#$&* Phy 201
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As the pearl bounces off the bracket, the sounds get closer and closer together, indicating that the frequency of the bouncing is increasing as time goes on. I heard the pearl clang against the metal and the sound getting more frequent but less pronounced as the bouncing slowed. #$&* 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 &&&&&&&&&&&&&&&&&&
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This time, the sound becomes less and less frequent with each bounce. In fact, when the ball comes to rest it stops touching the bracket altogether. #$&* If the bracket is placed on a perfectly level surface, the pearl will hang straight down, just barely touching the bracket. However most surfaces on which you might place the bracket aren't perfectly level. Place the bracket on a smooth surface and if necessary tilt it a bit by placing a shim (for a shim you could for example use a thin coin, though on most surfaces you wouldn't need anything this thick; for a thinner shim you could use a tightly folded piece of paper) beneath one end or the other, adjusting the position and/or the thickness of the shim until the hanging pearl just barely touches the bracket. Pull the pearl back then release it. If the rhythm of the pearl bouncing off the bracket speeds up or slows down, adjust the level of the bracket, either tilting it a bit forward or a bit backward, until the rhythm becomes steady. Describe the process you used to make the rhythm steady, and describe just how steady the rhythm was, and how many times the pendulum hit the bracket..your response &&&&&&&&&&&&&&&&&&
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The bracket was placed on a level glass surface, and the ball was released. The sounds were relatively uniform although it appeared that the bouncing became slightly more frequent toward the end as the pearl slowed. Because of this, three sheets of paper were placed under the far end of the bracket to balance this out. It was successful. #$&* 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 &&&&&&&&&&&&&&&&&&
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While parallel to the sides of the text book, the pearl was released and was noted to exhibit a slight increase in the frequency of the bounces as it slowed to rest. Once rotated 45 degrees counterclockwise, the sound still showed the same trend; however, it seemed to be less marked (ie it bounced quickly 3 times before stopping versus 4 or 5 times in the previous trial). Upon another 45 degree rotation counterclockwise, the bracket was perpendicular to the long edges of the textbook. The sounds again hastened toward the end as the pearl came to rest, which is to be expected since the position of the pearl at rest is slightly touching the bracket. The third 45 degree rotation made the pearl strike with a relatively uniform sound from beginning to end. Once back to the starting position (another 45 degree rotation), the same behavior as originally noted was observed with the pearl hitting more frequently as the pearl slowed. #$&* Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.your response &&&&&&&&&&&&&&&&&&
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Ideal bracket orientation would be the one I constructed using three sheets paper to balance out the difference and have the pearl strike the bracket at relatively uniform time intervals. This would provide the most regulat 'beat' of the pendulum because the surface was altered to be as uniform as possible and the reasonably uniform striking pattern of the pearl to bracket reflects this. #$&* 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 &&&&&&&&&&&&&&&&&&
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Trial Time interval for each strike (s) 1 0.52, 0.62, 0.63, 0.59, 0.71 2 0.62, 0.71, 0.69, 0.73, 0.77 3 0.60, 0.53, 0.63, 0.57, 0.65, 0.49 4 0.39, 0.38, 0.32, 0.30, 0.27, 0.33 5 0.43, 0.39, 0.44, 0.37, 0.41, 0.36 6 0.47, 0.49, 0.42, 0.39, 0.36, 0.51 7 0.51, 0.56, 0.47, 0.54, 0.60, 0.59 8 0.49, 0.48, 0.38, 0.51, 0.47 The time intervals were measured for each of the 8 trials beginning with the second 'hit' of the pearl to the bracket. Measurements were concluded when the ball stopped and began to roll against the bracket. #$&* Finally, you will repeat once more, but you will time every second 'hit' until the pendulum stops swinging. That is, you will release, time the second 'hit', then time the fourth, the sixth, etc.. Practice until you think you are timing the events accurately, then do four trials. Report your time intervals for each trial on a separate line, with commas between the intervals. For example look at the format shown below: .925, .887, .938, .911 .925, .879, .941 etc. In the example just given, the second trial only observed 3 intervals, while the first observed 4. This is possible. Just report what happens in the space below. Then on a new line give a brief description of what your results mean and how they were obtained.your response &&&&&&&&&&&&&&&&&&
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Trial Time interval for every other even strike (s) 1 0.41, 0.44, 0.43 2 0.62, 0.69, 0.77 3 0.47, 0.51, 0.60, 0.59 4 0.38, 0.49, 0.47 5 0.52, 0.63, 0.71 6 0.36, 0.42, 0.47 7 0.60, 0.63, 0.65 8 0.27, 0.32, 0.34, 0.33 The time intervals were measured for each of the 8 trials beginning with the second 'hit' of the pearl to the bracket and continuing measuring every other hit. Results were obtained by measuring each hit and then ignoring the odd hits to find the values for the 2nd, 3rd and 4th hits. Measurements were again concluded when the ball stopped and began to roll against the bracket. #$&* 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 &&&&&&&&&&&&&&&&&&
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Using the regular scaled paper ruler, the pendulum length from the bottom of the bar magnet to the middle of the pearl was found to be 10.8 cm. #$&* If you have timed these events accurately, you will see clearly that the time from release to the second 'hit' appears to be different than the time between the second 'hit' and the fourth 'hit'. On the average, how much time elapses between release and the second 'hit' of the pendulum, how much time elapses between the second and fourth 'hit' and how much time elapses between the fourth and sixth 'hit'? Report your results as three numbers separated by commas, e.g., .63, .97, .94your response &&&&&&&&&&&&&&&&&&
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2nd 4th 6th 0.40 s, 0.52 s, 0.56 s #$&* 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. If 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 &&&&&&&&&&&&&&&&&&
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One interval has taken place after the pearl is released and strikes the pendulum. The starting point represents the one extreme, and the bracket is the equilibrium position. #$&* How many intervals, as the word was described above, occur between the first 'hit' and the second 'hit'? Explain how your description differs from that of the motion between release and the first 'hit'.your response &&&&&&&&&&&&&&&&&&
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Three intervals of this sort have taken place in total. One between initial position and the first strike, another after it moves back out to the extreme, and the third once it strikes the bracket for the second time. #$&*your response &&&&&&&&&&&&&&&&&&
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3 intervals occur between release and the second hit. Between the second and fourth hit, 4 intervals have taken place (7 in total from the starting point). This differs because between the second and fourth hit, the string is now starting at its equilibrium point, making time for another interval to take place. #$&* How many intervals occur between the second 'hit' and the fourth 'hit', and how does this differ from a similar description of the motion between the fourth 'hit' and the sixth 'hit'?your response &&&&&&&&&&&&&&&&&&
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There are 4 intervals between the second and the fourth hit. Between the fourth and the sixth hit, there would theoretically also be 4 intervals; however, the pendulum is clearly slowing down, meaning that the number of intervals is reduced or even halved because the pearl is no longer reaching out to the extreme point at which it started. #$&* 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 &&&&&&&&&&&&&&&&&&
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The time interval from release to second hit should be shorter than the subsequent intervals because the pendulum starts out going quickly and gradually slows as it hits the bracket and loses some of its kinetic energy. #$&* Would we expect additional subsequent time intervals to increase, decrease or stay the same?your response &&&&&&&&&&&&&&&&&&
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Subsequent times as the pearl slows to a stop may actually decrease again depending upon how measurements are made because often the pearl will bounce a few times quite rapidly before coming to a stop against the bracket. #$&*your response &&&&&&&&&&&&&&&&&&
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We created a pendulum that only goes from one extreme to its equilibrium point and back, which shortened the distance it actually swung. This altered the behavior of the pendulum and shows that length is not necessarily the only factor that influences pendulum behavior. Pearl position before each cycle was also not measured to ensure that each trial began at exactly the same point. As a result, different time intervals were recorded for each trial. In an ideal full pendulum that has motion from one extreme to the other the length certainly does appear to be the predominating factor. #$&*Revision isn't requested, but if you do choose to submit revisions, clarifications or questions, please insert them into a copy of this document, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#