PHY 201
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.
** #$&* Your optional message or comment: **
July 12 around 10:50 am
** #$&* 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? **
Most students report completion times between 2 and 3 hours, with some as short as 1 hour and some as long as 5 hours.
For part of this experiment you will use the calibrated rubber band you used in the preceding experiment 'Force vs. Displacement 1', as well as the results you noted for that experiment.
For this experiment you will need to use at least one rubber band in such a way as to make it useless for subsequent experiments. DO NOT USE ONE OF YOUR CALIBRATED RUBBER BANDS. Also note that you will use four of the thin rubber bands in a subsequent experiment, so DO NOT USE THOSE RUBBER BANDS HERE.
If your kit has extra rubber bands in addition to these, you may use one of them.
You are going to use the rubber band to bind three of your dominoes into a block. If you don't have extra rubber bands, you could use some of the thread that came with your kit, but rubber bands are easier to use.
The idea of binding the dominoes is very simple. Just set one domino on a tabletop so that it lies on one of its long edges. Then set another right next to it, so the faces of the two dominoes (the flat sides with the dots) are touching. Set a third domino in the same way, so you have a 'block' of three dominoes.
Bind the three dominoes together into a 'block' using a rubber band or several loops of thread, wrapping horizontally around the middle of the 'block', oriented in such a way that the block remains in contact with the table. The figure below shows three dominoes bound in this manner, resting on a tabletop.
Now place a piece of paper flat on the table, and place the block on the paper, with the block at one end of the paper.
Give the block a little push, hard enough that it slides about half the length of the paper.
Give it a harder push, so that it slides about the length of the paper, but not quite.
Give it a push that's hard enough to send it past the other end of the paper.
You might need to slide the block a little further than the length of one sheet, so add a second sheet of paper:
Place another piece of paper end-to-end with your first sheet.
Tuck the edge of one sheet slightly under the other, so that if the block slides across the first sheet it can slide smoothly onto the second.
You are going to use a calibrated rubber band to accelerate the blocks and make them slide across the table.
Tie two pieces of thread through to the rubber bands holding the blocks, at the two ends of the block, so that if you wanted you could pull the block along with the threads. One thread should be a couple feet long--long enough that if the block is at one edge of one paper, the other end of the thread extends beyond the edge of the other paper. The other thread needs to be only long enough that you can grasp it and pull the block back against a small resistance.
At the free end of the longer thread, tie a hook made from a paper clip.
Use the rubber band you used in the preceding experiment (the 'first rubber band' from your kit, the one for which you obtained the average force * distance results). Hook that rubber band to the hook at the free end of the longer thread.
Make another hook, and put it through the other end of the rubber band loop, so that when you pull on this hook the rubber band stretches slightly, the string becomes taut and the block slides across the tabletop.
You will need something to which to attach the last hook:
Now place on the tabletop some object, heavy enough and of appropriate shape, so that the last hook can in one way or another be fixed to that object, and the object is heavy enough to remain in place if the rubber band is stretched within its limits. That is, the object should be able so remain stationary if a few Newtons of force is applied. Any rigid object weighing, or being weighted by, about 5-10 pounds ought to be sufficient.
Your goal is to end up with a moderately massive object, to which the last hook is tied or attached, with the rubber band extending from the hook to another hook, a thread from that hook to the block (with a shorter thread trailing from the other end of the block)
With a slight tension in the system the block should be a few centimeters from the 'far' edge of the paper which is furthest from the massive object.
If the block is pulled back a little ways (not so much that the rubber band exceeds its maximum tolerated length) the rubber band will stretch but the last hook will remain in place, and if the block is then released the rubber band will snap back and pull the block across the tabletop until the rubber band goes slack and the block then coasts to rest.
The figure below shows the block resting on the paper, with the thread running from a hook to the rubber band at the far end, which is in turn hooked to the base of a flatscreen monitor.
At the far end the rubber band is ready to be stretched between two hooks. A measuring device is shown next to the rubber band; to get accurate measurements of rubber band length it is recommended that a piece of paper be placed beneath the rubber band, and two points carefully marked on the paper to indicate the positions of the ends. The separation of the points can later be measured. Alternatively the two points can be marked in advance at the desired separation and the system stretched accordingly.
Consult your previous results and determine the rubber band length required to support the weight of two dominoes. Pulling by the shorter piece of thread (the 'tail' of thread), pull the block back until the rubber band reaches this length, and on the paper mark the position of the center of the block (there might well be a mark at the center of the domino; if not, make one, being sure it is within 1 millimeter of the center, and mark the paper according to this mark). Release the thread and see whether or not the block moves. If it does, mark the position where it comes to rest as follows:
Make a mark on the paper where the center mark comes to rest by drawing a short line segment, perhaps 3 mm long, starting from the center mark and running perpendicular to the length of the block.
Make another mark about twice the length of the first, along the edge of the block centered at the center mark.
This will result in a mark that looks something like the following, with the longer line indicating the direction of the block and the two lines coming together at the center mark: __|__. In the first figure below the lowest two marks represent the positions of the center of the dominoes at initial point and at the pullback point. The mark next to the domino is the horizontal part of a mark that looks something like |- ; the vertical part of that mark is obscured by the blocks, and the mark it also tilted a bit to coincide with the slightly rotated orientation of the block. In the second figure most of the |- mark can be seen.
You will make a similar mark for the final position for each trial of the experiment, and from these marks you will later be able to tell where the center mark ended up for each trial, and the approximate orientation of the block at the end of each trial.
Based on this first mark, how far, in cm, did the block travel after being released, and through approximately how many degrees did it rotate before coming to rest?
If the block didn't move, your answers to both of these questions will be 0.
Answer in comma-delimited format in the first line below. Give a brief explanation of the meaning of your numbers starting in the second line.
Your answer (start in the next line):
0, 0
At the time when the rubber band was holding 2 dominoes, the block of dominoes did not move.
#$&* _ 2 rb tension how far and thru what angle
Tape the paper to the tabletop, or otherwise ensure that it doesn't move during subsequent trials.
Repeat the previous instruction until you have completed five trials with the rubber band at same length as before.
Report your results in the same format as before, in 5 lines. Starting in the sixth line give a brief description of the meaning of your numbers and how they were obtained:
Your answer (start in the next line):
0, 0
.03 cm, 5 degrees
0, 0
0, 0
.02 cm, 2 degrees
I pulled the rubber band back to the desired length and let it go. If the block of dominoes moved I recorded the movement, which was very little or nothing at all.
#$&* _ trials on paper
Now, without making any marks, pull back a bit further and release.
Make sure the length of the rubber band doesn't exceed its original length by more than 30%, with within that restriction what rubber band length will cause the block to slide a total of 5 cm, then 10 cm, then 15 cm.
You don't need to measure anything with great precision, and you don't need to record more than one trial for each sliding distance, but for the trials you record:
The block should rotate as little as possible, through no more than about 30 degrees of total rotation, and
it should slide the whole distance, without skipping or bouncing along.
You can adjust the position of the rubber band that holds the block together, the angle at which you hold the 'tail', etc., to eliminate skipping and bouncing, and keep rotation to a minimum.
Indicate in the first comma-delimited line the rubber band lengths that resulted in 5 cm, 10 cm and 15 cm slides. If some of these distances were not possible within the 30% restriction on the stretch of the rubber band, indicate this in the second line. Starting in the third line give a brief description of the meaning of these numbers.
Your answer (start in the next line):
Approx.: 9 cm, 9.5 cm, 10 cm
When estimating the slide of the pack of dominoes, I pulled the string back and marked a point at the end and released it and then marked a point at where the domino landed after the slide, which the length from the first point to the second point is the distance it traveled.
#$&* _ rb lengths for 5, 10, 15 cm slides
Now record 5 trials, but this time with the rubber band tension equal to that observed (in the preceding experiment) when supporting 4 dominoes. Mark and report only trials in which the block rotated through less than 30 degrees, and in which the block remained in sliding contact with the paper throughout.
Report your distance and rotation in the same format as before, in 5 lines. Briefly describe what your results mean, starting in the sixth line:
Your answer (start in the next line):
3.5 cm, 5 degrees
2.9 cm, 5 degrees
3.25 cm, 3 degrees
3 cm, 5 degrees
3.3 cm, 2 degrees
The lengths are the distances between when the domino stack was pulled back and where it slid when released. The degrees are how much the domino stack rotated during the slide.
#$&* _ 5 trials 4 domino length
Repeat with the rubber band tension equal to that observed when supporting 6 dominoes and report in the same format below, with a brief description starting in the sixth line:
Your answer (start in the next line):
6.7 cm, 10 degrees
6.5 cm, 12 degrees
6.4 cm, 15 degrees
6.3 cm, 8 degrees
6.8 cm, 10 degrees
#$&* _ 5 trials for 6 domino length
Repeat with the rubber band tension equal to that observed when supporting 8 dominoes and report in the same format below, including a brief description starting in the sixth line:
Your answer (start in the next line):
11.4 cm, 15 degrees
11.5 cm, 20 degrees
11.9 cm, 16 degrees
12.2 cm, 10 degrees
12.5 cm, 15 degrees
#$&* _ 5 trials for 8 domino length
Repeat with the rubber band tension equal to that observed when supporting 10 dominoes and report in the same format below, including your brief description as before:
Your answer (start in the next line):
12.7 cm, 10 degrees
13.2 cm, 15 degrees
13.3 cm, 10 degrees
13.8 cm, 20 degrees
13.5 cm, 12 degrees
#$&* _ 5 trials for 10 domino length
In the preceding experiment you calculated the energy associated with each of the stretches used in this experiment.
The question we wish to answer here is how that energy is related to the resulting sliding distance.
For each set of 5 trials, find the mean and standard deviation of the 5 distances. You may use the data analysis program or any other means you might prefer.
In the space below, report in five comma-delimited lines, one for each set of trials, the length of the rubber band, the number of dominoes supported at this length, the mean and the standard deviation of the sliding distance in cm, and the energy associated with the stretch.
You might choose to report energy here in Joules, in ergs, in Newton * cm or in Newton * mm. Any of these choices is acceptable.
Starting in the sixth line specify the units of your reported energy and a brief description of how your results were obtained. Be sure to give a good description of how you obtained the energy associated with each stretch:
Your answer (start in the next line):
8.02, 2, .01, .01414, .75 N *mm
8.3, 4, 3.19, .2408, 1.28 N*mm
8.57, 6, 6.54, .2074, 2.03 N*mm
8.84, 8, 11.9, .4637, 2.36 N*mm
9.13, 10, 13.3, .4062, 2.53 N*mm
The units for the energy is Newtons * mm. I used the graph that was given and estimated the length from the cms to mms to obtain the estimated energy.
Data look good but I can't see how you got your energies. I might need you to give a detailed description of how you got the energies for, say, your third interval.
#$&* _ for each set of trials length, # dom, mean, std of sliding dist, energy _ describe how results obtained esp energy calculations
Sketch a graph of sliding distance vs. energy, as reported in the preceding space.
Fit the best possible straight line to your graph, and give in the first comma-delimited line the slope and vertical intercept of your line.
In the second line specify the units of the slope and the vertical intercept.
Starting in the third line describe how closely your data points cluster about the line, and whether the data points seem to indicate a straight-line relationship or whether they appear to indicate some sort of curvature.
If curvature is indicated, describe whether the curvature appears to indicate upward concavity (for this increasing graph, increasing at an increasing rate) or downward concavity (for this increasing graph, increasing at a decreasing rate).
Your answer (start in the next line):
6.73, -5.2
The slopes unit is: cm / N*mm, the unit for the y-intercept is: cm.
Most of the data points are very close to the line, but do drift off from the line a bit. I think that the data points fit a straight line, more than a curve.
#$&* _ sliding dist vs. energy slope, vert intercept of st line, how close to line, describe curvature if any
Now repeat the entire procedure and analysis, but add a second rubber band to the system, in series with the first.
For each trial, stretch until the first rubber band is at the length corresponding to the specified number of dominoes, then measure the second rubber band and record this length with your results.
When graphing mean sliding distance vs. energy, assume for now that the second rubber band contributes an amount of energy equal to that of the first. You will therefore use double the energy you did previously.
When you have completed the entire procedure report your results in the spaces below, as indicated:
Report in comma-delimited format the length of the first rubber band when supporting the specified number of dominoes, and the length you measured in this experiment for second band. You will have a pair of lengths corresponding to two dominoes, four dominoes, ..., ten dominoes. Report in 5 lines:
Your answer (start in the next line):
8.02, 7.8
8.3, 7.9
8.57, 8.1
8.84, 8.5
9.13, 8.7
#$&* _ lengths of 1st and 2d rbs in series each of 5 trials
Report for each set of 5 trials your mean sliding distance and the corresponding standard deviation; you did five sets of 5 trials so you will report five lines of data, with two numbers in each line:
Your answer (start in the next line):
3.167, .3559
3.56, .4219
7.46, .3049
12.6, .5612
15.84, .6693
#$&* _ sliding dist and std dev each tension
Give the information from your graph:
Give in the first comma-delimited line the slope and vertical intercept of your line.
In the second line specify the units of the slope and the vertical intercept.
Starting in the third line describe how closely your data points cluster about the line, and whether the data points seem to indicate a straight-line relationship or whether they appear to indicate some sort of curvature.
If curvature is indicated, describe whether the curvature appears to indicate upward concavity (for this increasing graph, increasing at an increasing rate) or downward concavity (for this increasing graph, increasing at a decreasing rate).
Your answer (start in the next line):
3.10, -2.13
Slope: cm / N*mm, y-intercept: cm
The data points for this line drift from the line a lot and dont go well with the best-fit straight line. My data points go more with a curve than a line.
The curvature of my curve seems to indicate upward concavity, meaning increasing at an increasing rate.
#$&* _ slope, vert intercept, describe curvature
In the space below, report in the first line, in comma-delimited format, the sliding distance with 1 rubber band under 2-domino tension, then the sliding distance with 2 rubber bands under the same 2-domino tension.
Then in the subsequent lines report the same information for 4-, 6-, 8- and 10-domino tensions.
You will have five lines with two numbers in each line:
Your answer (start in the next line):
.01, 3.167
3.19, 3.56
6.54, 7.46
11.9, 12.6
13.3, 15.84
#$&* _ 5 lines comparing 1 rb to 2 rb trials
Your preceding answers constitute a table of 2-rubber-band sliding distances vs. 1-rubber-band sliding distances.
Sketch a graph of this information, fit a straight line and determine its y-intercept, its slope, and other characteristics as specified:
Give in the first comma-delimited line the slope and vertical intercept of your line.
In the second line specify the units of the slope and the vertical intercept.
Starting in the third line describe how closely your data points cluster about the line, and whether the data points seem to indicate a straight-line relationship or whether they appear to indicate some sort of curvature.
If curvature is indicated, describe whether the curvature appears to indicate upward concavity (for this increasing graph, increasing at an increasing rate) or downward concavity (for this increasing graph, increasing at a decreasing rate).
Your answer (start in the next line):
1.01, 1.89
cm, cm
My data points do not fit particully well to a straight line. They fit better to a curve.
My curve has an upward concavity, meaning that is increasing at an increasing rate.
#$&* _ graph 2 rb dist vs 1 rb dist _ slope and intercept _ describe any curvature
To what extent do you believe this experiment supports the following hypotheses:
The sliding distance is directly proportional to the amount of energy required to stretch the rubber band. If two rubber bands are used the sliding distance is determined by the total amount of energy required to stretch them.
Your answer (start in the next line):
Yes, I think this experiment clarifies that the sliding distance is directly proportional to the amount of energy required to stretch the rubber band. The more you stretch the rubber band, the more the sliding distance is going to be, and vice versa.
#$&* _to what extend is hypothesis of sliding dist prop stretching energy supported _ to what extent for 2 rb
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