course Phy 231
3/2 9
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' **
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. At first I could clearly hear the pearl hit the bracket maybe once or twice, and then I hear it tap at a faster pace with a faint noise.
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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.
This time I only heard three taps and they seemed more constant than having it on a flat surface. During this run, I did not hear multiply tiny faint taps at all.
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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 pendulum hit the bracket 5 times and it was at a very steady pace. The taps occurred in rhythm. I put the pendulum on top of a piece of wood, which kept it on a solid, flat surface.
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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.
When having the bracket parallel to the sides of my textbook, the pearl made the same noises as it did when it was on a completely flat surface except towards the last tap, the tap started to fade out. The other taps, 5 total, all seemed to be about the same pitch level and in a rhythmic pattern. For each angle I moved the pendulum to, I got the same results. The only difference was that the amount of the taps varied from 3-5 each time. There was one position that was a little different though. Turning the pendulum 180 degrees from the start, which had the pendulums back facing me as I sat behind the front of the book. When it was at that location, I did not hear any faint taps, but only the clear ones.
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Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.
I would keep it 180 degrees from the start which is when the back of the pendulum is facing me while I sit behind the front of the book as if I were about to read it. When it was at this location, I did not hear any faint taps which makes me think that the ‘beat’ was most regular.
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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.
0.41
0.20
0.25
0.18
0.25
0.18
0.25
0.24
These numbers represent the time interval between when I let go of the pendulum, and when the pearl hit the board for the second time. I found these numbers by taking the time interval given from the TIMER program from my start and stop clicks.
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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.
0.289, 0.273, 0.242
0.242, 0.210, 0.195
0.234, 0.227, 0.195
0.211,0.242, 0.172
The results are each time intervals for when the pearl hit the board after its second hit. They were obtained by using the timer program. I was not able to get the 4th and 6th values but instead just did the 3rd and 4th and 5th because my pendulum was very short and did not hit the board enough times.
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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?
6.3 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
0.244, 0.251, 0.201
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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'?
7 intervals occur between release and the first ‘hit.’
In 7 intervals the pendulum would go from extreme point to equilibrium to opposite extreme point to equilibrium to original extreme point, then nearly complete the same sequence of positions (but ending up at equilibrium, just short of the original point). Motion from release to first 'hit' is much shorter than that.
&&&& The idea makes more sense now. &&&&
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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'.
2 intervals. The description differs from the motion between release and the first ‘hit’ because there is an extra motion between the first ‘hit’ and 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'?
3 intervals. There are three intervals between the second ‘hit’ and fourth ‘hit.’
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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'?
5 intervals between the second ‘hit’ and the fourth ‘hit.’ This is very similar to the fourth ‘hit’ and the sixth ‘hit’ in the sense that they have the same amount of interval movements.
&&&& I miscalculated because it should be 6 intervals &&&&
Both 'hits' occur at equilibrium. An odd number of intervals will not get you from equilibrium to equilibrium.
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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.)?
The time interval between release to 2nd hit should be shorter than other timed intervals because the other ones have more movement.
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Would we expect additional subsequent time intervals to increase, decrease or stay the same?
Additional subsequent time intervals would increase.
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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 pendulum’s swing does not depend only on its length because it depends on the distance it swings as well because the distance will change over time no matter what.
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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?
2 hours
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&#Please see my notes and submit a copy of this document with revisions and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end). &#
&#Please let me know if you have questions. &#