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 sounds get closer together. I imagine a graph would show a dampening effect.
** Your description of the rhythm of the pendulum when tilted 'forward' **
The sounds still get closer together, but at a slower rate.
** Your description of the process used to keep the rhythm steady and the results you observed: **
I don't understand how it is possible to obtain a steady rhythm. The closest I came to a steady sounding rhythm was when the bracket neared a 45 degree angle. Each consecutive bounce is going to occur less frequently then the last.
If the pendulum at equilibrium is hanging 'away from' the bracket then the sounds will get further apart. If at equilibrium it's resting against the bracket, they will get closer together. If at equilibrium it's just barely touching the bracket, then the sounds will be at regular intervals.
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
Using the apparatus described above, orient on the surface of the book parallel to the longest sides of the book(having been shimmed on one end with one domino on each corner) with the pearl touching the bracket. Each trial consists of pulling the pearl away from the bracket, with the thread taut, and releasing.
-The frequency the pearl strikes the surface increases at a given rate.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate less than the first trial. The pearl strikes the surface with less energy than the previous trial.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate less than the previous trial. The pearl strikes the surface with less energy than the previous trial.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate less than the previous trial. The pearl strikes the surface with less energy than the previous trial.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at the least rate. The pearl strikes the surface with least amount of energy.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate greater than the previous trial. The pearl strikes the surface with more energy than the previous trial.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate greater than the previous trial. The pearl strikes the surface with more energy than the previous trial.
Turn 45 degrees clockwise.
-The frequency the pearl strikes the surface increases at a rate greater than the previous trial. The pearl strikes the surface with more energy than the previous trial.
Turn 45 degrees clockwise.
-Original position
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would orient the bracket with the pearl furthest from the bracket initially.
** Your report of 8 time intervals between release and the second 'hit': **
.328
.328
.336
.336
.328
.336
.391
.391
These numbers represent the amount of time it takes for the pearl to travel an unknown distance to the bracket(different each time the pendulum is pulled back), strike the bracket, retract, and strike the bracket a second time.
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.328, .336, .438
.265625, .328125, .5
.328125, .328125, .4375
.3203125, .328125, .4453125
It appears from your data that the rhythm of the 'hits' is decreasing in frequency; the 'hit' are occurring at greater and greater time intervals.
In your report you seem to indicate an increasing rate and also a decreasing rate, in answer to different questions.
Can you clarify?
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
9.5 cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
** Your description of the pendulum's motion from release to the 2d hit: **
I'd say it travels an arched path equal to pi over four radians with respect to the point the string is held at the top of the bracket.
&#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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** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The motion is as described above, only less after the first hit.
** 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: **
** 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: **
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
** **
** **
I can picture a number of molecules arranged in a convex shape on the surface of the pearl. I can imagine the intermolecular forces, behaving like springs as the number of atoms displace into a flatter shape transferring some energy to the atoms in the metal and the air, making sound. Then, when all the kinetic energy of the mass attached to the surface molecules of the pearl have traveled through them and been absorbed by their bonds, the intermoleclar forces throw the group back to a convex shape thrusting them and the rest of the pearl away from the bracket. The energy that exceeds that which is absorbed by the bonds of the molecules on the surface of the pearl that collide with the bracket travels into the bracket(and bursts into the molecules in the air) displacing and exciting the molecules there. The energy that is left thrusts the pearl away to repeat the process again, only with less kinetic energy as before. I'm sorry, but the questions above were frustrating me.
You have an excellent understanding of the molecular interactions.
However you haven't described the details of the motion of the pendulum; and your reports of the rhythm seem to be inconsistent. See my notes and please clarify as indicated.