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course Phy 241
7/9/2013 11:10 pm
Using a piece of typing paper (actually any paper will do as long as its corners are not rounded), cut out a right triangle by trimming one of its corners in the manner indicated by the figure below (cut along the red line, remove the triangle, which will look like the triangle shown in the lower-right-hand corner of the figure). Make the triangle fairly short. The longest side should be between 1 and 2 inches long.Measure the hypotenuse of your triangle, using each level of reduction. For each level of reduction you have a 'block' consisting of several rulers; for each level, measure in about the center of the middle ruler. Estimate each measurement to the nearest 1/10 of a division (you won't be accurate at 1/10 division and on the smallest reductions it will be difficult to estimate, but that's no excuse for not doing your best).
We'll make the following conventions for our units of measurement:
• Let 'cm' stand for centimeters as measured with the full-sized ruler.
• Let 'cm_s' stand for centimeters as measured with the singly-reduced ruler.
• Let 'cm_d' stand for centimeters as measured with the doubly-reduced ruler.
• Let 'cm_t' stand for centimeters as measured with the triply-reduced ruler.
Give your results for the hypotenuse below, separated by commas. A sample format, which gives a brief but complete (though not very accurate) answer, might be '3.14 cm, 5.37 cm_s, 9.48 cm_d, 13.25 cm_t'. Your numbers of course will differ from those given here.
4.4 cm, 6 cm_s, 9.2 cm_d, 14.3 cm_t
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Describe in words what you did to make your measurements as accurate as possible:
I made sure that both the rulers and the triangle were flat as possible to ensure accuracy. I also made sure that the start of the triangle was as close as possible to the starting line multiple times before recording my measurements.
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Which of your measurements do you think would be the most accurate, in the sense of having the least uncertainty?
In the sense of having the least uncertainty, I would say the full sized image because the clarity of the image is much higher than the others.
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In the same way measure the shorter of the two legs of the triangle and give your results below:
3.1 cm, 4.2 cm_s, 6.4 cm_d, 10.2 cm_t
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Repeat for the longer of the two legs of the triangle and give your results below:
3.2 cm, 4.4 cm_s, 6.8 cm_d, 10.6 cm_t
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Consider the two sides whose lengths are closest. This might be the hypotenuse and the longer leg, or it might be the longer leg and the shorter leg, depending on how you cut your triangle.
According to each ruler, what is the difference between these two sides? Give you answer in a format similar to that of the first question, as four quantities separated by commas.
0.1 cm, 0.2 cm_s, 0.4 cm_d, 0.4 cm_t
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For each level of reduction, give the difference between the two sides as a percent of the length of the hypotenuse. Give your results in the first line as a series of four numbers separated by commas, in order with the result with for the full-sized ruler first, the result for the triply-reduced ruler last. Use the appropriate number of significant figures in your results. Starting in the second line, give your explanation of how you got your results.
≈ 2.273%, ≈ 3.333%, ≈ 4.348%, ≈ 2.797%
I divided the difference by the length of the hypotenuse.
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According to your results, what would be the length of an object that measures exactly 1 cm on the full-sized copy, if measured using the singly, the doubly, and the triply-reduced copy? Give your answer in the usual comma-delimited format in the the first line, then starting in a new line explain how you got your results.
≈ 1.364 cm_s, ≈ 2.091 cm_d, 3.25 cm_t
I divided each of the reduced measurements I gathered above by the full sized measurement (of the same side of the triangle) to get the percentage and the multiplied by 1 of each specific measurement
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What would be the lengths, in units of cm of the full-sized ruler, of three objects, whose respective lengths measure 1 cm_t, 1 cm_d and a cm_s? Give the three lengths separated by commas in one line, then starting in a new line explain how you got your results.
≈ 0.733 cm, ≈ 0.4783 cm, ≈ 0.308 cm
I divided my full sized measurement I obtained above by each of the reduced measurement (all of the same side of the triangle) to get the percentage and the multiplied by 1 cm
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According to your present results what would be the length, on each of your rulers, of an object whose length on a the doubly-reduced ruler was determined to be 8.34 cm_d?
≈ 3.989 cm, ≈ 5.439 cm_s, ≈ 12.963 cm_t
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You made your measurements in the middle of each 'block' of rulers. We might expect that, due to optical distortions in the copying process, there might be some difference in measurements made at different places on each ruler 'block'. Investigate this question.
Are there places on the triply-reduced copies where an object measured at one location gives a different result, due to distortions of the copy, than the same object measured at another location? If so, at what positions and at what level of reduction do you observe the most distortion?
Give your results and explain how you investigated this question.
In the triply-reduced copy, these discrepancies are present virtually everywhere. There are many portions of the rulers that are 'whited-out' and would not be viable choice to make an accurate measurement what-so-ever. The triply-reduced copy has by far the most distortion, although each reduction level has it's fair amount.
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If you believe you did detect distortion, how much of the observed difference in measurements do you think you can attribute to actual distortion, and how much to limits on your accuracy and the precision of the markings?
If you did not detect them, this doesn't mean that there aren't distortions. There almost certainly are, but they might be too slight for you to measure. In this case, how small would they have to be before you would be unable to detect them? How big is the largest discrepancy you would be unable to discern? Give your results and explain your thinking.
Although the markings on the triply-reduced are small I believe I was highly accurate (after sticking my eyeball about 1mm from the page) and would only account the limits on my own accuracy to about 40%. The other 60% I would attribute to the 'whited-out' parts of the ruler or other imperfections.
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Don't actually do this, but if you were to write a 100-word paragraph with a #2 pencil, measuring the pencil before and after, which level of reduction do you think would allow you to determine most accurately the difference in the length of the pencil from eraser to point?
I believe the singly-reduced ruler is a good balance between accuracy (as far as legibility) and the size of the pencil reduction
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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?
About 1.5 hours
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&#Good work on this lab exercise. Let me know if you have questions. &#