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 gets closer and closer but the sound gets fainter and fainter
** Your description of the rhythm of the pendulum when tilted 'forward' **
I think the rhythm sounds about the same. About 4 or 5 ticks that get closer together and fainter
** Your description of the process used to keep the rhythm steady and the results you observed: **
I added some quarters to the front of the bracket
** Your description of what happened on the tilted surface (textbook and domino), rotating the system 45 degrees at a time: **
12;00, 5 beats
10:30, 5 beats
9:00, 5 beats
7:30, 6 beats
6:00 5 beats
4:30, 5 beats
3:00, 6 beats
1:30, 5 beats
12:00 5 beats
** Your description of how you oriented the bracket on the tilted surface to obtain a steady rhythm: **
I would orientate the bracket at either 7:30 or at 3:00 looking at the book bottom
** Your report of 8 time intervals between release and the second 'hit': **
.281
.344
.328
.359
.328
.297
.266
.344
The numbers indicate the release of the pendulum and the second strike time interval in seconds
** Your report of 4 trials timing alternate hits starting with the second 'hit': **
.656, .625
.531, .516
.688, .547
.578, .531
The results are for 3 hits because the first hit just starts the timer.
The TIMER should start simultaneously with the release. If you try to start on the first 'hit' you will tend to either anticipate or delay the click (everyone has one tendency or the other). If you release the pendulum with one hand and at the same instant click with the other, you will have much less error on that first 'click'.
On the other hand, if your anticipation or delay on the first 'hit' is the same as on the last, you will get a correct time interval.
However, the bottom line is that here you were asked for the time from the second 'hit' to the fourth, in which case the TIMER would start with the second 'hit', not the first.
** The length of your pendulum in cm (you might have reported length in mm; the request in your instructions might have been ambiguous): **
8cm
** Your time intervals for alternate 'hits', starting from release until the pendulum stops swinging: **
.28, .66, .53
.34, .53, .52
.33, .69, .53
.36, .58, .53
** Your description of the pendulum's motion from release to the 2d hit: **
I release the pendulum from my set extreme point and then when it makes contact, its direction changes and reverses its direction having experienced the pendulum's two extreme points.
** Your description of the pendulum's motion from the 2d hit to 4th hit: **
The motion after the first hit is away from the bracket reversing its swing until gravity slows the swing and returns the pendulum for another hit against the bracket. The motion from the free fall is acceleration only until the pearl hits the bracket while the return is acceleration from a stop until it stops again
** 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: **
The release motion and hit differs from the 2nd-4th hits in that the pendulum return motion back toward the starting position keeps getting shorter and shorter which means it takes less time to return and hit the bracket
** 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: **
I'm going to say that the motion from the 4th-6th hit is shorter and faster than the 2nd-4th hits. I never could get this data
** Your conjecture as to why a clear difference occurs in some intervals vs. others: **
I would think that you are only timing 1.5 cycles of the hit for the 1st interval while the 2nd-4th interval is 2 complete cycles
Actually you are timing 3/4 of a cycles for one and 1 cycle for the other. A cycle woult run from one extreme position through equilibrium to the other extreme position, then back through equilibrium to the original extreme position. The motion naturally divides into four quarter-cycles, with each quarter cycle running from equilibrium to extreme or from extreme to equilibrium. Release to second 'hit' constitutes 3 quarter-cycles, then subsequent 'hits' occur at intervals of a half-cycle.
This pendulum, of course, never gets to actually complete a full cycle. The bracket interrupts the cycle in the middle, so that 'hits' are always separated by a half-cycle.
** What evidence is there that subsequent intervals increase, decrease or remain the same: **
The 2nd-4th interval should be longer then each subsequent period should get shorter
If the pendulum is set up so that the rhythm of the 'hits' is steady, then these intervals should in fact be unchanging, or should be changing so little that the differences are smaller than the uncertainty in measurement.
There is a tendency for your data to indicate how a shortening period. This could be for any of a number of reasons.
One possibility is that an expectation of shorter periods affects your timing. Everyone, even the best-trained observers, are susceptible to this effect. Most observers, when they recognize this tendency, then attempt in various ways, some conscious and some subconscious, to compensate. This can be helpful, but like everything else it can be overdone, resulting in even greater uncertainties.
Another possibility is that the pendulum might not have been set up in such a way as to make the intervals uniform. To an extent this is inevitable, since there is always some uncertainty in any setup. In this experiment the setup depends on the user's ability to detect evenness of intervals, and as with everything else, nobody's perfect in this regard.
These errors tend to 'smooth out' if you time more 'hits'. Most students report 3 intervals, starting with the 2d 'hit', indicating that they observed at least 8 'hits'. Some report two (as in your case) and a few report four. So the number of detectable 'hits' of this system appears to be between 6 and 10.
** What evidence is there that the time between 'hits' is independent of the amplitude of the swing? **
The longer the pendulum, the longer it will take for the pendulum to swing and return after hitting the bracket. The distance it swings will be determined by the rebound of the pearl and acceleration of the gravity. The longer the pendulum the more acceleration is possible. Think of a 3 feet long pendulum and a 3 inch pendulum. Gravity will act the same on both but the longer one will have more time to achieve the maximum while the shorter will have hit the bracket almost instantly.
Greater amplitude implies greater speed, which by itself would imply a shorter time, but also greater distance, which by itself would imply a longer time. The two effects in fact tend to 'cancel', resulting in a very nearly uniform period for the relatively small amplitudes that occur after the second 'hit'.
For very large amplitudes, the effect of the greater speed 'wins out' over the effect of greater distance and the period becomes a little shorter.
To completely understand the motion of the pendulum requires a knowledge of first-year calculus.
The bottom line for all but University Physics students is that for amplitudes less than about 1/3 the length of the pendulum, the period is very nearly the same, regardless of amplitude.
This fact was the basis for the earliest accurate clocks.
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This lab took me 1 hour and 50 minutes.
** **
This lab took me 1 hour and 50 minutes of which it took me about 25 minutes to hand drill with a 1/16 drill bit and a pair of side cutters holding the drill bit to get a hole in the pearl were there was a string.
Good work, but see my comments to clarify a few important properties of pendulum motion, as well as some of the subtleties of the observation process..