phy 121
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? **
5.8, 8
The first number is how far the block of 3 dominoes traveled when the rubber band was stretced to 7.41cm and released. The 2nd number is how many degrees it rotated as it moved.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of two dominoes: **
6.23, 0
9.25, 1
8.2, 1
7.94, 1
4.86, 1
The first number in each line is the distance the block of dominoes traveled when released and the 2nd #is how many degrees it rotated. I adjusted the thread between the first trial and these five trials so there was minimal rotation.
** Rubber band lengths resulting in 5 cm, 10 cm and 15 cm slides: **
7.4, 7.9, 8.6
NA
The numbers represent the length that the rubber band was stretched in order to send the block of dominoes traveling 5,10, and 15cm respectively. I chose these lengths by calculating 10% of the unstretched length of my rubber band and adding it to the unstretched length. (7.19 * 10% = .72 then .72+7.19 = 7.9). I tried the original pullback lenght first and found that I was coming close to 5cm most times. I added the 10% and tried 7.4cm and found it came close to 10cm each time. etc.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of four dominoes: **
5.5, 2
7.6, 2
7.6, 2
6.08, 2
7.4, 1
The 1st # in each pair is the distance the block traveled with each trial for a pullback distance of 7.6cm (which is equivalent to a 4 domino tension). The 2nd # in each pair is the degree rotation the block experienced during travel.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of six dominoes: **
8.6, 0
8.15, 2
10.4, 3
8.63, 2
8, 2
The distance and degree rotation for each of 5 trials for a pullback distance of 7.85cm, which is equivalent to a 6 domino tension.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of eight dominoes: **
15.55, 1
13.62, 2
14.9, 2
12.05, 3
13.4, 0
The distance and degree rotation for each of 5 trials for a pullback distance of 8.0cm, which is equivalent to an 8 domino tension.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of ten dominoes: **
23, 1
21.3, 9
18.25, 4
18.55, 3
21.85, 9
The distance and degree rotation for each of 5 trials for a pullback distance of 8.3cm, which is equivalent to a 10 domino tension.
** 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: **
7.41, 2, 7.276, 1.728, 2.82
7.6, 4, 6.836, .9800, 5.78
7.85, 6, 8.756, .9594, 8.95
8.0, 8, 13.90, 1.357, 12.16
8.35, 10, 20.59, 2.094, 15.87
N*cm, I mulitplied the distance in cm that the rubber band was stretched to by the Force in N that the distance is associated with. For example the 2 domino tension is equivalent to 7.41 cm and .38 N. Multiplied together gives 2.83 N*cm energy.
Energy would be calculated as the average force multiplied by the displacement. It appears that you used the maximum force experienced on each pullback. This maximum force acts only at the position of maximum pullback, with the force decreasing to zero as the rubber band returns to its unstretched length. You wouldn't go far wrong by averaging the maximum force with the zero force. This would give you half as much work on each trial, and would not affect the question of linearity posed below. It would result in half the slope on the graph of sliding distance versus calculated energy.
Note that the ave force * distance total is the area beneath the force versus length graph, as in the preparatory lab exercise.
** 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: **
1.25, 0
N*cm, cm
The 1st point is way off from the others and does not seem to cluster around the line like the others do. Really, none of the points seeme to cluster close to the line,but they seem to indicate a curve that increases at an increasing rate, upward concavity.
** Lengths of first and second rubber band for (first-band) tensions supporting 2, 4, 6, 8 and 10 dominoes: **
.29, 3.5
N*cm, cm
The points cluster very close to the line and indicate a straight line relationship.
** Mean sliding distance and std dev for each set of 5 trials, using 2 rubber bands in series: **
7.4, 7.6
7.6, 7.6
7.84, 7.65
8.02, 7.7
9.35, 7.75
** 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: **
5.316, 1.006
6.65, .6727
8, .6624
9.9, 1.109
12.15, 1.779
** 1-band sliding distance and 2-band sliding distance for each tension: **
7.276, 5.316
6.836, 6.65
8.756, 8
13.90, 9.9
20.59, 12.15
** 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: **
.46, 3.3
N*cm, cm
The points are closer to the line than the first graph, but farther away than the second. The also seem to indicate a straight line relationship.
** 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 don't think my data supports the hypothesis. With two rubber bands and twice the energy I should have increased distances. I actually have mostly decreased distances. If the distances are directly proportional I think that with twice the energy my slope should be much closer to 1, but my slope is only 0.46. I am not very certain of my answer though.
** How long did it take you to complete this experiment? **
2.5-3 hours to complete plus 40 mins to type up.
** Optional additional comments and/or questions: **
Very good work, but see my note on your calculation of rubber band energies, which are basically twice as great as they should be.