#$&*
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.
** Energy Conversion 1_labelMessages **
10/21 10:53 pm
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Energy conversion 1
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Note that the data program is in a continual state of revision and should be downloaded with every lab.
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):
2.1, 5
First number is the distance traveled in cm. Second number is the rotation in degrees.
#$&* _ 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):
2.1, 5
2.4, 5
2.9, 5
2.7, 5
3.0, 5
First number is the distance traveled in cm. Second number is the rotation in degrees. Rotation was rather small : 5 degrees was the approximation of a just noticeable angle.
#$&* _ trials on paper
Now, without making any marks, pull back a bit further and release.
Make sure the length of the rubber band doesn't exceed its original length by more than 30%, with within that restriction what rubber band length will cause the block to slide a total of 5 cm, then 10 cm, then 15 cm.
You don't need to measure anything with great precision, and you don't need to record more than one trial for each sliding distance, but for the trials you record:
The block should rotate as little as possible, through no more than about 30 degrees of total rotation, and
it should slide the whole distance, without skipping or bouncing along.
You can adjust the position of the rubber band that holds the block together, the angle at which you hold the 'tail', etc., to eliminate skipping and bouncing, and keep rotation to a minimum.
Indicate in the first comma-delimited line the rubber band lengths that resulted in 5 cm, 10 cm and 15 cm slides. If some of these distances were not possible within the 30% restriction on the stretch of the rubber band, indicate this in the second line. Starting in the third line give a brief description of the meaning of these numbers.
Your answer (start in the next line):
8.1, 8.6, 8.8
All distances were possible
Rubber band lengths in cm that resulted in 5cm, 10cm, and 15cm slides respectively.
#$&* _ 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):
2.3, 0
3.3, 0
2.7, 5
3.4, 0
3.3, 5
In each line, first number is the distance traveled in cm. Second number is the rotation in degrees
#$&* _ 5 trials 4 domino length
Repeat with the rubber band tension equal to that observed when supporting 6 dominoes and report in the same format below, with a brief description starting in the sixth line:
Your answer (start in the next line):
3.2, 0
2.8, 0
2.5, 0
3.8, 0
4.1, 0
In each line, first number is the distance traveled in cm. Second number is the rotation in degrees
#$&* _ 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):
3.9, 0
4.4, 0
4.6, 5
4.6, 5
4.4, 0
In each line, first number is the distance traveled in cm. Second number is the rotation in degrees
#$&* _ 5 trials for 8 domino length
Repeat with the rubber band tension equal to that observed when supporting 10 dominoes and report in the same format below, including your brief description as before:
Your answer (start in the next line):
6.5, 0
6.7, 0
7.2, 5
8.0, 0
7.6, 0
In each line, first number is the distance traveled in cm. Second number is the rotation in degrees
#$&* _ 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. Include your detailed calculations and specific explanation for the third interval. Be sure to give a good description of how you obtained the energy associated with each stretch:
Your answer (start in the next line):
7.8, 2, 2.6, .37, .076
8.0, 4, 3.0, .48, .15
8.1, 6, 3.3, .67, .28
8.2, 8, 4.4, .29, .45
8.4, 10, 7.2, .62, .76
Units for energy are in Newton *cm. Energy was calculated by subtracting the length of the rubber band when no dominoes are weighing it down from the length when stretched by a specific number of dominoes. This distance is then multiplied by the average force over the stretch. Average force is determined by adding the force at the full stretch adding zero for the force at no stretch and then dividing this sum by 2 to get the average. As an example. For the trial involving the force associated with six dominoes the band was stretched to 8.1cm which is .5cm more than the original slack position. The average force is calculated by taking the 1.1 Newtons from our calibration graph adding zero for the force when slack and then dividing by 2 to get the average force of .55 Newtons. We multiply this .55N by .5m to get approximately .28 Newton *cm.
#$&* _ for each set of trials length, # dom, mean, std of sliding dist, energy _ describe how results obtained esp energy calculations
Sketch a graph of sliding distance vs. energy, as reported in the preceding space .
Fit the best possible straight line to your graph, and give in the first comma-delimited line the slope and vertical intercept of your line.
In the second line specify the units of the slope and the vertical intercept.
Starting in the third line describe how closely your data points cluster about the line, and whether the data points seem to indicate a straight-line relationship or whether they appear to indicate some sort of curvature.
If curvature is indicated, describe whether the curvature appears to indicate upward concavity (for this increasing graph, increasing at an increasing rate) or downward concavity (for this increasing graph, increasing at a decreasing rate).
Your answer (start in the next line):
6.3, 1.7
@&
The slope of a graph of sliding distance vs. energy would have units of cm / (N * cm) = 1/N, or N^(-1).
*@
Slope is in cm/N. y-intercept is in cm
A curvature is suggested. The first four points could be seen to indicate a straight line, but the fifth point seems to suggest it is better suited to a curve with upward concavity, increasing at an increasing rate.
#$&* _ 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 space es 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):
7.8, 7.5
8.0, 7.7
8.1, 7.8
8.2, 7.9
8.4, 8.5
Values are rubber band lengths in cm.
#$&* _ lengths of 1st and 2d rbs in series each of 5 trials
Report for each set of 5 trials your mean sliding distance and the corresponding standard deviation; you did five sets of 5 trials so you will report five lines of data, with two numbers in each line:
Your answer (start in the next line):
2.5, .11
5.0, .64
4.6, .50
6.8, .70
9.6, .27
Above numbers are mean and standard deviations in cm for the 2 rubber band trials. The second and third lines raise a flag since it would be expected that the mean would increase in each line which does not happen here.
#$&* _ 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):
5.4, 1.9
Units for slope are cm/Newton. Units for y-intercept at cm.
These point indicate a straight line with a seemingly anomalous point at (.3, 5.0)
Curiously when I replotting the previous graph on the same sheet as this one I noticed that my first four points from the previos graph lay on very close to the best fit line for this graph. This may suggest that the 5th point in the previous graph was an anamoly and that the previous graph does indeed suggest a straight line.
#$&* _ slope, vert intercept, describe curvature
In the space below, report in the first line, in comma-delimited format, the sliding distance with 1 rubber band under 2-domino tension, then the sliding distance with 2 rubber bands under the same 2-domino tension.
Then in the subsequent lines report the same information for 4-, 6-, 8- and 10-domino tensions.
You will have five lines with two numbers in each line:
Your answer (start in the next line):
2.6, 2.5
3.0, 5.0
3.3, 4.6
4.4, 6.8
7.2, 9.6
Values are mean sliding distance in cm for 1 and 2 rubber band set ups respectively in each line.
#$&* _ 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):
1.4, -.25
The slope has no units. The units for rise are cm and the units for run are cm so they cancel out. The units for y intercept are cm.
The points do cluster fairly closely along a line, but there is one anamoly with the point (3.3, 4.6), if that data point were different it might change our perceptions of the straight line versus curve question. At this point its almost equally easy to see a straight line as it is to see a curve. If we had information for a 12 or 14 domino tension, i predict we would see a curve. In this case it would be downward concavity, thus increasing at a decreasing rate.
#$&* _ graph 2 rb dist vs 1 rb dist _ slope and intercept _ describe any curvature
To what extent do you believe this experiment supports the following hypotheses:
The sliding distance is directly proportional to the amount of energy required to stretch the rubber band. If two rubber bands are used the sliding distance is determined by the total amount of energy required to stretch them.
Your answer (start in the next line):
The experiment provides some evidence that the sliding distance is directly proportional to the amount of energy required to stretch the rubber band. Four of the five points in the graph of sliding distance vs energy on one rubber band suggest a straight line which may suggest proportionality. The last point in the graph, however, gives us reason for doubt. Sliding distances resulting from longer stretches might be needed to clarify.
The experiment seems to somewhat support the the hypotheses that if two rubber bands are used the sliding distance is determined by the total amount of energy required to stretch them. I base this on the fact that by combining the one and two rubber band graphs the sliding distance vs. energy both seem to fit roughly along the same line. Combining however does give us tw outliers (out of 2) that suggest we may have some significant uncertainty.
@&
I agree with your analysis.
Further experiment and analysis would of course provide more conclusive results, by the hypothesis that sliding distance and rubber band energy are proportional is not contradicted by the data.
*@
#$&* _to what extend is hypothesis of sliding dist prop stretching energy supported _ to what extent for 2 rb
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
3 hours
:
#$&*
&#Very good data and responses. Let me know if you have questions. &#