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Phy 202
Your 'cq_1_00.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The videos
There are four short videos, all of the same system. The smaller files are around 500 kB and will download faster than the larger files, which are about 4 times that size (about 2 mB or 2000 kB), but the larger files are a bit better in quality. If you have a fast connection any of these files should download fairly quickly. Video 1 and Video 2 probably contain the best information; Video 4 is the shortest.
The quality of these videos is not that great, and that is deliberate. These are medium-definition videos, taken with a camera that doesn't have a particularly high shutter speed. It's not important here to even know what a shutter speed is, but the effect of the slow shutter speed is to cause images of moving objects to be blurry.
* All data in any science is in effect 'blurry'--there are limits to the precision of our measurements--and we start off the course with images that have obvious imperfections. We will later use images made with a high-definition camera with a fast shutter, where imperfections, though still present, are difficult to detect.
Video 1 (smaller file) Video 1 (larger file)
Video 2 (smaller file) Video 2 (larger file)
Video 3 (smaller file) Video 3 (larger file)
Video 4 (smaller file) Video 4 (larger file)
View these videos of a white roll of tape rolling down an incline next to a dark swinging pendulum, using Windows Media Player or a commercial media player. By alternately clicking the 'play' and 'pause' buttons you will be able to observe a series of positions and clock times.
The measuring tape in the video may be difficult to read, but it is a standard measuring tape marked in feet and inches. At the 1-foot mark, a little to the left of the center of the screen, there is a black mark on the tape. If you want to read positions but can't read the inches you can count them to the right and left of this mark. You can estimate fractions of an inch. You don't need to write anything down; just take a good look.
Begin by forming an opinion of the following questions; for the moment you may ignore the computer screen in the video. You don't have to write anything down at this point; just play with the videos for a couple of minutes and see what you think:
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Technically, 'at this point' refers to the time at which you read and follow the first instruction. The question about the motion of the tape is at a later point.
Practically, it wouldn't be a bad idea for me to be more specific about what I mean.
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* Is the tape speeding up or slowing down?
???? When you say that I don't have to write anything down, do you mean that I don't have to write down any data or that I don't have to write down an answer? In case it's the former: ???? RESPONSE: The tape's acceleration is positive and constant at (g sin[angle of ramp] * (1 - [coefficient of friction between tape and ramp])); I believe that this breaks down to (g sin [angle of ramp] * [(1 - CoefficientOfFriction:Tape)(1 - CoefficientOfFriction:Ramp)]).
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That would be expected to define the motion of the tape. Whether or not it actually does would be based on observations of position and clock time.
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* Is the pendulum speeding up or slowing down?
???? When you say that I don't have to write anything down, do you mean that I don't have to write down any data or that I don't have to write down an answer? In case it's the former: ???? RESPONSE: The pendulum speeds up until it reaches its equilibrium point, and then it slows again until it stops and reverses direction at the opposite side.
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Once more, that is the expectation and would be a reasonable hypothesis to test. How would we use data to test the hypothesis?
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* Which speeds up faster, the tape or the pendulum?
???? When you say that I don't have to write anything down, do you mean that I don't have to write down any data or that I don't have to write down an answer? In case it's the former: ???? RESPONSE: The tape's and pendulum's accelerations are roughly equal until the midpoint (re: both distance and time) of their travels, which happens at about the one-foot mark that you mentioned, but after that, the pendulum starts slowing down because it goes back up, whereas the tape continues to accelerate.
* What is going to limit your ability to precisely measure the positions of these objects?
???? When you say that I don't have to write anything down, do you mean that I don't have to write down any data or that I don't have to write down an answer? In case it's the former: ???? RESPONSE: Factors limiting the precision with which one can measure the objects' positions include:
- a) i) The shutter speed of the camera, ii) the sampling rate of the video conversion and/or compression software in use, and iii) the relationship between these, especially to the extent that each is not an integer divisor or integer multiple of the other(s)
- b) The minimum frame-by-frame progression rate of
- c) The fact that the thick portion (bob) of the pendulum is in the way of the tape for most of the first half of their travel; this effect is magnified by the parallax effect that you mention below, which increases as the camera gets closer to the pendulum, as the tape gets farther away from the pendulum, and as the angle of the camera lens gets wider / its focal length gets shorter.
The computer in the video displays the running 'clock time', which is accurate to within something like .01 second. Think about how the information on this screen can help answer the above questions.
You don't have to think about the following right now, so I'm going to make it easy to ignore by putting it into small type. There is a parallax issue here. You don't even have to know what this means. But if you do, and if you want the information, here it is:
* The measuring tape is pretty much parallel to the paths of the pendulum and the tape roll, about 5 inches further from the camera than the path of the pendulum, and the path of the ball ???? I don't see a ball in these videos. Is the mention of the ball from an older version? ???? is about halfway between the two. The camera is about 5 feet away from the system.
The problem:
You don't have to actually do so, but it should be clear that if you wished to do so, you could take several observations of positions and clock times. The main point here is to think about how you would use that information if you did go to the trouble of collecting it. However, most students do not answer these questions in terms of position and clock time information. Some students do not pause the video as instructed. To be sure you are thinking in terms of positions and clock times, please take a minute to do the following, which should not take you more than a couple of minutes ???? Wouldn't I have to be traveling at close to the speed of light for that? ????:
* Pick one of the videos, and write down the position and clock time of one of the objects, as best you can determine them, in each of three different frames. The three frames should all depict the same 'roll' down the ramp, i.e. the same video clip, at three different clock times. They should not include information from two or more different video clips.
* For each of the three readings, simply write down the clock time as it appears on the computer screen, and the position of the object along the meter stick. You can choose either object (i.e., either the pendulum or the roll of tape), but use the same object for all three measurements. Do not go to a lot of trouble to estimate the position with great accuracy. Just make the best estimates you can in a couple of minutes.
Which object did you choose and what were the three positions and the three clock times?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE: Readings for pendulum are in (clock time, measuring tape reading) format; measurements are from downhill side of pendulum because that's what was even with the leading edge of the tape roll:
- 1) (20.453 seconds, approx. 5 inches [reading is lower, but see above re: parallax error])
- 2) (20.671 seconds, approx. 10 inches [pendulum is more in line with camera, so parallax error is less but still present])
- 3) (21[even] seconds, approx. 15.5 to 16 inches [pendulum is again out of line with camera, so parallax error is reintroduced])
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In the following you don't have to actually do calculations with your actual data. Simply explain how you would use data of this nature if you had a series of several position vs. clock time observations:
* If you did use observations of positions and clock times from this video, how accurately do you think you could determine the positions, and how accurately do you think you would know the clock times? Give a reasonable numerical answer to this question (e.g., positions within 1 meter, within 2 centimeters, within 3 inches, etc; clock times within 3 seconds, or within .002 seconds, or within .4 seconds, etc.). You should include an explanations of the basis for your estimate: Why did you make the estimate you did?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE:
- a) Position to within 0.25 inches at 1-foot mark, i.e., at camera's focal axis (this is about the parallax error at one edge of the pendulum when center is along this axis); position to about .75 inches or 1 inch at extremes of pendulum's oscillation (pendulum width appears to block out about .5 or .75 additional inches of tape measure at extremes; adding this to .25-inch figure earlier yields .75 inches to 1 inch)
- b) Time to about .015625 seconds ([1/64] second): See our discussion of the TIMER program's measurement intervals in the Using the TIMER program set.
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* How can you use observations of position and clock time to determine whether the tape rolling along an incline is speeding up or slowing down?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE: Plot position vs. time and note second derivative of line or, if plot is too fuzzy (see above) to get a good mathematical approximation, look at the general concavity of the graph: Concave up + position increasing = going forward and speeding up; concave down + position increasing = going forward but slowing down; concave up + position decreasing = going backward but slowing down; concave down + position decreasing = going backward and speeding up
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* How can you use observations of position and clock time to determine whether the swinging pendulum is speeding up or slowing down?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE: Same as above (the motion pattern will be different, but the plotting procedure and standards for interpretation of the graph are the same)
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* Challenge (University Physics students should attempt answer Challenge questions; Principles of Physics and General College Physics may do so but it is optional for these students): It is obvious that a pendulum swinging back and forth speeds up at times, and slows down at times. How could you determine, by measuring positions and clock times, at what location a swinging pendulum starts slowing down?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE: Examine plot drawn in second Response above and see where the graph of the second derivative crosses zero: This will denote a concavity change, i.e., a change of second derivative (= acceleration) from positive to negative (from speeding up while traveling in positive direction to slowing down while traveling in positive direction) or from negative to positive (from speeding up while traveling in negative direction to slowing down while traveling in negative direction)
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* Challenge (University Physics students should attempt answer Challenge questions; Principles of Physics and General College Physics may do so but it is optional for these students): How could you use your observations to determine whether the rate at which the tape is speeding up is constant, increasing or decreasing?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
RESPONSE: Same as above; here, the graph of the second derivative should be positive and (roughly) constant.
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Check to see that you have followed the instructions:
* The instructions told you to pause the video multiple times. It appears that some students are not following this instruction. If you haven't used the 'pause' and 'play' buttons on your media player, you should go back and do so.
* The questions are phrased to ask not only what you see when you play the video, but what you see when you pause the video as instructed ???? I listed data re: the position of the pendulum when I paused the video, but I didn't know that I was supposed to list other observations such as its position in relation to the position of the leading edge of the tape roll. Was I supposed to have done this as well? ????, and what you think you could determine if you were to actually take data from the video. You aren't asked to actually take the data, but you need to answer how you would use it if you did. It's OK if you have given more general descriptions, which are certainly relevant. But answers to the questions should include an explanation of how you could use the series of position and clock time observations that are may be observed with this video.
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You clearly did as instructed.
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* The questions also ask how much uncertainty there would be in the positions and clock times observable with this specific video. Different people will have different answers, and some reasonable answers might vary from one clip to the next, or from one part of a clip to another. However the answers should include a reasonable quantitative estimate (i.e., numbers to represent the uncertainty; e.g., .004 seconds of uncertainty in clock times, 2 inches in position measurements. Use your own estimates; neither of these example values is necessarily reasonable for this situation). You should also explain the basis for your estimate: why did you make the estimate you did? You should have estimated the number of seconds or fraction of a second to within which you think the time displayed on the computer screen might be accurate (e.g., is it accurate to within 10 seconds of the actual clock time, or to within 1 second, within .1 second, maybe even within .01 or .001 second). You might not yet know enough about the TIMER to give an accurate answer, but give the best answer you can. You should also indicate a reasonable estimate of the number of inches or fraction of an inch to within which you could, if asked, determine the position of each object.
RESPONSE: Except as noted in the question in the second item above, I believe that I've followed all of the above instructions. ??? If I've missed something, I'm happy to submit revisions. ???
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Approximately 1 hour and 30 minutes
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??? Question: The file name in the URL of this site (ph1_cq_I_00_1.htm) mentions the designations ph1 and I, but the title refers to this form as the common questions form -- are these questions common to both first- and second-semester classes, or did the term common refer to something else, such that this question set is for first-semester students only? ???
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Your responses are very good.
The primary purpose of this exercise for second-semester students is to draw the student's attention to the fact that uncertainties exist and that we need to estimate them and use them in our analysis. Unfortunately, not all students coming into a second-semester course are aware of this.
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