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Submitting Assignment: Rotating Straw _ Opposing Rubber Bands

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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 strap, 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.

There are two separate experiments in this exercise.  If you don't have time to complete them both, you can submit them one at a time.  If you do so, submit the entire document, but copy the word 'deferred' into the responses for the part you haven't completed, or the words 'previously done' into the responses for the part that has already been completed.

Rotating Strap Experiment

(formerly 'rotating straw' experiment)

NOTE:  The setup for this part of the experiment is identical to that of the later experiment Angular Velocity of a Strap.  You can refer to that document for pictures of the setup.  Also, once you have this experiment set up, it would be fairly easy, and would not take long, to go ahead and take your data for that experiment.  There's no need to do so at this time, but it would probably save you time to go ahead and get it out of the way.

If you do not yet have your complete lab materials package, you may delay this part of the experiment until you do.  Your Initial Materials package contains the rubber bands and paperclips you need for the second part of this experiment, so even if you don't have the full package, you should complete that part now.

Spin the strap and time it

You have a metal 'strap' (a thin strap of framing metal, a foot long and an inch or two wide) and a die (i.e., one of a pair of gaming dice) in your lab materials package. 

• Place the strap on the die, similar to the way the straw was place on a die in one of the video clips you viewed under the line Introduction to Key Systems under the Introductory Assignment.  It is not difficult to balance the strap on the die, provided the die rests on a level surface, so that it will stay on the strap when given a spin.
• Spin the strap (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 released (i.e., after it loses contact with your finger), 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 strap spinning, leaving your other hand free to operate the TIMER. 

A revolution consists of a 360-degree rotation of the strap 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 strap 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.

-------->>>>>>>>>> `dt in sec and deg of rotation, description

Put weights on the ends of the strap and repeat

Two magnets came with your materials.  Attach them to the ends of the strap and repeat.  Spin the strap.  You can determine if the system is more stable and hence easier to use with the magnets on top of the strap, or hanging underneath it, but it should work either way.

Then repeat the above exercise.

Report your results as indicated:

• Report in the first line the time in seconds and the number of degrees of rotation from the time you released the strap
   to the instant it came to rest. 
• Use comma-delimited format.  In the second line give the length of your strap 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.

Time at least a few 180-degree intervals and find midpoint clock times for intervals

Repeat one more time.  This time click the TIMER every time an end of the strap 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 strap, 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.

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 read 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. 

-------->>>>>>>>>> timer output, vAve vs midpt t, explain calculations

What is your evidence that the strap  is speeding up or slowing down?  Is there any way you can find in a meaningful measure of the rate at which the strap is speeding up or slowing down (i.e., how quickly the velocity is changing)?

-------->>>>>>>>>> evidence speeding up or slowing, can we determine rate at which speeding up or slowing

Opposing Rubber Bands Experiment (Measure the lengths of two opposing rubber bands)

In the Introduction to Key Systems videos, you saw a chain of rubber bands, connected with hooks made of paper clips then pulled apart a little ways at the ends.

Choose one of the thin rubber bands and one of the thicker rubber bands from your materials.  Make sure there are no obvious defects on the rubber bands 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.

-------->>>>>>>>>>  lengths 1 cm total stretch; 2 cm stretch; 3 cm stretch; 4 cm stretch

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:

------->>>>>>>>>> slope & intercept, quality of fit

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

• a description of your system
• 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.

-------->>>>>>>>>> describe system, how slope differs, why, expectations if thin rb identical, support for hypothesis not identical

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? 

Please copy your completed document into the box below and submit.