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.

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

The Pearl Pendulum was submitted 7 Feb 11 around 10:13 PM.

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

The Pearl Pendulum

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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).

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 sound gets closer together when I tilt the bracket back a bit. The rhythm gets faster.

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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 sound remains steady for a while before it gets closer together. The rhythm remains constant and then gets faster but eventually it will stop.

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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):

The sound gets closer together when the bracket is leveled. The rhythm eventually gets faster and then it eventually stops.

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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):

When placed on the middle of the book, with the base of the bracket parallel to one of the sides of the book, the sound gets further apart.

When I rotated the bracket 45 degrees counterclockwise, the sound gets further apart as well.

When I rotated the bracket another 45 degrees counterclockwise, the sound gets closer together.

When I rotated the bracket another 45 degrees counterclockwise, the sound gets closer together.

When I rotated the bracket another 45 degrees counterclockwise, the sound gets closer together.

When I rotated the bracket another 45 degrees counterclockwise, the sound gets closer together as well.

When I rotated the bracket another 45 degrees counterclockwise, the sound again gets closer together.

When I rotated the bracket another 45 degrees counterclockwise, the sound gets further apart.

When I rotated the bracket another 45 degrees counterclockwise (back to its original position), of course the sound gets 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):

I oriented the bracket counter-clockwise in 45 degree increments, which total 8-45 degree angles turns to equal a complete 360 degree rotation.

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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):

1st Trial

1 4.619 4.619

2 5.333 0.714

3 5.758 0.425

4 6.149 0.391

5 6.571 0.422

6 7.069 0.498

7 7.604 0.535

2nd Trial

1 4.237 4.237

2 4.989 0.752

3 5.402 0.413

4 5.794 0.392

5 6.23 0.436

6 6.749 0.519

7 7.282 0.533

3rd Trial

1 3.53 3.53

2 4.219 0.689

3 4.611 0.392

4 5.022 0.411

5 5.483 0.461

6 5.943 0.46

7 6.466 0.523

4th Trial

1 2.937 2.937

2 3.654 0.717

3 4.029 0.375

4 4.456 0.427

5 4.88 0.424

6 5.365 0.485

7 5.983 0.618

5th Trial

1 4.671 4.671

2 5.45 0.779

3 5.837 0.387

4 6.237 0.4

5 6.662 0.425

6 7.158 0.496

7 7.669 0.511

6th Trial

1 3.327 3.327

2 4.078 0.751

3 4.468 0.39

4 4.869 0.401

5 5.33 0.461

6 5.802 0.472

7 6.372 0.57

7th Trial

1 4.686 4.686

2 5.461 0.775

3 5.853 0.392

4 6.228 0.375

5 6.675 0.447

6 7.197 0.522

7 7.744 0.547

8th Trial

1 3.774 3.774

2 4.584 0.81

3 4.972 0.388

4 5.397 0.425

5 5.834 0.437

6 6.283 0.449

7 6.756 0.473

These numbers presented in the 8 trials represent the calculated interval times the pendulum hit the back of the bracket and the differences in each time intervals.

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@& You have reported the entire TIMER output.

This would be OK, but you need to specify that the time intervals are in the third column, and you need to eliminate any number in that column that doesn't correspond to one of your timed intervals (e.g., the very first number in the column should always be eliminated since it represents the time between starting the program and the first click).*@

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):

1st Trial

6.516, 7.281, 8.166, 9.270,

2nd Trial

5.585, 6.333, 7.217, 8.272,

3rd Trial

4.479, 5.243, 6.068, 7.088,

4th Trial

5.240, 5.969, 6.841, 7.920,

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@& Those look like clock times, not intervals.

This should be corrected.*@

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):

The length of the pendulum is 12.5 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):

0.751, 0.867, 1.064

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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):

An interval consists of motion from equilibrium to extreme point. There were a total of 4 intervals between release and the first hit.

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@& Between release and the first hit the pendulum travels from extreme to equilibrium, which is only one interval.*@

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 were a total of two intervals between the first hit and the second because there was a hit between the first and second hit that did not get counted by the timer.

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@& Good.*@

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):

There were a total of two intervals between release and the second hit and also a total of two intervals between the second and fourth hit.

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@& There were two intervals between the first and second hit.

It took time to get from release to the first hit.

How long did that take, and how long did it therefore take from release to the second hit?*@

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 were a total of two intervals between the second and fourth hit. The difference between the description of motion between the fourth and sixth hit is the timing. The time was longer between the fourth and sixth hit.

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@& There were two intervals between the first and second hit, as you indicated.

How many between the second and third?

How many between the third and fourth?

How many then between the second and fourth?*@

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):

The time interval between the release and 2nd hit was shorter because it was very close to the initial strike against the bracket. Over time the time interval got longer or increased until the pendulum stopped.

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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 time interval will increase in subsequent time.

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@& This can happen in practice, but to the extent you have successfully set the pendulum to maintain a steady rhythm it wont be the case.*@

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):

This evidence does provide some truth to the hypothesis because I believe if the pendulum’s length was shorter, the time intervals will be shorter or increase.

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*#&!

@& You have good data, but you will need some revisions.

Shouldn't be difficult and shouldn't take you long, and you'll get a clearer picture of the motion.

&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions and/or questions, 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.

If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you.

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