#$&*
course Phy 201
Rotating Straw ExperimentThe straw has a hole drilled in it. If you trim the straw at the short flexible segment then the hole will be approximately in the middle of the remaining section of the straw.
The die has a hole drilled in or near the middle of one of its faces.
Place the die on a level tabletop with this hole facing upward.
Place the straw over the die so you can look down through the hole in the straw to the hole in the die.
Insert the end of a small paper clip through the holes in the straw and into the hole in the die (unbend the clip before inserting it).
Spin the straw (not too fast, so you can count its revolutions) and see 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. A revolution would be a 360-degree revolution of the straw. 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 no need to bother with a protractor or any other way to actually measure the angle.
In the box below 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. Starting in the second line give a brief description of what you did and how you made your measurements.
________________ **
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.
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:
It spins around 3 1/4 times before stopping.
It takes 4.93 seconds to spin around 4 complete times.
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
Your answer (start in the next line):
360 degrees * 4 revolutions = 1440 degrees total
4.93 sec, 1440 degrees
1440 degrees / 4.93 seconds = 292.1 degrees per second
#$&*
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:
It spins around 3 3/4 times without stopping.
It takes 6.76 seconds for 3 1/2 revolutions.
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.
-------->>>>>>>>>> `dt and # deg, length, description
Your answer (start in the next line):
360 degrees per rotation * 3.5 rotations = 1277.5 degrees total
6.76 seconds, 1276 degrees
Strap length = 0.28 m as measured by full length paper ruler
There are 360 degrees in a circle, so rotations were multiplied by 360 to get total degrees rotated within 6.76 seconds before coming to rest.
#$&*
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.
180 degree intervals:
1.19 s, 1.38 s, 1.29 s, 1.38 s, 1.25 s
Midpoint: ((x1+x2)/2), ((y1+y2)/2) = 1.285
Rotations time interval (sec)
0.5 1.16
1 1.45
1.5 1.37
2.0 1.13
2.5 1.78
3.0 2.98
(1 rotation = 360 degrees)
Average strap velocity = 180 degrees / change in clock time (sec)
v = 180 degrees / 1.16 sec = 87.0 degrees per second
v2 = 180 deg / 1.45 s = 124.1 deg/s
v3 = 180 deg / 1.37s = 131.4 deg/s
v4 = 180 / 1.13 s = 159.3 deg/s
v5 = 180 / 1.78 s = 101.1 deg/s
v6 = 180 / 2.98 s = 60.4 deg/s
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
Your answer (start in the next line):
Rotations* time (s) clock time (s) median time (s)
0.5 1.16 1.16 0.58
1 1.45 2.61 1.885
1.5 1.37 3.98 1.99
2.0 1.13 5.11 2.56
2.5 1.78 6.89 3.445
3.0 2.98 9.87 4.94
median clock time (s) Average velocity (m/s)
0.58 465.5
1.885 143.2
1.99 135.7
2.56 105.4
3.445 78.4
4.94 54.7
At the median clock time, there were 270 degrees rotated. 270 degrees / median clock time will give you the average velocities at that point.
#$&*
@& The average velocity for an interval is (change in position) / (change in clock time)
Between two clock times the change in position is 180 degrees, and the change in clock time is almost certainly not equal to the midpoint clock time.
The quantity you listed as 'time' is in fact the time interval, the change in clock time. This quantity will never be referred to as 'the time'.
The quantity we call 'clock time' is the one that is often referred to as 'the time' or just 'time'.
However the recommended usage here is 'clock time', for the time as represented by a running clock, and 'time interval', the change in clock time from the beginning to the end of the interval.**@
@& It also appears that the time you have identified as 'median time' is not the midpoint clock time. The midpoint clock time occurs halfway between the beginning and the end of the interval. Most of the median times you report are not in the time interval; for example 3.445 is not in the interval between 5.11 and 6.89 (the midponit of this interval would be 6.00 seconds), nor is it between 6.89 and 9.87.
Please check the instructions again and see if you can correct these 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
Your answer (start in the next line):
If you trace the average velocities for the median clock times, there is a consistent pattern of the velocity slowing down as more rotations are completed, which would be expected considering the device must eventually stop. To find the rate of velocity change, we need to find the acceleration, which is equal to the change in the velocity over time (m/s^2).
#$&*
@& average acceleration for an interval is change in velocity / change in clock time, not change in velocity / time
Be sure you understand the difference.*@
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.
Thicker rubber band length = 0.75 m
Thinner rubber band length = 0.65 m
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
Your answer (start in the next line):
Stretch Thin band length Thick band length
1 cm 0.68 m 0.76 m
2 cm 0.69 m 0.77 m
3 cm 0.70 m 0.77 m
4 cm 0.72 m 0.77 m
To ensure uniform measurements, the same regular scale paper ruler was used for all of the measurements. Measurements were taken from the 0 m mark, so all measurements displayed are representative of the raw data collected. After each stretch, each rubberband was individually measured on the paper ruler from the same point to see how much each had stretched. The slimmer rubberband exhibited more change as anticipated.
#$&*
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
Your answer (start in the next line):
Because the thick band hardly showed any stretch, the line was essentially a vertical line, so there is no slope. The vertical intercept took place at x = 0.77, and the line constructed did not have any curvature but was rather a vertical line through the points.
#$&*
@& You did observe some change in length for the thick band.
But you do not appear to have stretched the thin band by 1, 2, or 3 cm.
It appears that for a stretch of the thin band by .3 cm you got maybe .1 cm of stretch for the thick band, which would imply a slope of about 3.*@
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 answer (start in the next line):
The new system consisted of two thick rubber bands on either side of the thin rubber band for the paperclip rubber band chain. When stretched, the thin rubber band exhibited nearly twice the stretch of the thicker rubber bands, indicating that the hypothesized graph would consist of a diagonal line with a slope of 2. This slope is different from the one observed in the previous part because now both rubber bands are being stretched (albeit to different degrees). Before, the thick band showed very little change, making there no slope. In this case, there is a rise of 2 over a run of 1 on the actual graph as hypothesized. For this experiment, the two thick rubber bands were indeed identical, making the hypothesized results consistent with the actual results. Had they not been, it would be expected that the shorter one would exhibit more of a change from its original length, which would cause the hypothesized slope to alter as well.
#$&*
@& This is a good explanation, and a plausible result given your previous data.*@
*#&!
@& Please see my notes and make revisions as appropriate.
&#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.
&#
*@"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
________________________________________
#$&*
@& I need to be able to quickly locate your insertions.
Please mark your insertions with &&&& (please mark each insertion at the beginning and at the end) and resubmit.*@