phy201
Your 'pearl pendulum' 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 general comment, if any: **
I have copied and paste my report in the box at the end.
Thanks
natalie
** Your description of the rhythm of the pendulum when tilted 'back' **
The simple device used in this experiment can serve as an accurate timing device when the 'beats' of the pendulum are synchronized with two events separated by a consistent time interval. Observations of
this system are consistent with the observed and theoretically predicted behavior of pendulums. Most students report that the experiment takes around an hour, with a range from 30 minutes to 2 hours, and in
a few cases longer.
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.
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 like this:
When suspended from the pendulum bracket by a thread the system might look something like this. 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.
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The sounds get closer together, so the rhythm gets faster. When the pearl hit the braket it was a quick tap tap sound.
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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.
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The sounds get further apart, so the rhythm gets slower. I heard the pearl hit the bracket but there was some time in between hits.
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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..
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To level the bracket I use a thin rubber band, that was on my desk from the las experiment, but it was sufficient so that the pear just barely touched the bracket. The sound seemed to be the most steady of
the two previous, the pearl hit the bracket consistently three times each time I pulled back and released the pearl. This seemed to be the most steady of the sounds, not to slow and not to fast.
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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.
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For the first rotation I had the bracket facing me with top of the book lifted by the dominos. When I pulled back on the pearl and released it it hit the brackes a total of three times at what seemed to be
a steady pace.
I then rotated the bracket 45 degrees to the left and pulled back and released the pearl, it hit the bracket a total of four times, at a much faster pace, the fourth hit seemed to be much closer in beat to
its previous third hit.
I then turned it another 45 degrees so that the back of the bracket was facing me and the pearl was on the other side. when I released the pearl it hit a total of three times at a faster rate than that of
the last 45 degree turn, the pearl hit the bracket a much faster rate compared to the previous rotation.
I then rotated the bracket another 45 degrees so the pearl was facing toward my right, it hit a total of four times with the fourth hit being close to the third hit as with the second rotation. The rhythm
seemed to be somewhat the same as the second rotation.
The last rotation was again facing me and agian the ball hit a total of three times, and the rhythm seems to be the most steady of the second, third, and fourth rotations and was the same as it was the first
time the pearl was facing me.
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Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.
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The most regular beat of the pendulum seemed to be the one in which the pearl was the most level with the bracket just barely touching the bracket as opposed to being to close in which it was laying on the
bracket or to far away in which it was leanig away from the bracket.
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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 quickly 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.
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0.625
0.609
0.813
0.855
0.730
0.516
0.559
0.906
The number above are the time intervals for the pearl to hit the bracket on the second hit. I obtained these number by subtracting the first clocktime when the pearl hit the bracket the second hit by the
the clcoktime after the hit, so around the third hit I stopped the clicking the timer.
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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.
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.297, .203, .266, .453
.250, .484, .699, .949
.266, .547
.281, .547, .8125
I obtained these interval by clicking on the timer when the pearl hit the bracket after the second hit. To find the clocktimes I subtracted each clocktime from the clocktime that was taken once the pearl
hit on the second hit. These time are reported by fractions of a second.
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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?
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7.4 centimeters
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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,
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.274, .358,
I had no fifth or sixth hits reported.
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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'?
There is one interval if the interval is consisting of motion from the extreme point to equilibrium, because the pearl is passing equilibrium just before it hits the bracket
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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'.
There are two intervals between the first hit and the second hit because the pearl goes from the first hit to equilibrium back to extreme point (one interval), and then from that extreme point to equilibrium
(second interval) until hit hits a second time.
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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'?
There are three intervals between the release and second hit, because the pearl goes from extreme point to equilibrium and then the first hit(one interval), it then goes from the point it hits to equilibrium
back to the extreme point( two intervals) and then from extreme point to equilibrium until it hits a second time(third interval). If you go from the second hit to the fourth hit you have an interval from the
second hit equilibrium to extreme point (1 interval), from extreme point to equilibrium (2 intervals) to the third hit, from the third hit equilibrium to extreme point (3 intervals) from extreme point to
equilibrium (4 interval) until it hits a fourth time. SO from the relase and second hit you have three intervals from the second hit and the fourth hit you have 4 intervals.
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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'?
There are 4 intervals between the second and fourth hit. From the third hit to equilibrium to extreme point (1 interval) from extreme point to equilibrium to fourth hit (2 interval) from fourth hit to
equilibrium to extreme point (3 interval) from extreme point to equilibrium fifth hit (4 intervals) from equilibrium to extreme point (5 interval) from extreme point to equilibrium until the sixth hit (6
intervals). So there is an increase by two interval from the fourth hit and the sixth hit in comparison to the second and fourth 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.)?
We expect that the time interval between release to second hit should be shorter that the subsequent time intervals because there are less intervals in between the release point to the the second hit. The
more hit the pearl make the added intervals it has in between hits.
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Would we expect additional subsequent time intervals to increase, decrease or stay the same?
Additional subsequent time intervals would increase the amount of intervals, as indicated by the increase to intervals in between each hit.
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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?
The evidence provided proves for the hypothesis that the length of a pendulums swing depends only on its lenghts and is undependent of how far it actually swings because of he amount of intervals in between
each hit. How far the pendulum swings does not seem to be a factor since the pearl is not going to go ack to the exact extreme point that you started it from or released it. The intervals are measured from
motion from extreme point to equilibrium from the start. The length may play a part in the amount of hits and how fast the pearl hits, but has no bearing on how far the pearl actually swings.
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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?
About two hours
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You may add optional comments and/or questions in the box below.
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&#Good responses. See my notes and let me know if you have questions. &#