pearl pendulum

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PHY 201

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):

The sounds of the bouncing pearl are getting slightly faster with each rebounce.

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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):

When the pearl is naturally hanging away from the bracket the rhythm gets slower.

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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):

I used a think piece of card stock to shim my bracket to the point where the pearl was bouncing

with steady constant rhythm. Over the course of four trials I consistently counted 23 bounces.

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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):

1, 0, further

2, 45, further

3, 90, constant

4, 135, closer

5, 180, closest

6, 225, closer

7, 270, constant

8, 315, further

The first column is the trial, the second is the orientation in degrees from zero with the length of

the base parallel to the spine of the book ( the bead was downhill and not touching the bracket

at 0 degrees) and the third column reports the frequency of the rhythm.

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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):

based on my trials, I would orient the bracket perpendicular to the spine of the book (90

degrees or 270 degrees) for a most regular beat.

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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):

0

.467

.406

.396

.367

.396

.356

.387

The numbers above are the intervals of the pearl bead hitting the metal bracket after the initial

bounce. I obtained these by clicking the TIMER at the same time that I released the pearl and

then every bounce I heard after that initial bounce.

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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):

.701, .738, .807, .813

.687, .726, .763, .735

.633, .729, .789, .738

.629, .789, .738, .767

The above results are the intevals between hits of the pearl against the bracket after the initial

release and skipping a beat between each timing.

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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):

13.4cm or 134mm

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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):

.70, .74, .81

.69, .73, .76

.63, .73, .79,

.63, .79, .74

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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):

Assuming that the release point is the same as the extreme point, there is one interval between

the extreme point of the pendulum and the first hit.

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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):

There are two intervals between the first and second hits. Since the interval is half that of a full

swing pendulum, there would be one interval between the equilibrium and extreme point (first hit

and return to extreme point) and then a second interval between the extreme point and the

return to the bracket for the second hit.

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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):

From release to the second hit there are three intervals: extreme/release point to first hit, first hit

to extreme point, and then a third from extreme point to second hit. Essentially after the intial

interval, there are two intervals between each of the 'hits'. This means that there are four hits

between the second and fourth hits.

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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):

I believe the same number of intervals occur, though the extreme point is not going to be as far

from the bracket with each subsequent hit.

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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):

There is energy that is being lost or absorbed by the bracket with each hit as well as drag on the

pendulum from air resistance.

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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):

We would expect subsequent time intervals to increase due to the slowing of the pendulum as a

result of loss of energy.

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The pendulum's average speed decreases, but so does the distance it moves between 'hits'. If it's positioned as instructed, the 'hits' (after the first one) will be equally spaced.

You have good data, but I'm not sure you timed the pendulum from release to the second 'hit'. You appear to have started the timing with the first 'hit', so you won't have had the opportunity to test the 4-to-3 ratio between alternate 'hits' and the release-to-second 'hit' interva.

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