#$&*
Phy 231
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 **
** **
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):
1.72, 0
Distance (in cm) and rotation (in deg) of block pulled back to
stretch Band #1 7.56cm (length in actual cm required to support two
dominos in previous lab).
#$&* _ 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):
1.64, 0
1.82, 0
1.88, 0
1.93, 5
2.05, 5
Distance (in cm) and rotation (in deg) for five additional trials of
block pulled back to stretch band 7.56cm. Very slight rotation
observed only for two longest distances; 5 deg is a rough estimate
to indicate barely-noticeable rotation.
#$&* _ trials on paper
Now, without making any marks, pull back a bit further and release.
Make sure the length of the rubber band doesn't exceed its
original length by more than 30%, with within that restriction what
rubber band length will cause the block to slide a total of 5 cm,
then 10 cm, then 15 cm.
You don't need to measure anything with great precision, and you
don't need to record more than one trial for each sliding distance,
but for the trials you record:
The block should rotate as little as possible, through no
more than about 30 degrees of total rotation, and
it should slide the whole distance, without skipping or
bouncing along.
You can adjust the position of the rubber band that holds the
block together, the angle at which you hold the 'tail', etc., to
eliminate skipping and bouncing, and keep rotation to a minimum.
Indicate in the first comma-delimited line the rubber band lengths
that resulted in 5 cm, 10 cm and 15 cm slides. If some of these
distances were not possible within the 30% restriction on the
stretch of the rubber band, indicate this in the second line.
Starting in the third line give a brief description of the meaning
of these numbers.
Your answer (start in the next line):
8.44, 9.19, 9.93
Length, in cm, of stretch required of Band #1 to propel block 5, 10,
and 15 cm.
#$&* _ 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):
2.85, 0
2.91, 0
3.08, 0
3.30, 5
3.39, 5
Distance, in cm, and rotation, in deg, of block's slide when Band #1
stretched to 7.83 cm, actual length required to support 4 dominoes
in previous lab.
#$&* _ 5 trials 4 domino length
Repeat with the rubber band tension equal to that observed when
supporting 6 dominoes and report in the same format below, with a
brief description starting in the sixth line:
Your answer (start in the next line):
3.78, 0
3.92, 0
4.07, 5
4.45, 0
4.60, 10
Distance, in cm, and rotation, in deg, of block's slide when Band #1
stretched to 8.16 cm, actual length required to support 6 dominoes
in previous lab.
#$&* _ 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):
4.64, 0
4.82, 0
5.11, 5
5.25, 5
5.50, 0
Distance, in cm, and rotation, in deg, of block's slide when Band #1
stretched to 8.28 cm, actual length requird to support 8 dominoes in
previous lab.
#$&* _ 5 trials for 8 domino length
Repeat with the rubber band tension equal to that observed when
supporting 10 dominoes and report in the same format below,
including your brief description as before:
Your answer (start in the next line):
5.95, 0
6.29, 0
6.41, 0
6.56, 10
6.75, 5
Distance, in cm, and rotation, in deg, of block's slide when Band #1
stretched to 8.59 cm, actual length requird to support 10 dominoes
in previous lab.
#$&* _ 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):
7.56, 2, 1.864, .1511, .103
7.83, 4, 3.106, .2361, .410
8.16, 6, 4.164, .3492, .992
8.28, 8, 5.064, .3414, 1.504
8.59, 10, 6.392, .3010, 2.47
Length (in actual cm) of stretch of Band #1, number of dominoes
supported at this length, mean distance travelled by block (in cm)
when Band #1 is stretched to this length, standard dev. of of
distance travelled by block, energy (in N*cm) associated with this
length of stretch.
The energy is based on the given weight of .19N per domino; total weight of dominoes required for each stretch length-- the force-- is mulitplied by length of stretch (stretched length minus unstretched length of 7.29cm)-- the distance through which the force is applied as the rubber band contracts. This allows us to determine total work done, which equals total energy associated with releasing the band stretched to that length. (For example, to support 8 dominos, band stretches to 8.28cm. So we multiply weight of 8 dominos (8*.19=1.52N) by amount of stretch (8.28cm-7.29cm=.99cm), for a result of 1.504N*cm.
@&
For a given amount of stretch the work done would be equal to that stretch multiplied by the average force, not by the maximum force. I suspect that your results for the energy are all double what they should be.
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#$&* _ for each set of trials length, # dom, mean, std of sliding
dist, energy _ describe how results obtained esp energy calculations
Sketch a graph of sliding distance vs. energy, as reported in the
preceding space .
Fit the best possible straight line to your graph, and give in
the first comma-delimited line the slope and vertical intercept of
your line.
In the second line specify the units of the slope and the
vertical intercept.
Starting in the third line describe how closely your data points
cluster about the line, and whether the data points seem to indicate
a straight-line relationship or whether they appear to indicate some
sort of curvature.
If curvature is indicated, describe whether the curvature
appears to indicate upward concavity (for this increasing graph,
increasing at an increasing rate) or downward concavity (for this
increasing graph, increasing at a decreasing rate).
Your answer (start in the next line):
1.8, 2.05
slope, in cm per Newton*cm, and vertical intercept, in cm
My best-fit line passes above the first and last points and below the middle three (with the middle point being farthest above the line). This indicates that a concave-downward curve is a more appropriate fit for this data. A smooth curve, increasing but at a decreasing rate, fits very nicely.
#$&* _ 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):
7.56, 5.90
7.83, 5.92
8.16, 6.19
8.28, 6.31
8.59, 6.42
#$&* _ lengths of 1st and 2d rbs in series each of 5 trials
Report for each set of 5 trials your mean sliding distance and the
corresponding standard deviation; you did five sets of 5 trials so
you will report five lines of data, with two numbers in each line:
Your answer (start in the next line):
3.782, .3129
4.422, .2159
5.764, .2473
6.688, .1577
8.280, .1914
#$&* _ 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):
1.09, 3.4
Slope, in cm of slide per Newton*cm of energy, and vertical intercept, in cm.
The data points cluster somewhat closer around the line, but still seem better suited to a curvature. Once again, the relationship appears to be a concave-downward curve, increasing at a decreasing rate.
#$&* _ slope, vert intercept, describe curvature
In the space below, report in the first line, in comma-delimited
format, the sliding distance with 1 rubber band under 2-domino
tension, then the sliding distance with 2 rubber bands under the
same 2-domino tension.
Then in the subsequent lines report the same information for 4-, 6-,
8- and 10-domino tensions.
You will have five lines with two numbers in each line:
Your answer (start in the next line):
1.864, 3.782
3.106, 4.422
4.164, 5.764
5.064, 6.688
6.392, 8.280
#$&* _ 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):
1.03, 1.8
Slope, in cm/cm, of 2 rubber band slides vs. 1 rubber band slides, y-intercept in cm.
These data cluster somewhat closely to the line. It is possible that the graph is more closely fit to a concave upward curve, increasing at an increasing rate, but if so the curve is slight.
#$&* _ graph 2 rb dist vs 1 rb dist _ slope and intercept _ describe
any curvature
To what extent do you believe this experiment supports the following
hypotheses:
The sliding distance is directly proportional to the amount of
energy required to stretch the rubber band. If two rubber bands are
used the sliding distance is determined by the total amount of
energy required to stretch them.
Your answer (start in the next line):
Yes, the relationship seems fairly proportional. I believe that under ideal conditions, the 2-bands vs. 1-band graph should be a straight line: that an equivalent increase in energy should bring about an equivalent increase in distance of slide, regardless of how much energy we start with.
The most compelling evidence for this, I believe, is that with the exception of the the 2-domino-length pull, the second set of data (with two rubber bands) would actually fit fairly well among the first set of data (with one rubber band). The sliding block doesn't know whether it's being propelled by one or two rubber bands; it only knows how much total energy is propelling it. Therefore, we should reasonably be able to graph all points together and come up with a fairly good curve. Now, that one point is a pretty definite outlier, and I'm not sure why. Maybe I unconsciously snapped more when I released, since it was such a short pull, causing it to go further than it would otherwise.
Either way, it seems that the trend is that as energy increases, distance increases, but at a decreasing rate. This bears out with both sets of data, both separate from and among each other. Perhaps the decreasing rate is due to friction catching up with with slide; the further it slides, the more dramatic the effect of friction.
#$&* _to what extend is hypothesis of sliding dist prop stretching
@&
This is the usual result. It doesn't fit the ideal expectation, that sliding distance should be proportional to the energy of the rubber band (which would make the graph linear). It isn't clear what is responsible for this discrepancy, but I get the same results when I perform the experiment.
*@
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):
: 2.5 hours
#$&*
@&
Good work, but be sure to check my notes (especially regarding the energy calculation for the rubber band, where I believe you got double the appropriate amount of energy).
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