#$&*
Phy 231
Your 'energy conversion 1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
#$&* 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? **
Energy conversion 1
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):
8.5 cm, 15 deg
how far, in cm, did the block travel after being released, and through
approximately how many degrees did it rotate
#$&* _ 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):
9.8 cm, 10 deg
10 cm , 5 deg
8.6 cm, 3 deg
7.4 cm, 3 deg
7.5 cm, 10 deg
how far, in cm, did the block travel after being released, and through
approximately how many degrees did it rotate
#$&* _ trials on paper
Now, without making any marks, pull back a bit further and release.
Make sure the length of the rubber band doesn't exceed its original length
by more than 30%, with within that restriction what rubber band length
will cause the block to slide a total of 5 cm, then 10 cm, then 15 cm.
You don't need to measure anything with great precision, and you don't
need to record more than one trial for each sliding distance, but for the
trials you record:
The block should rotate as little as possible, through no more than about
30 degrees of total rotation, and
it should slide the whole distance, without skipping or bouncing along.
You can adjust the position of the rubber band that holds the block
together, the angle at which you hold the 'tail', etc., to eliminate
skipping and bouncing, and keep rotation to a minimum.
Indicate in the first comma-delimited line the rubber band lengths that
resulted in 5 cm, 10 cm and 15 cm slides. If some of these distances were
not possible within the 30% restriction on the stretch of the rubber band,
indicate this in the second line. Starting in the third line give a brief
description of the meaning of these numbers.
Your answer (start in the next line):
7.8,8.5, 9.1
#$&* _ 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):
8.6 cm, 5 deg
9.9 cm, 3 deg
9.2 cm, 5 deg
10.4 cm, 10 deg
11.2 cm, 8 deg
how far, in cm, did the block travel after being released, and through
approximately how many degrees did it rotate
#$&* _ 5 trials 4 domino length
Repeat with the rubber band tension equal to that observed when supporting
6 dominoes and report in the same format below, with a brief description
starting in the sixth line:
Your answer (start in the next line):
14 cm, 2 deg
12.6 cm, 15 deg
14 cm , 15 deg
14.9 cm, 25 deg
15.3 cm, 40 deg
how far, in cm, did the block travel after being released, and through
approximately how many degrees did it rotate
#$&* _ 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):
19.5 cm, 20 deg
19 cm, 30 deg
18.2 cm 10 deg
17.6 cm 25 deg
19.6 cm, 35 deg
how far, in cm, did the block travel after being released, and through
approximately how many degrees did it rotate
#$&* _ 5 trials for 8 domino length
Repeat with the rubber band tension equal to that observed when supporting
10 dominoes and report in the same format below, including your brief
description as before:
Your answer (start in the next line):
#$&* _ 5 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):
7.85, 2, 8.66, 1.228, .2 N cm
7.91, 4, 9.86, 1.014, .24 N cm
8.21, 6, 14.16, 1.041, .48 N cm
8.32, 8, 18.78, .861, .60 N cm
Newton * cm well the first two number are sef explanitory. The third is
the mean and the fourth is the deviation as obtained from the data
program. The fifth is the energy associated with the stretch: I faond the
change in rubberband length divided by .4 cm then mutiplied that number by
.19 N and then multiplied that number by the distance stretched to get the
energy.
#$&* _ for each set of trials length, # dom, mean, std of sliding dist,
energy _ describe how results obtained esp energy calculations
Sketch a graph of sliding distance vs. energy, as reported in the
preceding space .
Fit the best possible straight line to your graph, and give in the first
comma-delimited line the slope and vertical intercept of your line.
In the second line specify the units of the slope and the vertical
intercept.
Starting in the third line describe how closely your data points cluster
about the line, and whether the data points seem to indicate a
straight-line relationship or whether they appear to indicate some sort of
curvature.
If curvature is indicated, describe whether the curvature appears to
indicate upward concavity (for this increasing graph, increasing at an
increasing rate) or downward concavity (for this increasing graph,
increasing at a decreasing rate).
Your answer (start in the next line):
21.88, 3.9
cm/N cm
The cluster pretty close to the line with a couple out away from it. It
looks to me to be a downward concavity.
#$&* _ 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):
#$&* _ lengths of 1st and 2d rbs in series each of 5 trials
Report for each set of 5 trials your mean sliding distance and the
corresponding standard deviation; you did five sets of 5 trials so you
will report five lines of data, with two numbers in each line:
Your answer (start in the next line):
#$&* _ 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):
#$&* _ slope, vert intercept, describe curvature
In the space below, report in the first line, in comma-delimited format,
the sliding distance with 1 rubber band under 2-domino tension, then the
sliding distance with 2 rubber bands under the same 2-domino tension.
Then in the subsequent lines report the same information for 4-, 6-, 8-
and 10-domino tensions.
You will have five lines with two numbers in each line:
Your answer (start in the next line):
#$&* _ 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):
#$&* _ graph 2 rb dist vs 1 rb dist _ slope and intercept _ describe any
curvature
To what extent do you believe this experiment supports the following
hypotheses:
The sliding distance is directly proportional to the amount of energy
required to stretch the rubber band. If two rubber bands are used the
sliding distance is determined by the total amount of energy required to
stretch them.
Your answer (start in the next line):
#$&* _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):
:
2 hrs
#$&*
*#&!
&#Very good responses. Let me know if you have questions. &#