Phy 231
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' **
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.
When you pull it away from the bracket and release it the taps get closer and closer together. At first there is some space between the sounds, but the pendulum begins to swing faster and soon the hits all blend together so that you cannot tell them apart. Then, finally, the pendulum stops swinging.
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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.
If the bracket is tilted so that the pendulum is not touching the metal and it is released, the taps get farther and farther apart. They begin pretty regularly spaced, but then the space between the taps becomes longer. This is because the pendulum has lost so much energy that it cannot reach the metal anymore and cannot make a tapping sound.
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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.
I placed a penny underneath the far end of the bracket to tilt it forward, so that the pearl barely touched the metal. The rhythm of the pearl was very steady after the bracket’s tilt was fixed. The taps were pretty close together; they began louder when the bead is first released, but then became quieter as the pendulum loses energy. However, the space between the taps was constant. I heard 12 distinct taps from the bead before they got so quiet that I could not distinguish them.
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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.
The orientation of the bracket in degrees refers to looking at a unit circle, where 180 degrees is when the bead is facing straight to the left of the book and 360 degrees is when the bead is facing straight to the right. The test began at 90 degrees with the bracket facing the top of the book. 45 degrees were added onto the orientation for each subsequent test. After 360 degrees, the measurement went back to 0 degrees, like a normal unit circle.
90 degrees closer together
135 degrees closer
180 degrees closer
225 degrees constant rhythm
270 degrees slower rhythm
315 degrees constant
360 degrees closer
45 degrees closer
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Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.
To get a constant beat from the pendulum, I would place my bracket so that it was facing the bottom left corner of the text book. This is where the rhythm was the most regular because the tilt of the book and the bracket canceled each other out.
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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.
.374
.328
.296
.328
.296
.312
.281
.328
These intervals were obtained beginning with the second tap of the pendulum. I used the timer program and stopped the clock every time the pendulum hit the metal and made a tap. The intervals represent the time in seconds it took for the pendulum to hit the metal, rebound and come back to hit the metal; this is the same as 1 cycle of the pendulum. &&&&This is the same as a half of a cycle of a pendulum, from one extreme point to the opposite extreme point.&&&&
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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
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.
.624, .609, .608
.64, .608, .64
.609, .592, .656
.593, .624, .608, .608
The numbers above are the time in seconds it took for the pendulum to complete two full cycles. &&&&This is the same as 1 full cycle of a pendulum, from one extreme point, through equilibrium, to the opposite point and back to the beginning extreme point.&&&&You get the results by stopping the time program on every second tap of the pendulum, starting with the second tap.
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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?
The pendulum is 8.6 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
.47, .62, .61
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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'?
One interval happens between the release and the first hit. It goes from the extreme point to 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'.
You get two intervals in the time between the first and second hits. It goes from extreme point to equilibrium and back to the extreme point. This is different from the previous question because between the release and first hit there was only one interval; it is double the distance travelled.
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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 3 intervals between the release and the second hit. The pendulum goes from the extreme point to equilibrium, and then it completes two more intervals to get it back to equilibrium for the second hit. This is one interval less than in the time between the second and fourth taps.
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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'?
Four complete intervals occur between the second and fourth hits. It takes 2 to goes from the 2nd to the 3rd and then another two to go from the 3rd to the 4th hits. This is the same description of the motion as occurs between the 4th and 6th hits.
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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.)?
Release to the second hit is only 3 intervals, while all of the other time intervals consist of 4 intervals of the pendulum. Fewer intervals result in less time.
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Would we expect additional subsequent time intervals to increase, decrease or stay the same?
You would expect for the other time intervals to stay the same length because the pendulum is swinging at a constant rate. After a while some of the energy in the pendulum might be lost, and, depending on if the pendulum is completely stable, the intervals might begin to lose or gain some time. However, most of the intervals of the pendulum will be the same length.
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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 length (like the distance travelled by the pendulum) is definitely affected by the length of the string. I do not think that there is evidence that shows that the pendulum’s length of swing is affected by the actual displacement. Although the pendulum in the test was only completing half swings, the intervals that it was moving on seemed to be constant like a normal pendulum.
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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 hour
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Excellent work. You have very good data, and it does nicely support the 4/3 ratio of these intervals.