** 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? **
1.82 cm,8 degrees
These numbers are the distance the dominoes traveled when a force equivalent to two dominoes is applied.
This is the potential energy stored in the rubber band moving the dominoes. This energy is 0.38 N (2 dominoes) over a length of 0.72 cm (stretch distance of rubberband) or 0.274 N*cm.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of two dominoes: **
1.82,8
2.05,0
2.05,0
2.30,0
2.22,0
These numbers are the distance the dominoes traveled when a force equivalent to two dominoes is applied.
** Rubber band lengths resulting in 5 cm, 10 cm and 15 cm slides: **
4.87,8
9.98,5
16.45,12
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of four dominoes: **
4.39,3
4.20,5
4.07,8
4.22,2
4.45,0
These numbers are the distance the dominoes traveled when a force equivalent to 4 dominoes is applied.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of six dominoes: **
6.29,5
6.10,9
6.35,0
6.15,3
6.50,0
These numbers are the distance the dominoes traveled when a force equivalent to 6 dominoes is applied.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of eight dominoes: **
7.15,5
7.61,0
7.68,0
7.33,10
7.28,6
These numbers are the distance the dominoes traveled when a force equivalent to 8 dominoes is applied.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of ten dominoes: **
8.98,2
9.68,0
9.35,8
9.50,6
9.42,5
These numbers are the distance the dominoes traveled when a force equivalent to 10 dominoes is applied.
** 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: **
7.49,2,2.09,0.185,0.274 N*cm
7.65,4,4.27,0.153,0.669 N*cm
7.85,6,6.28,0.160,1.231 N*cm
7.91,8,7.41,0.226,1.733 N*cm
8.11,10,9.39,0.258,2.546 N*cm
My ballpark estimate for the energy in the last line would be as follows:
About 2 Newtons force at maximum stretch.
Average force from 0 stretch to maximum stretch: average of 0 N (at 0 stretch) and 2 N (at max stretch) for average of about 1 N.
Distance of stretch: around 1 cm, probably a little less.
This gives a rough estimate of about 1 N * cm. Your 2.5 N * cm estimate seems high.
Perhaps it was based on maimum force rather than average force? You didn't explain how you got your results for these energies and I haven't been able to reverse-engineer your numbers with any confidence, but I'll bet that's it.
** 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: **
0.312,-0.5459
units of slope would be Newtons, vertical intercept would be N*cm
They appear to indicate a curve
upward concavity which is increasing at a increasing rate.
** Lengths of first and second rubber band for (first-band) tensions supporting 2, 4, 6, 8 and 10 dominoes: **
0.5301,-0.8697
units of slope would be Newtons, vertical intercept would be N*cm
They appear to indicate a slight curve would be possible
upward concavity which is increasing at a increasing rate slightly.
** Mean sliding distance and std dev for each set of 5 trials, using 2 rubber bands in series: **
7.49,7.30
7.65,7.41
7.81,7.49
7.91,7.53
8.11,7.65
** 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: **
2.35,0.166
4.66,0.153
6.53,0.187
7.74,0.148
11.27,0.155
** 1-band sliding distance and 2-band sliding distance for each tension: **
2.09,2.35
4.27,4.66
6.28,6.53
7.41,7.74
9.39,11.27
** 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: **
1.1751,-0.4061
slope is unitless, y intercept is cm
They appear to indicate a slight curve would be possible
upward concavity which is increasing at a increasing rate slightly.
** 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 believe that the data supports this. The slope of my trendline when comparing the 1 and then 2 rubber bands is close to one and following a tight path. This would indicate that they are proportional.
** How long did it take you to complete this experiment? **
2 hours 45 min
** Optional additional comments and/or questions: **
Looks good. However be sure to see my notes on your calculation of the energies at various lengths.