph is fairly linear, and just looking at the numbers, they all appear to be almost double assuming double energy. I did think it was weird that the over-under pattern for points 2 and 4 showed up again in the 2-rubber band test, but maybe that's just a property of my first rubber band. Or maybe I made some identical human error that created that pattern again.
There aren't that many points, so a purely statistical coincidence can't be ruled out. However the coincidence is unlikely enough that it would merit further consideration (in this case, of course, time doesn't permit that).
** How long did it take you to complete this experiment? **
2 hrs 15 min
** Optional additional comments and/or questions: **
Very good work, with excellent results.