Phy 201
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.
** #$&* Your general comment, if any: **
** #$&* Your description of the rhythm of the pendulum when tilted 'back' **
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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.
The sounds get closer together and the rhythm speeds up. There is a very small pause between bounces.
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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.
The sounds get farther apart and the rhythm is slower. Since the bracket is tilted forward it takes longer for the bead to travel back to the bracket. The bead is covering more distance and therefore hitting the bracket in a slower rhythm.
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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..
The pearl bounced off the bracket 5 times. I would listen for a good rhythmic beat and readjust the bracket until I could hear a consistent rhythm. For my bracket I had to shim up the front of the bracket about 2mm to obtain a steady rythym.
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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.
My starting point is for the pearl side of the bracket to be facing towards the top center of the book. I rotated clockwise.
0 degrees, fast rhythm, sounds are close
45 degrees, slows a bit, sounds still closer
90 degrees, slows a bit more, bad rhythm
135 degrees, good rhythm and consistent sound, still slower than last
180 degrees, good rhythm, distance between sound has increased
225 degrees, speeds up, bad rhythm
270 degrees, speeds up more, sounds becoming farther apart
315 degrees, speeds up even more, sounds still increasing in distance
360 degrees, original position.
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Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.
I got my best rhythm and consistency at 135 degrees rotation from my starting position. I rotated the bracket clockwise.
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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.
.422
.422
.305
.391
.406
.367
.360
.340
These numbers are the time it takes the pearl to travel from the time I release it to the time it contacts the bracket the second time.
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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.
.570, .648
.531, .680
.578, .711
.477, .633
I never could get the pearl to bounce off of the bracket more than 5 times. We can see from the times above that it takes longer for the pearl to contact the bracket in the second interval. This tells us that the pearl is slowing down.
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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?
9.5cm
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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
.539, .668
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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'?
If an interval consists of motion from extreme point to equilibrium then the answer is 1. We release the pearl from an extreme point and then it contacts the bracket at the equilibrium.
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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'.
This would be 2. We have one interval from the first hit back to the extreme point. Then another interval from that extreme point to the bracket for the second hit.
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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'?
From release to the second hit we would have:
release to bracket(hit 1)
bracket to extreme
extreme to bracket(hit 2) Total of 4 intervals.
second hit to extreme
extreme to bracket(hit 3)
bracket to extreme
extreme to bracket(hit 4) Total of 4 intervals.
The motion difference is that the pearl is going to be slowing down the more times it contacts the bracket. So the pearl will complete the first 4 intervals faster than the last 4.
not so if the rhythm is constant
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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'?
second hit to extreme
extreme to bracket(hit 3)
bracket to extreme
extreme to bracket(hit 4) Total of 4 intervals.
Again we would have the same intervals but the pearl will be slowing down the longer that it is bouncing back and forth.
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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.)?
As the pearl travels back and forth it is losing velocity. As the pearl slows down it will take it longer to complete a cycle.
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Would we expect additional subsequent time intervals to increase, decrease or stay the same?
As we go the times should increase to a point and then level off or even start increasing a bit until the motion stops. As the pearl slows down it is going to travel a shorter distance from the bracket. At some point it will be so close that the shortness of distance will overcome the lack of speed and the times will start decreasing.
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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?
I am unsure of how to answer this question. I feel that many variables control the pendulums swing. One would be the type of pearl or ball on the end. Another would be the weight of the ball, or even the orientation of the bracket holding the pendulum. I am unsure as to how this experiment would provide me these answers though. We know that the farther the pendulum has to travel the more time it will take to complete an interval or cycle and that the orientation of the bracket will change the rhythm of the swing.
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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?
1.5 hours
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