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: **

5.2.11

#$&* 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 pearl strikes the bracket at a constant, steady rate. The pearl taps the braket regularly and at even time intervals.

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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):

Closer together, the pearl strikes the bracket more frequently than in the previous test and the time interval decreases at the test goes on.

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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):

Rhythm was steady and constant. The pearl tapped the bracket 11 times. I placed the system on the table with a piece of cardstock underneath it.

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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):

With a domino under each to the top two corners:

Test 1

With the ball facing you, the pearl, once released, taps the bracket at evenly spaced time intervals.

Test 2

Rotate the system to the left 45 degrees.

Once released, the pearl taps the bracket at evenly spaced time intervals.

Test 3

Rotate 45 degrees to the left (90 degrees from original position).

Once released, the pearl taps the bracket at an increasing rate.

Test 4

Continue rotating, 45 degrees (135 degrees from original position).

The pearl taps the bracket at an increasing rate.

Test 5

Roate another 45 degrees ( 180 degrees from original).

Pearl strikes bracket at an increasing rate.

Test 6

Rotate another 45 degrees (225 from original).

Pearl strikes at an increasing rate.

Test 7

Rotate 45 degrees (270 degrees from original).

Pearl strikes bracket at a constant rate.

Test 8

Roate 45 degrees (315 from original).

Again, contstant rate.

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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 pendulum should be facing you of 45 degrees off center one way or the other.

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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):

0.531

0.5

0.489

0.547

0.547

0.531

0.469

0.531

It takes about 1/2 second from the time of release for the pearl to tap the bracket. These figures support that the pearl is striking at a constant rate.

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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):

0.609, 0.641, 0.766, 0.75

0.547, 0.641, 0.719, 0.812

0.563, 0.688, 0.75, 0.766

0.672, 0.641, 0.859, 0.797

The intervals indicate every other tap of the pearl against the bracket. The intervals increase each time which indicates that it may not be tapping at a constant 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):

106 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):

0.598, 0.0705, 0.121

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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):

There is one interval between release and the first hit if you don't take into account the opposite extreme position.

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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 1st and 2nd hit. It has to travel the same distance twice, as opposed to once in the previous 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):

Three intervals between release and second hit. There would be four intervals between the 2nd and 4th 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):

There are 4 intervals and it would be the same for the distance between 4th and 6th hit, assuming it went on for that long.

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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 being released from a different starting point. Counting from the release of the pearl is different than counting from the 2nd, 3rd, 4th hit, etc.

It has more energy at the initial release.

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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):

Time intervals will decrease as energy is removed from the system.

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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):

It can only swing as far as the attached string allows it.

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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):

45 minutes

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*#&!

&#Your work on this lab exercise is good. Let me know if you have questions. &#