#$&*
course PHY 121
September 28, 2011 at 7:14 p.m.
•Follow the instructions, fill in your data and the results of your analysis in the given format. •Any answer you given should be accompanied by a concise explanation of how it was obtained.
• To avoid losing your work, regularly save your document to your computer.
• When you have completed your work:
Copy the document into a text editor (e.g., Notepad; but NOT into a word processor or html editor, e.g., NOT into Word or FrontPage).
Highlight the contents of the text editor, and copy and paste those contents into the indicated box at the end of this form.
Click the Submit button and save your form confirmation.
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 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'.
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):
Here the pearl hits and bounces off. The rhythm speeds up until it does not bounce far enough off of the bracket and comes to rest.
#$&*
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):
Here again the hits begin and then slows down until ultimately not hitting the bracket. Once it settles into a somewhat constant rhythm it continues this for a while until slowing to a stop.
#$&*
If the bracket is placed on a perfectly level surface, the pearl will hang straight down, just barely touching the bracket. However most surfaces on which you might place the bracket aren't perfectly level. Place the bracket on a smooth surface and if necessary tilt it a bit by placing a shim (for a shim you could for example use a thin coin, though on most surfaces you wouldn't need anything this thick; for a thinner shim you could use a tightly folded piece of paper) beneath one end or the other, adjusting the position and/or the thickness of the shim until the hanging pearl just barely touches the bracket. Pull the pearl back then release it.
If the rhythm of the pearl bouncing off the bracket speeds up or slows down, adjust the level of the bracket, either tilting it a bit forward or a bit backward, until the rhythm becomes steady.
Describe the process you used to make the rhythm steady, and describe just how steady the rhythm was, and how many times the pendulum hit the bracket..
Your response (start in the next line):
Mine begins with the noises occurring at a faster rate and slows down until it becomes more gradual. However, once mine gets into a sort of rhythm it quits hitting the bracket and just oscillates back and forth, gradually slowing to a stop.
#$&*
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):
Beginning with the base of the bracket (end with the magnet opposite the pearl) touching the right side of the book, pulling the pearl back it begins hitting the bracket at a fast pace and slows. The pearl eventually slow to a rhythm where you do not hear it hit the bracket and then comes to a stop.
Rotating clockwise 45 degrees until the pearl appears to be pointing between what would be 10 and 11 on a clock.
The pearl does the same as before, however, it seems to come to rest against the bracket at a faster rate than before.
Rotating clockwise 45 degrees until pearl appears to point at 12 on a clock.
Here the results are similar to the previous. This time, however, the pearl speeds up and comes to a rest sooner that at the previous 45 degree interval.
Rotating 45 degrees until the pearl appears to be facing between 1 and 2 o clock.
Here the pearl did similarly to what the pearl did when facing clock position between 10 and 11 o clock.
Rotating 45 degrees until pearl facing 3 o clock.
Here the results appears to do the same as the pearl did in the initial position above:
Hitting at a progressively slower pace before evening out to a rhythm without touching the bracket audibly and ultimately coming to a stop.
Rotating bracket 45 degrees clockwise, facing between 4 and 5 o clock.
Here the pearl begins to hit the bracket at a faster pace slowing down to an ultimate point where it abruptly stops hitting the bracket and oscillates without hitting the bracket until coming to a stop about 1 cm away from the bracket.
Rotating bracket 45 degrees clockwise, facing 6 o clock.
Here it repeats the same hitting the bracket at a faster rate initially and slowing down to a slower oscillation without touching the bracket. This time, however, the oscillation continues at a slowing pace without touching for much longer than before.
Rotating bracket 45 degrees clockwise, facing between 7 and 8 o clock.
Here, it does more as it did above when facing between 10 and 11 o clock. It hits at a fast rate initially slowing down to where it no longer hits the bracket but oscillates back and forth. The oscillations slow down, but contrary to above go much longer before coming to a halt.
#$&*
Describe how you would orient the bracket to obtain the most regular 'beat' of the pendulum.
Your response (start in the next line):
I most regular beat would occur with the pearl facing 6 o clock and would even out to its most regular interval once it quits striking the bracket and settles into its oscillations.
#$&*
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):
.359
.383
.586
.508
.5
.625
.664
.656
This shows, inconsistently probably due to human error and how quickly the pearl stopped audibly striking the bracket, how the speed of the oscillations slowed down increasingly as time progressed.
#$&*
Finally, you will repeat once more, but you will time every second 'hit' until the pendulum stops swinging. That is, you will release, time the second 'hit', then time the fourth, the sixth, etc..
Practice until you think you are timing the events accurately, then do four trials.
Report your time intervals for each trial on a separate line, with commas between the intervals. For example look at the format shown below:
.925, .887, .938, .911
.925, .879, .941
etc.
In the example just given, the second trial only observed 3 intervals, while the first observed 4. This is possible. Just report what happens in the space below. Then on a new line give a brief description of what your results mean and how they were obtained.
Your response (start in the next line):
.961, .984, 1.242, 1.289
1.156, 1.234, 1.25, 1.289
1.219, 1.219, 1.219, 1.219, 1.258, 1.297
.75, .742, .859, .961, 1.227
These results were obtained the same way as above and show the same results. The pearl begins at a faster rate of oscillation and slows down in each progression.
#$&*
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 from the pearl to the top of the bracket, mine is the pearl tied to the thread hanging across the top of the bracket and anchored at the far end with a magnet, is 10.7 cm from the base of the pearl to the top of the bracket.
#$&*
If you have timed these events accurately, you will see clearly that the time from release to the second 'hit' appears to be different than the time between the second 'hit' and the fourth 'hit'.
On the average,
• how much time elapses between release and the second 'hit' of the pendulum,
• how much time elapses between the second and fourth 'hit' and
• how much time elapses between the fourth and sixth 'hit'?
Report your results as three numbers separated by commas, e.g.,
.63, .97, .94
Your response (start in the next line):
.961, .984, 1.242
1.156, 1.234, 1.25
1.219, 1.219, 1.219
.75, .742, .859
#$&*
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 interval
#$&*
How many intervals, as the word was described above, occur between the first 'hit' and the second 'hit'? Explain how your description differs from that of the motion between release and the first 'hit'.
Your response (start in the next line):
Two intervals. The pearl goes from extreme point to equilibrium, then from the next extreme point to equilibrium when striking twice.
#$&*
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):
In the second hit, as described above, it actually encounters two intervals, and the second, if 2 intervals = 1 hit has 4 intervals because it has two hits.
#$&*
How many intervals occur between the second 'hit' and the fourth 'hit', and how does this differ from a similar description of the motion between the fourth 'hit' and the sixth 'hit'?
Your response (start in the next line):
Here is again the same as above, 1 hit = 2 intervals
2 hits = 4 intervals
3 hits = 6 intervals
#$&*
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 as each hit occurs, the intervals have encountered two hits from its previous maximum position to its new maximum position based off of the bounce from the previous hit. Each resulting in smaller and smaller increments.
#$&*
Would we expect additional subsequent time intervals to increase, decrease or stay the same?
Your response (start in the next line):
We would expect further intervals to decrease in time as the maximum distance from oscillation becomes shorter and shorter.
#$&*
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 shows that the rate at which oscillation occurs happens at a slower rate to begin with based upon how long the pendulum is because the shorter the pendulum the shorter the maximum length for the pendulum to travel and if the the pendulum’s maximum reduces after each strike, the shorter the pendulum the shorter it swings, the shorter it stays in motion before coming to rest.
#$&*
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
• Approximately how long did it take you to complete this experiment?
Your response (start in the next line):
1 hour
#$&*
"
@& You apparently had difficulty achieving a constant rhythm in the 'strikes' agains the bracket, and you accurately reported your results, so you're OK here. But note the following:
If the constant rhythm of the 'strikes' is achieved, the pearl will continue striking the bracket until it comes to rest against the bracket.
It takes one quarter-interval to strike the first time, two more for a total of three to strike the second time, and two more for each subsequent cycle.
The intervals recorded from rest to the second 'strike' will therefore be different than the intervals between alternate subsequent 'strikes'.*@