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Phy 231
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:
Is the tape speeding up or slowing down?
Is the pendulum speeding up or slowing down?
Which speeds up faster, the tape or the pendulum?
What is going to limit your ability to precisely measure the positions of these objects?
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 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:
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):
I chose the roll of tape in video #4.
Time Position
19.468 Initial position, ready to be released.
20.562 6.5, same position as pendulum
21.109 Bounced off tape measure.
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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):
I think the positions could be determined to the nearest half-inch. I can see the outline of both objects and it is appears clear where the inch markers are and where the half inch markers are. The problem is that I can't get a good straight-on perspective with the camera angle (the parallax issue). Clock times are good to .001, because the clock can be frozen and all digits can be seen properly with minimal ghosting on most frames.
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@& Very good.
However the clock times don't refresh at an interval of .001 seconds (the screen doesn't refresh 1000 times per second), so the clock isn't as accurate as the display. The clock uncertainty in this experiment is still negligible compared to other uncertainties.*@
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):
You can compare clock time and an initial position, clock time and a central position, and clock time and a final position to see the speed at the first half of the track and at the second half of the track. d/t=speed
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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):
You can also compare the pendulum's speed at several different points along its trajectory using several different positions and times and comparing them. The pendulum has a different form of motion, though and so it will speed up and then slow down. More data points should be used with the pendulum to check speed at several locations throughout its path.
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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):
Just thinking about the pendulum's motion is an easy way to determine where it speeds up and slows down. The pendulum is released at its upper-most point in its trajectory, so the only way it can travel is down. the gravity speeds the pendulum's motion up until the pendulum gets to its lowest point, right under its anchor point. The pendulum then begins an upward climb where it loses speed due to the gravity resisting its upward motion. Once the force of gravity exceeds the force of the pendulum's momentum, the pendulum stops and turns back to head for its lowest point once again to repeat the process.
The way to determine this using measurements is to just pick two points and measure the speed between them. The answer will become more clear as more points are chosen and as the points get closer together.
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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):
We already know that the tape is speeding up, and that's known as acceleration. The acceleration of the acceleration, or jerk, is found by taking the second derivative of velocity.
I'm not sure this can be observed easily.
To detrimine that the tape is accelerating is easy, though. Since the tape begins at rest and ends in motion, we can be sure that it has sped up throughout the experiment.
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@& Excellent work. Check my one note regarding the accuracy of the clock.*@