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.

#$&* Your general comment, if any: **

#$&* Your description of the rhythm of the pendulum when tilted 'back' **

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).

You will need to construct the pendulum using the small bead and thin copper wire

packed in your lab materials package. In the Spring 2010 version the bead and the

wire were taped to the bracket, or packed in a separate bag with another small

object.

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 like this:

When suspended from the pendulum bracket by a thread the system might look something

like this. 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'.

When the pearl is released it swings back to the bracket, bounces off the swings

back again, repeatedly striking the bracket. The magnet can be used to clamp the

thread so 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 get closer together.

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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 sounds get closer together.

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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):

It was fairly steady and hit 5 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):

Dominos under 12 o'clock end of book, pendulum in center of book.

Bracket at 12 o'clock

Bracket at 10:30 o'clock further apart

Bracket at 9 o'clock about the same

Bracket at 7:30 o'clock about the same

Bracket at 6 o'clock closer together

Bracket at 4:30 o'clock closer together

Bracket at 3 o'clock about the same

Bracket at 1:30 o'clock further apart

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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):

Dominos under 12 o'clock end of book, pendulum in center of book.

Bracket at 12 o'clock

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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):

.469

.469

.484

.5

.484

.5

.484

.484

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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):

.516,.359,.289,.266

.5,.375,.361,.265

.531,.368,.328,.313

.484,.375,.297,.265

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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):

9.82cm

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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):

.14,.05,.04

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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 It is released and hits the bracket.

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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):

Three It hits the bracket (hit 1), returns to equilibrium, hits the bracket (hit 2)

It differs from release and first hit because it returns to equilibrium and hits the

bracket again.

@& Your explanation is great, but wouldn't it be two intervals between the first 'hit' and the second (eq to extreme then back to eq)?*@

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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 Release, hits the bracket (hit 1), returns to equilibrium,hits the

bracket (hit 2)

It has one less interval because it has one less hit

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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 It hits the bracket (hit 2), returns to equilibrium,hits the bracket (hit

3),returns to equilibrium, hits the bracket (hit 4)

The number of the hit would be the only difference

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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):

It is moving faster because of the longer distance.

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@& Moving faster for a longer distance, or moving more slowly for a lesser distance, could balance out to give the same interval.

If the rhythm is steady this is indeed what happens.*@

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

the same?

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

(start in the next line):

They should decrease because the pendulum is swinging a shorter distance.

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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):

The longer the length, the longer the swing from extreme to extreme.

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*#&!

&#Good responses on this lab exercise. See my notes and let me know if you have questions.

Revision isn't requested, but if you do choose to submit revisions, clarifications or questions, please insert them into a copy of this document, 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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