pearl pendulum

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PHY 121

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 rhythm seems to remain steady, although the volume decreases as the pendulum comes

to rest.

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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):

The rhythm still seems to remain constant until it no longer strikes the bracket. If I

watch it, I expect the sounds to get closer together because of the way that it is

making smaller swings, but if I close my eyes and listen the rhythm does not seem to

change. Just the volume of the strikes until it stops.

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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 placed a quarter under the front of the bracket. The rhythm was even and less than a

second apart. The pendulum hit the bracket 21 times.

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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):

The bracket is about 3 1/2 inches from the top of the book and about 1 inch from the

bottom. The part with the bead is toward the top of the book with the bead facing the

top of the book.

I could tell that the rhythm sped up before it came to a stop.

The book is 11 inches long, so the bracket is centered over the 5 1/2 inch mark. The

bracket 1 1/2 inches from the spine of the book.

The sounds get softer but the rhythm stayed the same.

The edge of the bracket where the pendulum is hanging is lined up with the bottom of the

blue picture on the book. The bracket is centered on the book with about 3 1/2 inches

on each side.

This time, as the sounds got softer, they also slowed down.

The bracket is again centered over the 5 1/2 inch mark. The side with the bead is 1 1/2

inches from the edge. The other end of the bracket is about 1/4 inch from the edge of

the book.

The sounds got softer, and it appeared that the rhythm may have slowed down a little.

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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 came from the orientation where the bracket is horiontal to the

word Physics on the frong of the book, about 2 1/2 inches from the title.

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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):

.4180

.3906

.3828

.3867

.4063

.4336

.4805

.4375

I did several tries and they all came out like this. These are numbers that show the

interval between clicks. I tried to listen and click, rather than watch the pendulum so

that I would not anticipate the next click, but I know that I did sometimes. The data

indicates that it takes about .4 of a second between strikes. The mean actually came

out to .417.

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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):

.7070313, .8476563, .8242188, .8945313, .9179688

These are the time intervals for every other click of the bead. I did several trials to

see if my results were consistent with each other. It was harder than I thought to

click on every other sound, so it took some practice to listen for that. The average of

these 5 numbers, divided by 2 (for every click) came out to .419 s, which is very close

to my first trial with every strike.

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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):

147 mm

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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):

. 57, .71, .85, .82, .89,

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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):

If I started on the 2nd hit, then it went, down/hit, back/extreme, down/hit, so it looks

like 3 intervals.

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@&

Your description would fit the time from release to 2d 'hit'.

That would require three 'intervals'.

However that's not the answer to the present question. The answer is pretty obvious, and I trust you'll get it, since you understand this motion.

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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):

4 intervals (hit to extreme, extreme to hit -not counted, hit to extreme, extreme to hit

- counted.

This is because the first one started at the extreme point. These go from counted hit

(uncounted hit) counted hit. with the swing backs in between.

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@&

Release occurs at the extreme point, 'hits' occur at the equilibrium point.

Release to 2d 'hit' doesn't take 4 intervals. In fact you described release to 2d 'hit' in your answer to the last question.

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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):

Between release and second hit (and I may be all mixed up here because I'm using the

every-other-time clicking)-- there are 7 intervals. There are 8 between 2nd hit and 4th

hit. This is because the first click comes after one interval. All of the others take

2 intervals before they hit again.

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Right idea, but you're thinking of a motion with more hits than specified in the question.

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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):

There are 8 between 2nd hit and 4th

hit. This is because the first click comes after one interval. All of the others take

2 intervals before they hit again. It would be the same as between fourth hit and sixth 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):

Because it consists of 3 back and forth swings, but the others consist of 4.

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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):

I would expect subsequent time intervals to increase based on the data. They slow down so gradually that it is difficult to hear it by just listening.

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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):

Since I didn't do anything with this experiment on adjusting the length of the pendulum and comparing that, I'm not sure that it does provide evidence about that.

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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):

1 hour 15 min

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@&

Very good. You really understand the part about the extreme points and 'hits', but your answers need to be adjusted.

There are 3 'intervals' between release and 2d 'hit', and 4 'intervals' between alternate subsequent 'hits'.

If you're not completely clear on this let me know. Otherwise I'll trust that you've reconciled these answers with yours.

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