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):

 When flat, the rhythm gets slower and slower. When tilted slightly, the rhythm speeds up slightly then stops.

 

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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 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 put a small washer at the rear of the stand, and the pendulum appeared to be steady after a few test.

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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):

 Pendulum position, progression of sound

270 deg, slower

225 deg, steady

180 deg, faster

135 deg, slower

90 deg, slower

45 deg, faster

0 deg, steady

315 deg, steady then slower

 

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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):

Apparently, oriented at 315 deg, 0 deg, or 225 deg showed signs of the most regular beat. I will chose 315 again. 

 

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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):

Test, time interval

1, 0.53

2, 0.5339

3, 0.488

4, 0.466

6, 0.489

7, 0.474

8, 0.447

The numbers were obtained by taking the time interval between the initial release of the pendulum and the second strike of the pendulum against the frame with the pendulum positioned at 315 degrees on the textbook with one domino under each top corner of the book.

 

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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):

 0.617, 0.767, 0.722

0.522, 0.754, 0.78

0.544, 0.747, 0.837, 1.212

It shows that the pendulum is obviously slowing down as the number of hits occur.

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Right. Note that if oriented for steady rhythm, the times would be about the same.

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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):

 13.6 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):

 0.561, 0.756, 0.7797

 

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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.

If 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):

 Wouldn't' it be a quarter of an interval. For a full-cycle, the pendulum goes from extreme point to equilibrium, which is a quarter of a cycle, from equilibrium to opposite extreme point which is half a cycle, from opposite extreme point back to equilibrium would be 3/4 of a cycle, and from equilibrium back to beginning extreme point would be 1 full cycle. But thinking about it in terms of this pendulum, from extreme point to equilibrium would be half a cycle, and then from equilibrium to extreme point one cycle.

 

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You understand this but I'm not sure you quite said it.

Release to first 'hit is 1/4 cycle, which is one interval, as 'interval' was defined.

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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):

 It would be a full cycle between the first hit and the second hit based on my description above. Its going from equilibrium to extreme point, half a cycle, and then from extreme point back to equilibrium which is another half cycle to equal 1 cycle.

 

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Equilibrium to extreme is an 'interval', which is a quarter-cycle, so equilibrium to extreme to equilibrium is two 'intervals', or two quarter-cycles, which is half a cycle.

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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):

 1.5 cycles between release and second hit, and a total of 2 cycles between second and fourth hit.

 

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This would be 3 'intervals' release to 2d 'hit', which is 3/4 cycle; and 4 'intervals', or 1 cycle, between 2d 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):

 Didn't really get many measurements between fourth and sixth hit.

2 cycles between second and fourth hit, and estimated 2 cycles 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 the cycle interval is shorter than the others.

 

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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):

 The intervals would decrease because the motion is slowing down.

 

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@&

If rhythm is constant intervals will remain constant.

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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 does not provide much evidence to draw a good conclusion. However, the pendulum's length remained constant throughout this experiment. The angle of the pendulum may of had more effect on the outcome on the swing then the lengths.

 

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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):

 

 

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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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