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course Phy 121
Sept 20 7:59 pmI ended up just redoing the Measuring Distortion of Paper Rulers
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.
6.4cm, 9.9cm_s, 15.4cm_d, 23.7cm_t
Describe in words what you did to make your measurements as accurate as possible:
To make my measurements as accurate as possible, I measured the triangle 3 times for each resolution, and I carried out the decimal place to the hundredths.
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Which of your measurements do you think would be the
In the same way measure the shorter of the two legs of the triangle and give your results below:
4cm, 6.2cm_s, 9.4cm_d, 14.6cm_t
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Repeat for the longer of the two legs of the triangle and give your results below:
5.1cm, 7.8cm_s, 12.1cm_d, 18.8cm_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.
1.1cm, 1.6cm, 2.7cm, 4.2 cm
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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.
17%, 16%, 18%, 18%
I added the 2 length measurements for each resolution, I divided the difference in length of the two sides by that number.
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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.
1cm, 1.5cm_s, 2.3 cm_d, 3.4cm_t
Each smaller ruler created a measurement of about 1.5 times the previous ruler so I applied this to 1 cm.
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1.5 is about the right ratio, though you could refine that to a 3-significant-figure ratio.
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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.
.30 cm, .44cm, .67cm
I divided 1 by 1.5, 3 times to get the full sized ruler from the triply reduced ruler , 2 times for the doubly reduced, and 1 time from the singly reduced ruler.
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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?
3.7cm, 5.6 cm_s, 12.5cm_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.
The full sized ruler and the singly reduced rulers were relatively easy to read. For the triple and double resolution rulers, I did see distortion in the lines and on the numbers. Towards the middle the level of distortion for the double and triple was easier to see than the outside part of them.
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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.
The last 2 rulers were rather hard to read, therefore I think the distortions on the smaller rulers varied about 1/10 of a cm.
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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 think the full-size ruler provided the most accuracy to any further measurements I may need out of the 4. There was little distortion and the lines were pretty clear.
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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:
0. Approximately how long did it take you to complete this experiment?
1 hour
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1.5 is much closer to the correct ratio than 1.25. However your measurements were well done and you can do better than the 2 significant figures of 1.5.
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Your measurements are accurate to more than the two significant figures you gave for your ratio.
Based on your first set of measurements
6.4cm, 9.9cm_s, 15.4cm_d, 23.7cm_t
the ratio would be between ..54 and 1.56.
The ratios for the measurements
5.1cm, 7.8cm_s, 12.1cm_d, 18.8cm_t
were all between 1.55 and 1.56.
You would very probably be correct if you were to declare that the ratio is
1.55 +- .01.
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