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? **
1.22, 25
cm block translated, approximate degrees block rotated
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of two dominoes: **
1.22, 25
1.26, 20
1.48, 25
1.27, 20
1.20, 20
cm block translated, approximate degrees block rotated - 5 trials
** Rubber band lengths resulting in 5 cm, 10 cm and 15 cm slides: **
8.2, 8.4, 8.9
Lengths the band needed to be stretch to to result in slides of 5, 10 and 15 cm
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of four dominoes: **
1.15, 15
1.15, 15
1.05, 15
1.15, 10
1.15, 15
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of six dominoes: **
3.48, 10
3.32, 10
3.98, 10
4.22, 10
4.57, 10
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of eight dominoes: **
4.22, 15
5.07, 15
5.40, 15
5.68, 15
5.96, 15
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of ten dominoes: **
7.31, 15
7.75, 15
8.12, 15
8.19, 15
8.80, 15
** 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: **
7.73, 2, 1.286, .1122, 0.0002
7.98, 4, 1.13, 0.04472, 0.0015
8.18, 6, 3.914, .5171, 0.0034
8.38, 8, 5.266, .6715, 0.0061
8.63, 10, 8.034, .5530, 0.0100
Energy here is represented in Joules calculated by multiplying the average force applied by the distance applied. Average force is assumed to be the average between 0.19N (the lowest measured force for the band calibration) and the force used for the trial.
It is possible to improve on this by calculating the work done for every 2-domino increment (e.g., if length changes by .5 cm between 4 dominoes and 6 dominoes, then the average force is close to the weight of 5 dominoes, or .95 N, so the work on this interval would be .5 cm * .95 N = .48 N cm). Adding up the work on every interval, up and to a given point, would account for most of the nonlinearity in the calibration curve.
However the curve is pretty well approximated by a straight line, so the accuracy of the linear approximation you used is likely to be well within the other margins of error on this experiment.
** 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: **
674, 1.3
N*100, cm
I have an r of 0.993 - indicating linear relationship
** Lengths of first and second rubber band for (first-band) tensions supporting 2, 4, 6, 8 and 10 dominoes: **
** Mean sliding distance and std dev for each set of 5 trials, using 2 rubber bands in series: **
This will result in identical force applied for approximately twice the distance resulting in a slide assumedly twice as long. I ran out of time to complete this experiment after working for 90 min to get to this point it was obvious I would not finish in the time allotted.
** 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: **
** 1-band sliding distance and 2-band sliding distance for each tension: **
** 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: **
** 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. **
Slide length will be proportional to length of stretch. When the first band is stretched to a known force then the force is not increased by adding another band in series. Only the distance the force is applied is increased, assumedly by a factor of 2 if the rubber bands are assumed to be identical.
Fd = slide length of x
F(2d) = 2x
(2F)d = 2x
(2F)(2d) = 4x
** How long did it take you to complete this experiment? **
0840-1010 = 90 min
** Optional additional comments and/or questions: **
There seem to be too many sources of error in this experiment. Friction from one trial to the next will change with change in domino contact patch. As the 'pack' of dominos shift with each trial the contact patch will be different for each trial. The stretch in the rubber band holding the 'pack' together is ignored when determining the length of pull. Lastly, I had great difficulty releasing my grip on the thread with any consistency. It was readily apparent that my inability to release the thread uniformly affected the results of each trial.
Despite the sources of error you got a pretty good linear relationship. As I believe you observed for the rotating strap, friction often increases slightly with speed; however the increase is not that substantial and given the uncertainties you mention, this is unlikely to affect the outcome of this experiment.
As long as the domino pack slides, as opposted to tumbling, the size of the contact patch won't have a major effect, since you still have the same average normal force. However there will be some variation and it's possible that could affect these outcomes.
The problem with release would be of the most concern. This could be remedied by using some sort of triggering mechanism, or holding the system back with a thread that is then cut or burned in order to release the pack. However the experiment is time-consuming enough as it is, as I'm sure you agree.
In any case, you did excellent work here.