course phy 121
2/10 at 7:35 p.m. I tried to move all data to before the symbols as requested.
rotating straw _ opposing rubber bandsPhy 121
Your 'rotating straw _ opposing rubber bands' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the
end.
Note that the data program is in a continual state of revision and should be downloaded with every lab.
With your CDs/DVDs you obtained some introductory materials. For this experiment you will use some of the rubber bands, the die ('die' is the singular of 'dice'; you have one
die, which was originally packed as one of ten dice), some paper clips, the straw, the push pin and , if they are included with your initial package, the two short bolts. You
will also use at least one of the paper rulers from the preceding experiment Measuring Distortion of Paper Rulers , and you will use the TIMER program.
Note that this experiment is designed to prepare you for later, more precise experiments using rotating objects and rubber bands. There is significant uncertainty in the
measurements you will be taking. You should try to get reasonably accurate data on this experiment but there is no need to be overly precise or meticulous in your data
measurements or your graphing.
Note however that, while it is not overly precise, it is important to analysis your data correctly, according to the instructions given here.
This experiment is designed to take about an hour. The average time reported by students is closer to 90 minutes, with reported times varying from 30 minutes to 3 hours or in
rare cases more.
You need to get some data here but don't worry if it isn't high-quality data. The main thing is to get some data and be sure you know what it is telling you.
You will in later experiments obtain and analyze more precise data using better-behaved systems.
Rotating Straw Experiment
Spin the straw and time it
You have a straw and a die in your lab materials package.
Place the straw on the die, as demonstrated in one of the video clips you viewed under the line Introduction to Key Systems under the Introductory Assignment.
Spin the straw (not too fast, so you can count its revolutions) and count how many times it goes around before stopping.
Now repeat the spin but this time use the TIMER to determine how long it takes to come to rest after being spun, and through how many revolutions it travels. You can hold onto
the clip with one hand and extend a finger of that hand to start the straw spinning, leaving your other hand free to operate the TIMER.
A revolution consists of a 360-degree rotation of the straw about the axis. You should easily be able to count half-revolutions and then estimate the additional number of
degrees, to come up with the rotation within an error of plus or minus 15 degrees or so. That's all the precision required here, so there is no need to bother with a
protractor.
Report your results as indicated:
Report in the first line below the time in seconds and the number of degrees of rotation from the time you released the straw to the instant it came to rest. Use comma-
delimited format.
Starting in the second line give a brief description of what you did and how you made your measurements, and be sure to indicate whether you used a trimmed or untrimmed straw.
2.35 sec, 190 degrees
I used the straw in the materials as is on the die provided. I put a paperclip down below the starting position of the straw so that I could keep up with the initial position
of the straw and just lightly tapped it with my finger to get it to move this amount.
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Put weights in the ends of the straw and repeat
Now insert the two bolts into the ends of the straw. If they won't work or if you don't have the bolts yet, slide a large paper clip or two onto each end. If necessary elevate
the die a bit to keep the clips from dragging (for example you could set it on top of an inverted drinking glass or mug). Spin the straw. If it is unbalanced you can move one
bolt (or paper clip) in or out a little, or if necessary trim whichever end needs it, a little at a time, until you achieve good balance. Then repeat the above exercise.
Report your results as indicated:
3.66 sec, 290 degrees#$&*
Report in the first line the time in seconds and the number of degrees of rotation from the time you released the straw to the instant it came to rest.
Use comma-delimited format. In the second line give the length of your straw and the units in which you measured the length. Starting in the third line give a brief
description of what you did and how you made your measurements.
4.05 sec, 200 degrees
21 cm.
I put nuts on either end to give good weight to the straw and put them at equal distances from the end of the straw. I lightly tapped the straw as done previously with one
finger while working the timer with the other hand. I measured the straw using a ruler I have. I estimated the degree of the rotation based on the position of the straw in
relation to a paperclip on the table below that reflected the starting position.
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Time at least a few 180-degree intervals and find midpoint clock times for intervals
8.41 sec, 450 degrees
3.48 sec, 185 degrees
3.92 sec, 250 degrees
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Repeat one more time. This time click the TIMER every time an end of the straw passes a selected point, so that you will have a timing for every 180 degrees of rotation. From
the data you obtain determine the average velocity of the straw, in degrees per second (this quantity is actually called 'angular velocity' because it is measured in units of
angle per unit of time), for each 180 degree rotation.
1 2090.172 2090.172
2 2091.984 1.8125
3 2093.875 1.890625
4 2096.25 2.375
This is the timer for the click every time the straw passed the paperclip on the table. The last click though was when the straw stopped about 60 degrees or so before reaching
the clip.
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Also calculate the clock time at the midpoint of each timed interval. Recall that 'clock time' is the time on a running clock.
The second column of the TIMER represents clock times; the third column represents time intervals. Several trials are typically included in TIMER output. However in the
process of analysis it is more convenient to think of a different clock for each trial.
The running clock for a given trial (e.g., a given spin of the strap) is generally assumed to reaI sd t = 0 at the initial instant.
The initial instant for a given trial would usually be the instant of the first 'click' of that trial.
Clock times can be found by successively adding up the time intervals. If you have time intervals of, say, 3 s, 5 s, 9 s and 15 s, then if the clock is started at t = 0 the
clock times of the corresponding events would be 3 s, 8 s, 17 s and 32 s.
Clock times can also be found by subtracting the TIMER's clock time for the first 'click' of a trial from the clock time of each subsequent 'click'. For example the TIMER might
show clock times of 63 s, 66 s, 71 s, 80 s and 95 s during a trial. This means that the second 'click' occurred 66 s - 63 s = 3 s after the initial click; the third click was
71 s - 63 s = 8 s after the initial click; the fourth and fifth clicks would have occurred 80s - 63 s = 17 s and 95 s - 63 s = 32 s after the initial 'click'. So the
corresponding clock times would have been t = 0 (corresponding to TIMER clock time 63 s), then 3 s, 8 s, 17 s and 32 s.
The midpoint clock times would be the clock times in the middle of the intervals. In the preceding example the first interval runs from clock time t = 0 to t = 3 s, so the
midpoint clock time is 1.5 s. The second interval runs from t = 3 s to t = 8 s, so the midpoint clock times is the midpoint of this interval, t = 5.5 sec. The midpoints of the
remaining two intervals would be t = 12.5 sec and t = 24.5 sec.
A clock time is generally designated by t, and if t is used for the variable then it refers to clock time. A time interval is generally referred to by `dt; a time interval is a
change in clock time. A midpoint clock time might be referred to as t_mid.
In the indicated space below.
Copy and paste the relevant part of the TIMER output.
Starting in the second line after your TIMER output, give a table of average velocity vs. midpoint clock time (each line should include the midpoint clock time, then the average
velocity for one time interval).
Starting in the line below your table, explain how you used your data to calculate your average velocities and the midpoint clock times.
1 2090.172 2090.172
2 2091.984 1.8125
3 2093.875 1.890625
4 2096.25 2.375
.90625, 180degrees/1.8125 sec.=99.31 degrees/sec
.9453125, 180 degrees/1.890625=95.21 degrees/sec
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What is your evidence that the straw is speeding up or slowing down? Is there any way you can determine in a meaningful way the rate at which the straw is speeding up or
slowing down?
I know that it would be better if I had more rotations to look at, but each time I hit it the straw harder, it would tend to fall off. Based on my little bit of evidence, the
straw is definitely slowing down. This is seen in how the degrees per second is getting smaller, and just the fact that it took a lot more time to not even complete the last
rotation.
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Measure the lengths of two opposing rubber bands thick - 7.4 cm thin 6.2 cm.
Now choose one of the thin rubber bands and one of the thicker rubber bands. Make sure there are no obvious defects on the rubber band you choose.
Bend three paperclips to form hooks.
Hook each rubber band to an end of one hook, and attach the other hooks to the free ends of the rubber band.
Pull gently on the end hooks until the rubber bands pretty much straighten out and take any data necessary to determine their lengths, as accurately as is reasonably possible
with the paper rulers.
Now pull a little harder so the rubber bands stretch out a little.
Stretch them so that the distance between the hooks you are holding increases by about 1 cm.
Take data sufficient to determine the lengths of the two rubber bands.
Repeat so that the distance between the end hooks increases by another centimeter, and again take data sufficient to determine the two lengths.
Repeat twice more, so that with your last set of measurements the hooks are 4 cm further apart than at the beginning.
In the indicated space below:
Report in the first line the lengths as determined by your first measurements, with the 1 cm stretch. Report in comma-delimited form, with the length of the thicker rubber band
first.
In the second, third and fourth lines make a similar report for the three additional stretches.
Starting in the fifth line, give a summary of how you made your measurements, your raw data (what you actually observed--what the actual readings were on the paper ruler) and
how you used your raw data to determine the lengths.
THICK, THIN
1 cm - 7.5 cm.,7.1 cm.
2 cm - 7.8 cm. ,7.8 cm.
3 cm - 8 cm., 9 cm.
4 cm - 8.3 cm., 9.3 cm.
I actually pulled the system tight against a plastic ruler to take my measurements.
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Sketch a graph of length_thin vs. length_thick, where length_thin is the length of the thin rubber band and length_thick is the length of the thick rubber band. (Put another
way, plot y vs. x, where y is the length of the thin rubber band and x is the length of the thick rubber band).
Fit the best straight line you can to the data, using manual fitting methods (i.e., actually draw the line on the graph--don't use a graphing calculator or a spreadsheet to find
the equation of the line, but measure everything as in the Fitting a Straight Line to Data activity).
In the space below
Give in the first line the slope and vertical intercept of your straight line.
Starting in the second line, discuss how well the straight line actually fit the data, whether the data seems to indicate curvature, and what the slope and vertical intercept
mean in terms of your rubber band system:
The slope is extremely steep, and the line appears to intercept the x axis at about 5.5.
slope = rise/run= (9.3 cm-7.1 cm)/ (8.3cm-7.5 cm)=2.2/.8= 2.75
There does appear to be a slight curve to the data.
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Observe 2 rubber bands in series vs. a single rubber band
The system you observed previously consists of a thin rubber band pulling against a thick rubber band.
Flip a coin.
If it comes up Heads, add a paper clip and a second thin rubber band to the system in such a way that your system consists of a chain of two thin rubber bands pulling against a
single thick rubber band.
If it comes up Tails, instead add a second thick rubber band in such a way that your system can be viewed as a chain of two thick rubber bands pulling on a single thin rubber
band.
You now have two rubber bands pulling against a single rubber band. To put this just a little differently, you have a 2-rubber-band system pulling against a 1-rubber-band
system.
Repeat the preceding experiment using this system. Observe the length of the 2-rubber-band chain vs. the length of the 1-rubber-band chain.
Report the slope of your graph in the indicated space below. Starting in the second line, discuss
how the slope of the this graph differs from that of your previous graph
why the slope should differ
how you would expect the slope to differ if the two thin rubber bands were identical
to what extent your results support the hypothesis that the two thin rubber bands do not in fact behave in identical ways.
1 cm - 7.4, 7.8
2 cm - 7.8, 8.8
3 cm - 8.2, 9.7
4 cm - 8.8, 10.2
I used two thin rubber bands. When I drew the graph, it looked very similar to me.
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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?
2 hours
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You may add optional comments and/or questions in the box below.
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Author information goes here.
Copyright © 1999 [OrganizationName]. All rights reserved.
Revised: 30 Jan 2010 20:01:15 -0500
Your work looks good here, but with apologies, I have to ask you to make some simple revisions and resubmit this. It should take you only a few minutes to make the necessary
revisions in format. You can just copy this document into a text editor and cut-paste each answer to the appropriate position, as indicated below:
What I need you to do is place your answers to the questions before the #$&* marks. The instructions in the labs pretty consistently ask you to start your answers on the 'next
line', and there is a line between the prompt and the #$&*.
Once you have done this, simply submit the document once more.
I'm not being picky in asking this--there are good reasons for the request. To do statistical studies on the large amounts of information I receive, and also to efficiently read
through and critique hundreds of pages of documents each day, the format of each document needs to be predictable to my programs, as well as to my eye."
&#This looks very good. Let me know if you have any questions. &#