pearl pendulum

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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.

** 19:56:41 02-09-2013 **

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The simple device used in this experiment can serve as an accurate timing device when the 'beats' of the pendulum are synchronized with two events separated by a

consistent time interval. Observations of this system are consistent with the observed and theoretically predicted behavior of pendulums. Most students report that

the experiment takes around an hour, with a range from 30 minutes to 2 hours, and in a few cases longer.

The Pearl Pendulum as shown below a bead (sometimes called a 'pearl', as the bead used in the original version was a fake plastic pearl) on a string, attached to bolt

glued to the top of a metal bracket, using a magnet to 'clamp' the string (in most current versions of the apparatus the bolt glued to the top of the bracket, which

proved to be unhelpful, is not included).

Your package will probably contain a bead about 1 cm in diameter, with a short piece of string through its center. This bead will be in your initial materials

package. The string protrudes from both sides of the bead, but will probably protrude more on one side than on the other. To suspend the bead, you need only tie a

piece of thread (a spool of which should be included in your package) around the longer bit of protruding string.

If your package didn't include the bead described above, it will include a bead and a piece of thin copper wire, as shown below. If you have this, you will need to

construct the pendulum as indicated below.

The wire is formed into a loop with the two ends protruding, and threaded through the bead.

The ends are pulled through forming a small loop at the top.

The protruding ends are twisted together then flattened against the bottom of the bead.

The above pictures were actually of a steel ball and a thicker wire. The bead and wire you have in your kit look something like this:

When suspended from the pendulum bracket by a thread the system might look something like the picture below. If the pendulum is pulled back and released, it will

bounce back to the bracket, rebound, and repeat its motion a number of times.

However note that in this picture the bracket is resting on end with the bolt glued to it; the bracket is not vertical.

The pearl appears to hanging in its equilibrium position, with a little space between it and the bracket.

As you will soon see, if the bead is just barely touching the bracket when it hangs at its equilibrium position, the rhythm of the bouncing pendulum will remain constant.

The bead is referred to below as the 'pearl', since the first design of this experiment used fake pearls cut from a cheap necklace. (The beads currently in use were also cut from a cheap plastic necklace; these beads have a higher coefficient of restitution than the originals, and they therefore work better).

When the pearl is released it swings back to the bracket, bounces off then swings back again, repeatedly striking the bracket. The magnet can be used to clamp the thread so, after being adjusted to the desired length, the length of the pendulum remains constant.

If you have just a plain bracket then you simply tilt the bracket in order to achieve a constant rhythm, as described below.

You should set the system up and allow the pearl to bounce off the bracket a few times. The bracket should be stationary; the pendulum is simply pulled back and released to bounce against the bracket.

Note whether the pearl strikes the bracket more and more frequently or less and less frequently with each bounce. If the pearl does not bounce off the bracket several times after being released, it might be because the copper wire below the pearl is getting in the way. If necessary you can clip some of the excess wire (being careful to leave enough to keep the bead from falling through).

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.

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

With the pearl totally at rest against the stainless steel, the rythem gets faster and faster as time passes. So it hits the stainless steel at an increasing rate until it returns to its equilibrium position resting against the stainless steel.

I used four pennies under bracket to have the pearl rest against the stainless steel in equilibrium, it hit the steel about 32 times, but the last few were pretty quick.

I released the pendulum about 1.5 inches measured horizontally from the equilibrium point. (x - axis)

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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.

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

With the pearl hanging a noticeable distance from the stainless steel as equilibrium, was released and the pearl strike the steel less frequently then it did in

resting equilibrium. It struck about 21 times, and the rhythm sounded consistent until the end where it did not strike the stainless steel.

I used 7 pennies under the bracket, to have the pearl hang in equilibrium an noticeable distance from the stainless steel.

I released the pendulum about 1.5 inches measured horizontally from the equilibrium point (x - axis)

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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..

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

On the kitchen floor I placed the system in a 1 foot by 1 foot tile. I used one american quarter, 2 american dimes, and an american penny as a shim, and it hung off the pendulum just barely away from the stainless steel. I released it about 1.5 inches in a horizontal distance and the rythem was consistent until the very end.

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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.

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

Level Pearl Pendulum on solid surface book plus 2 dominoes on top corners.

1st run, 0 degrees,

35, Sounds seem even, until pendulum cannot reach the stainless steel.

First entry is number of clicks/impacts, Second is human auditory judgement

2nd run, 45 degrees

30, Sounds seem even until last few impacts, then they get slower and slower.

First entry is number of clicks/impacts, Second is human auditory judgement

3rd run, 90 degrees

37, Sounds seem even until last few impacts, then they get slower and slower.

4rth run 135 degrees

36, Sounds seem even throughout.

5th run, 180 degrees

30, Sounds are even in the start, but get noticeably slower towards the end.

6th run, 225 degrees

33, Sounds are even in the start, then get slower near the end.

7th run, 270 degrees

27, Easier to notice sounds getting longer and longer.

8th run, 315 degrees

34, Sounds are even in the start, then get slower near the end.

9th run, 360 degrees

34, Sounds are even in the start, then get slower near the end.

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Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

The most regular beat would be at about 90 degrees With both dominoes face up and directly under the corners.

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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 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 &&&&&&&&&&&&&&&&&&

(start in the next line):

.359, .386, .390, .433, .394, .414, .386, .421, .417, .425, .441, .441, .433, .414, .5, .453, .460, .480, .484, .437, .503, .566, .468, .535, .480, .480, .535, .558, .523, .562, .589

.394, .417, .410, .410, .410, .390, .421, .433, .441, .402, .464, .429, .460, .414, .460, .402, .468, .480, .5, .464, .535, .535, .515, .519, .550, .621

.375, .394, .433, .406, .398, .429, .441, .437, .421, .429, .398, .484, .460, .437, .488, .464, .488, .464, .488, 5.03, .5, .527, .632, .472, .582, .542, .582,

.382, .390, .367, .437, .375, .421, .328, .425, .449, .410, .445, .433, .453, .453, .507, .464, .527, .496, .511, .511, 1.09, .558, .589, .574

.367, .363, .441, .398, .445, .378, .398, .417, .421, .394, .425, .421, .425, .402, .417, .433, .453, .453, .917, .476, .441, .476, .507, .507, .496, .546, .503, .511, .558, .566

.386, .398, .371, .425, .378, .402, .386, .417, .390, .414, .410, .375, .429, .421, .394, .472, .429, .417, .414, .437, .464, .421, .441, .453, 1.37, .484, .5, .507, .507, .554, .523, .613

.378, .421, .429, .359, .382, .410, .382, .437, .425, .417, .417, .406, .429, .453, .460, .453, .437, .464, .5, .472, .507, .519, .492, .496, .484, .503,

,390, .390, .394, .441, .375, .398, .394, .414, .406, .375, .445, .410, .406, .453, .421, .417, .414, .449, 1.351, .460, .496, .453, .472, .535, .488, .519, .507, .539, 523, .574

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You were asked only to time the very first interval, between the first mouse click at the instant of release and the second mouse click at the second following 'hit'. I assume that corresponds to the first timed interval.

The additional data, however, is useful in assessing the regularity of the 'hits'.

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These numbers are the differences in times to pendulum impact, one interval after another. If these times were plotted with interval vs time, the trendline for each of the eight graphs would increase at an increasing rate. This means that the time between intervals is increasing.

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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

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 &&&&&&&&&&&&&&&&&&

(start in the next line):

.542, .777, .800, .785, .820, .800, .789, .851, .859, .808, .839, .859, .847, .910, .972, .882, .984, .972, .992, 1.011, 1.078, 1.066

.792, .828, .855, 1.13, .828, .859, .855, .812, .851, .875, .898, .910, .933, .957, 1.01, .980, 1, 1.097, 1.003, 1.160, 1.210, 1.312, 1.234, 1.339

.75, .816, .808, .773, .864, .773, .867, .832, .859, .871, .859, .925, .917, .980, .996, .988, 1.078, 1.007, 1.203, 1.140, 1.218, 1.246, 1.300, 1.457

.558,, .765, .774, .839, .808, .804, .832, .804, .832, .804, .863, .835, .867, .898, .875, .855, .953, .980, .945, .968, .984, 1.097, 1.191, 1.242

With my system set up on the floor, on a book elevated by two dominoes on the corners. I had my wireless keyboard on my lap and i moved the pearl pendulum 4 cm in the x direction using a small stick like object, and the shadow it cast on a small 45 degree ruler at the base of the pendulum.

The shadow was used as a release point and i clicked the mouse on my wireless keyboard every second tap.

This part of the experiment again showed that the time between the intervals was increasing at an increasing rate. This time two taps were considered to be one period. On a graph of time vs interval number, the x distance ( interval would increase at a increasing rate.

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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?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

14.35 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

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

.745, .823, .808

From First data.

0.765, 0.839, 0.823,

From 6th data

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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'?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

One interval occurs between release and the first hit. It is from an extreme point to 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'.

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

Two intervals occur between the first hit and the second hit. From equilibrium to an extreme point, one interval, and from the extreme point to equilibrium, Two intervals.

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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'?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

Three intervals occur from release to the second hit. Extreme point to equilibrium, one interval. Equilibrium to extreme point, two intervals. Extreme point to Equilibrium, 3 intervals.

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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'?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

Four intervals occur, Equilibrium to extreme, 1 interval. Extreme to equilibrium, 2 intervals. Equilibrium to extreme, 3 intervals total. extreme to equilibrium 4

intervals total.

The motion between the fourth hit and the sixth hit would have the same number of intervals, but the time would be longer than the first four intervals.

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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.)?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

The subsequent intervals have a longer period to complete the defined cycle. It takes longer and longer to complete 4 cycles, as the pendulum progresses.

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Would we expect additional subsequent time intervals to increase, decrease or stay the same?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

Subsequent time intervals would increase, as the system progresses and eventually stops.

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Your data do establish that progression, but it's a very gradual progression. Besides, ideally the system is set up to have an even rhythm, amd if so this won't be the case.

There is another reason that will account for the very significant differences we expect to observe.

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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?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

When the pendulum is optimized, and is close to natural equilibrium, the bounces, or intervals between hits are extremely close to being equal throughout the entire experiment. The system creates a natural rythm, and hits the wall at almost the same period of time throughout.

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Actually the period decreases with increasing amplitude. The effect is minimal for small angles, but if the pendulum is released from a position more than about 15 degrees from equilibrium, it gets to equilibrium measureably more quickly, and progressively more so as the angle increases.

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No matter the amplitude of the release point for a given length, the period between intervals will remain the same, no matter how high the pendulum is released.

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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?

your response &&&&&&&&&&&&&&&&&&

(start in the next line):

4 hours, Pendulum was a little too good.

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self-critique #$&*

#$&* self-critique

self-critique rating

rating #$&*:

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Very good work and good data. However the last couple of questions need revision. Fortunately it should take you much, much less than 4 hours to make the revisions.

&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, 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.

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