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? **
2.4 cm, 0 degrees (negligible degree movement in the sideways direction)
The 2.4 cm is how far the block moved from release to rest by using a distinguishing point mark in the center of the domines and noting the displacement. The degree amount is approximately 0 degrees movement, as the dominoes are moving in a fairly straight line.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of two dominoes: **
1st trial: total distance= 2.4 cm
2nd trial: total distance= 1.5 cm
3rd trial: total distance= 2.1 cm
fourth trial: total distance- 1.7 cm
fifth trial: total distance= 1.6 cm
THese numbers show the total distance from the release to the stop point of each trial, respectively. I obtained these by pulling the short string back until the rubber band reached 7.6 cm from the original rest point of 7.2 cm and then releasing the rubber band. I marked both the original and the stop points on the peice of paper so as to keep track onf the distances for each trial.
** Rubber band lengths resulting in 5 cm, 10 cm and 15 cm slides: **
5cm stretch: 1.5cm stretch
10cm stretch: 1.9cm stretch
15cm stretch: 2.4cm stretch
These numbers show how many cm the midpoint of the dominoe stack was away from once we aimed to get the midpoint mark of the dominoe stack to 5cm, 10cm, and 15cm away from the original mark, respectively. We took 9.36cm to strech it to no more than 30% of the rest position of the rubber band.
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of four dominoes: **
1st trial: 2.1 cm
2nd trial: 2.8 cm
3rd trial: 2.6 cm
4th trial: 2.8 cm
5th trial: 2.5 cm
In this set of trials, we used the 4 dominoe support length of the rubber band, as indicated from the previous experiment. This length was 7.7 cm. The trial cm lengths that are listed above are the distances away from the release point to the stop point (from where the midpoint mark of the stack was released to the point where the midpoint lies after it stops moving).
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of six dominoes: **
1st trial: 3.2cm
2nd trial: 3.5 cm
3rd trial: 3.9 cm
4th trial: 3.5 cm
5th trial: 3.5 cm
In this set of trials, we used the 6 dominoe support length of the rubber band, as indicated from the previous experiment. This length was 8 cm. The trial cm lengths that are listed above are the distances away from the release point to the stop point (from where the midpoint mark of the stack was released to the point where the midpoint lies after it stops moving).
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of eight dominoes: **
I did not do the previous experiment with 8 dominoes, because I was only given 7 dominoes in my lab package. Therefore, these measurements are only up to 7 dominoes. (You specified that this was alright in the other experiment).
1st trial: 3.4 cm
2nd trial: 4.4 cm
3rd trial: 3.5 cm
4th trial: 4.4 cm
5th trial: 4.3 cm
In this set of trials, we used the 7 dominoe support length of the rubber band, as indicated from the previous experiment. This length was 8.2 cm. The trial cm lengths that are listed above are the distances away from the release point to the stop point (from where the midpoint mark of the stack was released to the point where the midpoint lies after it stops moving).
** 5 trials, distance in cm then rotation in degrees, with rubber band tension equal to the weight of ten dominoes: **
I did not have 10 dominoes to use, as there were not enough in my lab kit. Thus, as you said it was alright to do with less than this in the other experimanet, I only went up to 7 dominoes.
** 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: **
For the first set of 5 trials: mean = 1.86 cm, st dev = 0.378 cm; length of rubber band = 7.6 cm, 2 dominoes, energy at mean = 0.329 Joules
For the second set of 5 trials: mean = 2.56 cm, st dev = 0.288 cm; length of rubber band = 7.7 cm, 4 dominoes, energy at mean = 0.623 Joules
For the third set of 5 trials: mean = 3.52 cm, st dev = 0.249 cm; length of rubber band = 8.0 cm, 6 dominoes, energy at mean = 1.18 Joules
For the fourth set of 5 trials: mean = 4 cm, st dev = 0.505 cm; length of rubber band = 8.2 cm, 7 dominoes, energy at mean = 1.52 Joules
I used joules for the units of the reported energy. To get the mean, I calculated the average of each set of 5 trials in an excel document. In excel also, I calculated the standard deviation for these sets using the stdev function. In order to calculate the energy for each set, I multiplied the square mean (x value) times the rubber band constant (k value) of 0.19 (which was given from the previous experiment) times one half. This follows the equation PE = 1/2 * k * x^2 = 1/2 * .19 * (mean of each set of stretches) ^2.
Your energies are probably in N * cm rather than in Joules. Otherwise OK.
** 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: **
Slope= 1.67 Joules/cm, y intercept= 1.2 Joules
The units of the slope are in Joules/cm. The units of the vertical intercept are in Joules. The data points seem to indicate a pretty straight line. There does not appear to be much curvature on the line; the points seem to be almost on top of the line.
** Lengths of first and second rubber band for (first-band) tensions supporting 2, 4, 6, 8 and 10 dominoes: **
Slope of the best fitted line is .315 Joules/cm. The vertical intercept is 0 Joules. (It appears to be a negative incercept, but we know we can't have a rubber band with a negative stretch, because the dominoe stack would not slide at that point).
THe data points are close to the linem but the fit does not appear to be as good as with the one rubber band set of trials. THus, there is some curvature, going concave up.
** Mean sliding distance and std dev for each set of 5 trials, using 2 rubber bands in series: **
2 Dominoes:
band 1 = 7.6 cm, band 2= 7.8 cm
4 Dominoes:
band 1 = 7.7cm, band 2 =8.0 cm
6 Dominoes:
band 1= 8.0 cm, band 2 = 8.4 cm
7 Dominoes:
band 1 = 8.2 cm, band 2 = 8.7 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 Dominoes:
mean= 1.12 cm, st dev= .0837
4 Dominoes:
mean= 1.5 cm, st dev = 0.235 cm
6 Dominoes:
mean= 2.12 cm, st dev = 0.13 cm
7 DOminoes:
mean= 2.94 cm, st dev = 0.288 cm
** 1-band sliding distance and 2-band sliding distance for each tension: **
1 Rubber Band with 2 dominoe tension: sliding distance = 1.86 cm
2 Rubber Bands with 2 dominoe tension: sliding distance = 1.12 cm
1 RB, 4 Dom: 2.56 cm
2RB, 4 Dom: 1.5 cm
1RB, 6 Dom: 3.52 cm
2RB, 6 Dom: 2.12 cm
1 RB, 7 Dom: 4 cm
2 RB, 7 Dom: 2.94 cm
** 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: **
The slope of the graph is 0.67. The y intercept is at 0 cm. The slope does not have specific units, because cm/cm cancels out. HOwever the y intercept is measured in cm. The data points do not form a perfect straight line. Rather, the line is a curved one, that is convex and pointing upwards. (Thus, it is upward concavity).
** 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. **
The relationship between the sliding distance and the energy required is an exponential one. This is due to the equation of PE = 1/2 * k * x^2. Thus, as the sliding distance increases, the energy will increase exponentially. In the exercise I just completed, the change in the distances is very small; hence the graph does not show a big exponential curve. So, they are both increasing, but at different rates. Therefore, they cannot be directly related. The sliding distance was measured after the 2 rubber band system was released. In every stretch, the one rubber band system had a greater slide than the two rubber band system. This tells me that the two rubber band system had less energy than the one rubber band system.
** How long did it take you to complete this experiment? **
I spent about three hours on this lab.
** Optional additional comments and/or questions: **
&#Your work looks good. See my notes. Let me know if you have any questions. &#