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 rhythm remains constant. I can't get the pearl to bounce more than 6 times off the bracket. But, while the pearl is in motion bouncing off of the bracket there are a concsistent series of metal panging sounds. When the pearl stops bouncing, it simply comes into contact with the metal bracket and doesn't come back off it again.
** Your description of the rhythm of the pendulum when tilted 'forward' **
I am going to say the sounds are more frequent. I did this several times and either the ball bounced fewer times off of the bracket, or the ball had a couple of really good bounces and then bounced a very small distance away from the bracket several times.
** Your description of the process used to keep the rhythm steady and the results you observed: **
First of all, the bracket pendulum on the table I was using and bounced the pearl off of the bracket to see how steady the rhythm was. It was not at all consistent so I took the large washer from my lab kit and slid it under the end of the bracket not attached to the pearl. The rhythm became slight more consistent. I slid the little foam stand from the collision experiment (not the pegged part, just the foam itself) under the end of the bracket where the washer was located (it was placed on top of the washer). I bounced the pearl off of the bracket, and this time I heard a series of six equally spaced consistent pangs against the bracket before the pearl stopped.
We usually see 10 or more returns, but 6 will be sufficient.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
I placed my physics book on the table in front of me so that the title of the book was closest to me. I placed dominoes under the top left and right corners of the book respectively. Then I oriented the bracket (with the pendulum attached) so that the pendulum part was facing me and the bracket was parallel with the longer sides of the book. When the non-pendulum end of the bracket was away from me on the upper part of the book (not where the title is) is where I achieved the most steady rhythm and maximized the number of bounces off of the bracket. When the non-pendulum was toward me the number of bounces decreased drastically, and no consistent rhythm was detectable.
6
6
5
4
4
2
3
4
5
5
6
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
The bracket would be oriented in its original starting position as described above.
** Your report of 8 time intervals between release and the second 'hit': **
.234
.453
.281
.297
.297
.391
.250
.375
These numbers were obtained according to the directions provided above. These numbers represent the time interval between when the pendulum was released and the second hit.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
Trial 1
1 745.5313 745.5313
2 745.8594 .328125
3 746.1094 .25
4 746.4219 .3125
5 746.7031 .28125
6 747 .296875
Trial 2
1 780.6875 780.6875
2 781.0781 .390625
3 781.4063 .328125
4 781.75 .34375
5 782.1094 .359375
Trial 3
1 834.6563 834.6563
2 834.9688 .3125
3 835.2813 .3125
4 835.5781 .296875
5 836.0313 .453125
6 836.3906 .359375
7 836.7813 .390625
Trial 4
1 855.7813 855.7813
2 856.1719 .390625
3 856.5938 .421875
4 856.8906 .296875
5 857.1563 .265625
6 857.5625 .40625
These numbers were obtained according to the instructions provided above. The numbers represent 4 separate trials of time intervals occur from the release of the pendulum to the repeated 'second hit' (all the times the ball bounces after the second hit).
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
The pendulum is 3 inches long.
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.328,.390,.312,.390 mean = .355
.14,.077,.015,.187 mean = .105
.079,.016,.047,.172 mean = .079
** Your description of the pendulum's motion from release to the 2d hit: **
When conducting this experiment, one does not observe a full cycle of a free pendulum. The pendulum itself never makes it to the opposite point of extreme because it comes into contact with the bracket. Therefore the full cycle is interrupted by the bracket.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
Because of the magnets, after coming into contact with the bracket (or the first hit) the pendulum is no longer able to return to its original release point. So when it comes (bounces) back off of the bracket the pendulum only travels as far as the magnetism will permit, and then is pulled back toward the bracket again. This differs from first hit because the original point of release is not initially affected by the magnets.
** Your description of the difference in the pendulum's motion from release to the 2d 'hit', compared to the motion from the 2d 'hit' to the 4th hit: **
Concerning the second hit, the magnets are just beginning to have a noticeable effect on the motion of the pendulum. Between the second and the fourth hit, the time interval should either be the same or slightly decreased due to the increased effect of the magnets. Or, that is to say that the more difficult it becomes for the pendulum to reach its original point of release the smaller the time interal.
** Your description of the difference in the pendulum's motion from the 2d to the 4th 'hit' compared to the motion from the 4th to 6th hit: **
See above answer. It also applies to hits 4 and 6.
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
No, I would think the first time interval would be longer because the magnets haven't yet had the chance to effect the initial reading.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
Decrease (at least they would decrease over time)
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
I am going to assume that the first length mentioned in this question pertains to time. In which case I am going to say that there is evidence in this experiment that would support this hypothesis. The cycle of a pendulum, from its original point of release to its opposite extreme and back, is the same for all pendulums; however the length of the pendulums itself is the variable that will determine the amount of time it takes for the full cycle to occur.
** **
3 hours
** **
The pendulum is not magnetic so the magnets should have no effect. The pendulum does lose energy when it collides and when it swings, so each swing covers less distance than the preceding, as you have observed. Your results appear to be consistent with those expected for a pendulum of length 3 inches (about 7.6 cm).
&#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 (almost) the original extreme point.
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.
Thus the period of the pendulum can be divided into four parts. From the steadiness of the rhythm we have good evidence that the motion between 'hits' takes the same time independent of the amplitude of the motion (the rhythm remains constant while the amplitude of the motion decreases). Theoretically each of the four parts of the cycle, as described above, takes the same time. Assuming this to be true, we can speak of the quarter-cycle from an extreme point to equilibrium or from equilibrium to an extreme point.
Through how many quarter-cycles does the pendulum move between release and the second 'hit'?
Through how many quarter-cycles does it move between the second and the fourth 'hit'?
What therefore should be the ratio of the time interval from 2d to 4th 'hit', to the interval from release to the 2d 'hit'?
How does this ratio compare with the results you just reported?
Does this constitute evidence for or against the theoretical hypothesis that the quarter-cycles all require the same time?
Suggested response title: description of motion of pearl pendulum &#
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