pearl pendulum

#$&*

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 **

** **

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 sounds get closer together/faster.

I could automatically tell that the sounds were closer than when they were in the normal position. As time went on, the sounds got even more closer and closer together before it finally stopped.

#$&*

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 further apart/slower.

When I first released the pearl/bead, it started at a pretty keen rate, but then as time went on it got slower and slower in hitting the bracket, and eventually stopped hitting it before it even stopped swinging.

#$&*

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 used a thickly folded piece of paper to make my bracket more level to where the bead was barely touching the bracket. The rythm was quite steady, only tankering off when it was about to quit moving. The pendulum hit the bracket 12 times

#$&*

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):

My first positioning of the bracket is with the pendulum side parallel to the spine of the book. The pendulum hits the bracket at a slower rate since the bracket is leaning forward. 8 full hits.

My second positioning of the bracket is 45 degrees counter clockwise. The pendulum hits the bracket at a faster rate than the first position, but still is not as fast as it could be. 10 full hits.

My third position is 45 degrees further counter clockwise. The pendulum is slanted to the left where it is tilted on its right side. The pendulum hits the bracket noticably faster than the original position and a little faster than the second position. 11 full hits.

My fourth position is 45 degrees further counter clockwise. The pendulum is slanted to the left because of the tilt of the book. The pendulum hits the bracket much faster than the first position. 11 full hits.

My fifth position is 45 degrees further counter clockwise (exactly 180 degrees from starting position. The pendulum is now at the side where the mouth of the book is. The hits are much faster, and there are not as many as the last 3. 9 full hits.

My sixth position is 45 degrees further counter clockwise from the last position. The pendulum is still going fast. 10 full hits.

My seventh position is 45 degrees further counter clockwise from the last position. The pendulum seems to still be going pretty fast. 11 full hits.

My eighth position is 45 degrees further counter clockwise from the last position. The pendulum has slowed down, but got it a good amount of hits. 12 full hits.

#$&*

Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.

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

(start in the next line):

To obtain the most regular beat of the pendulum, in my opinion, would be to slightly increase the height of the back of the bracket to make the bead barely touch the bracket (as we did in a problem earlier). I used a thickly folded piece of paper to accomplish this.

#$&*

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):

.441

.434

.438

.445

.480

.531

.438

.484

These numbers represent the difference in the time the pendulum hits the bracket for the second time and the initial letting go of the pendulum.

#$&*

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):

.695, .668, .641, .594, .547, .547

.648, .672, .679, .664, .628, .605, .559

.625, .637, .668, .633, .613, .625

.633, .648, .637, .621, .578, .566

The results that are given are the time intervals between every other hit of the pendulum (every second hit). These numbers were obtained by hitting the timer button when each second hit was detected.

#$&*

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):

10.2 centimeters

#$&*

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):

0.65, 0.66, 0.66, You can't really tell that it was that big of a change by just those three for my experiment, so here are my remaining 4 average numbers. 0.62, 0.59, 0.59, 0.56

#$&*

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):

1 interval between the release and first hit.

#$&*

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):

2, since it goes from equilibrium to extreme point and then hits again, that would be two intervals.

#$&*

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):

3 intervals occure between release and the second hit. The release begins the interval at the extreme point when comparing the release and the second hit, while the second hit to the fourth hit begins from the equilibrium point.

#$&*

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):

4 intervals occur between the second hit and the fourt hit. The pendulum is losing energy in the interval is from the fourth hit to the sixth hit.

#$&*

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 has the most momentum, which compensates for the bigger distance than the rest of the intervals.

#$&*

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

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

(start in the next line):

I would expect them to increase and then decrease as energy is lost compensating for the shorter distances the pendulum has to travel.

@&

To the extent you had a steady rhythm, this will not be the case. Everything will balance out to give you the steady rhythm (e.g., the pendulum speed decreases but it doesn't go as far between 'hits' to the time interval stays the same).

*@

#$&*

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 pendulum travels the farthest in the initial release, but is also the quickest time due to the energy behind it, so it does travel farther than the rest of the intervals and is quicker, therefore it is not only dependent on its length.

#$&*

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):

2 hours

<