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course PHY 201
09/23/2011 9:30 PMI have tried to submit this twice before now. I am trying to use a normal submit form since the pearl pendulum submit form is not allowing me to submit my results.
The Pearl Pendulum as shown below a bead (sometimes
called a 'pearl', as the bead used in the original
version was a fake plastic pearl) on a string, attached
to bolt glued to the top of a metal bracket, using a
magnet to 'clamp' the string (in most current versions
of the apparatus the bolt glued to the top of the
bracket, which proved to be unhelpful, is not included).
You will need to construct the pendulum using the small
bead and thin copper wire packed in your lab materials
package. In the Spring 2010 version the bead and the
wire were taped to the bracket, or packed in a separate
bag with another small object.
The wire is formed into a loop with the two ends
protruding, and threaded through the bead.
The ends are pulled through forming a small loop at the
top.
The protruding ends are twisted together then flattened
against the bottom of the bead.
The above pictures were actually of a steel ball and a
thicker wire. The bead and wire you have in your kit
look something like this:
When suspended from the pendulum bracket by a thread the
system might look something like the picture below. If
the pendulum is pulled back and released, it will bounce
back to the bracket, rebound, and repeat its motion a
number of times.
However note that in this picture the bracket is resting
on end with the bolt glued to it; the bracket is not
vertical.
• The pearl appears to hanging in its equilibrium
position, with a little space between it and the
bracket.
• As you will soon see, if the bead is just barely
touching the bracket when it hangs at its equilibrium
position, the rhythm of the bouncing pendulum will
remain constant.
The bead is referred to below as the 'pearl'.
When the pearl is released it swings back to the
bracket, bounces off the swings back again, repeatedly
striking the bracket. The magnet can be used to clamp
the thread so the length of the pendulum remains
constant.
If you have just a plain bracket then you simply tilt
the bracket in order to achieve a constant rhythm, as
described below.
You should set the system up and allow the pearl to
bounce off the bracket a few times. The bracket should
be stationary; the pendulum is simply pulled back and
released to bounce against the bracket.
Note whether the pearl strikes the bracket more and more
frequently or less and less frequently with each bounce.
If the pearl does not bounce off the bracket several
times after being released, it might be because the
copper wire below the pearl is getting in the way. If
necessary you can clip some of the excess wire (being
careful to leave enough to keep the bead from falling
through).
If the bracket is tilted back a bit, as shown in the
next figure below, the pearl will naturally rest against
the bracket. Tilt the bracket back a little bit and,
keeping the bracket stationary, release the pendulum.
Listen to the rhythm of the sounds made by the ball
striking the bracket.
• Do the sounds get closer together or further
apart, or does the rhythm remain steady? I.e., does
the rhythm get faster or slower, or does it remain
constant?
• Repeat a few times if necessary until you are
sure of your answer.
Insert your answer into the space below, and give a good
description of what you heard.
Your response (start in the next line):
With the bracket tilted back the sounds get closer
together, or faster.
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If the bracket is tilted forward a bit, as shown in the
figure below, the pearl will naturally hang away from
the bracket. Tilt the bracket forward a little bit (not
as much as shown in the figure, but enough that the
pearl definitely hangs away from the bracket). Keep the
bracket stationary and release the pendulum. Note
whether the pearl strikes the bracket more and more
frequently or less and less frequently with each bounce.
Again listen to the rhythm of the sounds made by the
ball striking the bracket.
• Do the sounds get closer together or further
apart, or does the rhythm remain steady? I.e., does
the rhythm get faster or slower, or does it remain
constant?
• Repeat a few times if necessary until you are
sure of your answer.
Insert your answer into the box below, and give a good
description of what you heard.
Your response (start in the next line):
When the bracket is tilted forward the sounds get
further apart, the rhythm gets slower.
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If the bracket is placed on a perfectly level surface,
the pearl will hang straight down, just barely touching
the bracket. However most surfaces on which you might
place the bracket aren't perfectly level. Place the
bracket on a smooth surface and if necessary tilt it a
bit by placing a shim (for a shim you could for example
use a thin coin, though on most surfaces you wouldn't
need anything this thick; for a thinner shim you could
use a tightly folded piece of paper) beneath one end or
the other, adjusting the position and/or the thickness
of the shim until the hanging pearl just barely touches
the bracket. Pull the pearl back then release it.
If the rhythm of the pearl bouncing off the bracket
speeds up or slows down, adjust the level of the
bracket, either tilting it a bit forward or a bit
backward, until the rhythm becomes steady.
Describe the process you used to make the rhythm steady,
and describe just how steady the rhythm was, and how
many times the pendulum hit the bracket..
Your response (start in the next line):
I placed the bracket on my desk. I placed a piece of
notebook paper, folded in half two times, under the back
side of the bracket until the bead was in equilibrium.
In this position, when the bead was pulled away from the
bracket and released, the bead held a steady rhythm. I
repeated the pull several times and the rhythm remained
constant pattern of 12 audible strikes or hits.
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On a reasonably level surface, place one domino under
each of the top left and right corners of your closed
textbook, with the front cover upward. Place the
bracket pendulum on the middle of the book, with the
base of the bracket parallel to one of the sides of the
book. Release the pendulum and observe whether the
sounds get further apart or closer together. Note the
orientation of the bracket and whether the sounds get
further apart or closer together.
Now rotate the base of the bracket 45 degrees
counterclockwise and repeat, being sure to note the
orientation of the bracket and the progression of the
sounds.
Rotate another 45 degrees and repeat.
Continue until you have rotated the bracket back to its
original position.
Report your results in such a way that another student
could read them and duplicate your experiment exactly.
Try to report neither more nor less information than
necessary to accomplish this goal. Use a new line to
report the results of each new rotation.
Your response (start in the next line):
1) Position the base of the bracket parallel to the
spine of the elevated textbook and the face of the
bracket facing downhill. The bead hangs away from the
face of the bracket. In this position the strikes get
further apart.
2) From this position I rotated the bracket 45 degrees
in a clockwise direction. In this position the strikes
get further apart but not as far apart as the previous
position.
3) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The base of
the bracket is now parallel with the top and bottom of
the textbook. In this position the bead strikes the
bracket in a very slightly increasing rhythm.
4) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The face of
the bracket is now pointing uphill. The bead is resting
against the face of the bracket. In this position the
strikes get closer together.
5) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The bracket
is now facing the opposite direction from where it
started. In this position the strikes are noticeably
closer together.
6) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The face of
the bracket is still facing uphill and away. The
strikes get closer together but not as quickly as the
previous position.
7) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The base of
the bracket is now parallel with the top and bottom of
the textbook. In this position the bead strikes the
bracket in a very slightly increasing rhythm.
8) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The face of
the bracket and the bead are now facing downhill at an
angle. In this position the strikes get further apart.
9) From this position I rotated the bracket through
another 45 degrees in a clockwise rotation. The bracket
is now in the original position. The strikes get
further apart, even more so than the previous position.
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Describe how you would orient the bracket to obtain the
most regular 'beat' of the pendulum.
Your response (start in the next line):
I would orient the bracket at approximately 15 degrees
below horizontal on the elevated book to obtain a steady
rhythm.
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Orient the bracket in this position and start the TIMER
program. Adjust the pendulum to the maximum length at
which it will still bounce regularly.
Practice the following procedure for a few minutes:
Pull the pendulum back, ready to release it, and place
your finger on the button of your mouse. Have the mouse
cursor over the Click to Time Event button. Concentrate
on releasing the pendulum at the same instant you click
the mouse, and release both. Do this until you are sure
you are consistently releasing the pendulum and clicking
the mouse at the same time.
Now you will repeat the same procedure, but you will
time both the instant of release and the instant at
which the pendulum 'hits' the bracket the second time.
The order of events will be:
• click and release the pendulum simultaneously
• the pendulum will strike the bracket but you
won't click
• the pendulum will strike the bracket a second
time and you will click at the same instant
We don't attempt to time the first 'hit', which occurs
too soon after release for most people to time it
accurately.
Practice until you can release the pendulum with one
mouse click, then click again at the same instant as the
second strike of the pendulum.
When you think you can conduct an accurate timing,
initialize the timer and do it for real. Do a series of
8 trials, and record the 8 time intervals below, one
interval to each line. You may round the time intervals
to the nearest .001 second.
Starting in the 9th line, briefly describe what your
numbers mean and how they were obtained.
Your response (start in the next line):
.359
.375
.391
.313
.375
.375
.328
.375
.359
The above numbers represent the time, in seconds; it
takes the bead to complete a cycle. A cycle consists of
being released and striking the bracket two times.
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Finally, you will repeat once more, but you will time
every second 'hit' until the pendulum stops swinging.
That is, you will release, time the second 'hit', then
time the fourth, the sixth, etc..
Practice until you think you are timing the events
accurately, then do four trials.
Report your time intervals for each trial on a separate
line, with commas between the intervals. For example
look at the format shown below:
.925, .887, .938, .911
.925, .879, .941
etc.
In the example just given, the second trial only
observed 3 intervals, while the first observed 4. This
is possible. Just report what happens in the space
below. Then on a new line give a brief description of
what your results mean and how they were obtained.
Your response (start in the next line):
.406, .719, .719, .679, .734
.422, .765, .689, .719, .750
.375, .813, .750, .734, .726
.484, .750, .689, .727, .766
The numbers above represent the time in seconds for
every second strike of the pendulum. I used the timer
program to capture the times. From the data it would
appear that I anticipated the first second strike on
each of the 4 test. This is also reflected in the
previous question where the times are approximately .3
seconds faster than the recorded rhythm.
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Now measure the length of the pendulum. (For the two-
pearl system the length is measured from the bottom of
the 'fixed' pearl (the one glued to the top of the
bracket) to the middle of the 'swinging' pearl. For the
system which uses a bolt and magnet at the top instead
of the pearl, you would measure from the bottom of the
bolt to the center of the pearl). Using a ruler marked
in centimeters, you should be able to find this length
to within the nearest millimeter.
What is the length of the pendulum?
Your response (start in the next line):
12.4 cm
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If you have timed these events accurately, you will see
clearly that the time from release to the second 'hit'
appears to be different than the time between the second
'hit' and the fourth 'hit'.
On the average,
• how much time elapses between release and the
second 'hit' of the pendulum,
• how much time elapses between the second and
fourth 'hit' and
• how much time elapses between the fourth and
sixth 'hit'?
Report your results as three numbers separated by
commas, e.g.,
.63, .97, .94
Your response (start in the next line):
.422, .762, .712
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A full cycle of a free pendulum is from extreme point to
equilibrium to opposite extreme point then back to
equilibrium and finally back to the original extreme
point (or almost to the original extreme point, since
the pendulum is losing energy as it swings)..
The pearl pendulum is released from an 'extreme point'
and strikes the bracket at its equilibrium point, so it
doesn't get to the opposite extreme point.
It an interval consists of motion from extreme point to
equilibrium, or from equilibrium to extreme point, how
many intervals occur between release and the first
'hit'?
Your response (start in the next line):
There is one interval.
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How many intervals, as the word was described above,
occur between the first 'hit' and the second 'hit'?
Explain how your description differs from that of the
motion between release and the first 'hit'.
Your response (start in the next line):
There are two intervals between the first hit and the
second hit. There is one more because the interval was
defined as the motion from an extreme point to
equilibrium or from equilibrium to extreme point. The
first hit is at equilibrium, the bead then travels to an
extreme point, and this is one interval. From this
point back to equilibrium is an additional interval.
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How many intervals occur between release and the second
'hit', and how does this differ from the motion between
the second 'hit' and the fourth 'hit'?
Your response (start in the next line):
There are three intervals between release and the second
hit; this is because release to strike is one interval.
From strike to extreme point is another, and from
extreme point to the second hit is the third interval.
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How many intervals occur between the second 'hit' and
the fourth 'hit', and how does this differ from a
similar description of the motion between the fourth
'hit' and the sixth 'hit'?
Your response (start in the next line):
There are four intervals between the second hit and the
fourth, there are also four intervals between the fourth
hit and the sixth hit.
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Why would we expect that the time interval between
release to 2d 'hit' should be shorter than the
subsequent timed intervals (2d to 4th, 4th to 6th,
etc.)?
Your response (start in the next line):
The time is shorter because there is one less interval.
I thought I was anticipating the strike and clicking
the timer too soon. I did not take into consideration
the interval of the pendulum.
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Would we expect additional subsequent time intervals to
increase, decrease or stay the same?
Your response (start in the next line):
If the bracket is perfectly level I would expect the
subsequent intervals to stay the same.
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What evidence does this experiment provide for or
against the hypothesis that the length of a pendulum's
swing depends only on its length, and is independent of
how far it actually swings?
Your response (start in the next line):
This experiment supports the hypothesis. The length of
the swing is dependent upon the length of the pendulum,
the distance of the swing did not affect the time of the
intervals.
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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 response (start in the next line):
1 hour and 40 minutes
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&#Very good data and responses. Let me know if you have questions. &#