course Phy 202 ्z퉲Kassignment #001
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12:12:40 Most queries in this course will ask you questions about class notes, readings, text problems and experiments. Since the first two assignments have been experiments, the first two queries are related to the experiments. While the remaining queries in this course are in question-answer format, the first two will be in the form of open-ended questions. Interpret these questions and answer them as best you can.
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RESPONSE --> ok
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12:12:59 Suppose you measure the length of a pencil. You use both a triply-reduced ruler and the original ruler itself, and you make your measurements accurate to the smallest mark on each. You then multiply the reading on the triply-reduced ruler by the appropriate scale factor. Which result is likely to be closer to the actual length of the pencil? What factors do you have to consider in order to answer this question and how do they weigh into your final answer?
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RESPONSE --> I think that the measured obtained by using the original ruler will be more accurate because even using the triply-reduced ruler will not be nearly as accurate, I would think, due to the optical distortion. Considering, that distortion, the scaling doesn't really matter because the markings are not accurate enough. The original ruler doesn't need to be scaled nor does it have the optical distortion as the triply-reduced one does from the copying process. confidence assessment: 2
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12:13:15 Answer the same question as before, except assume that the triply-reduced ruler has no optical distortion and you know the scale factor accurate to 4 significant figures.
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RESPONSE --> Ok, in this situation. I would assume that either ruler would suffice. I mean I'd still use the original to cut out having to do the work with the scaling, but seeing as how the scale factor is accurate to 4 sig figs, I don't see why it wouldn't be acceptable to use and rely on its accuracy. confidence assessment: 2
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12:14:44 Suppose you are to measure the length of a rubber band whose original length is around 10 cm, measuring once while the rubber band supports the weight of a small apple and again when it supports the weight of two small apples. You are asked to report as accurately as possible the difference in the two lengths, which is somewhere between 1 cm and 2 cm. You have available the singly-reduced copy and the triply-reduced copy, and your data from the optical distortion experiment. Which ruler will be likely to give you the more accurate difference in the lengths? Explain what factors you considered and how they influence your final answer.
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RESPONSE --> I would say the singly-reduced ruler because the triply-reduced ruler seems to have triple the distortion. If we are supposed to be as accurate as possibly I would bank on the ruler who has been manipulated the least. The singly-reduced ruler's measurements most closely coincide with a regular ruler. And the is more room for measurement error if we use the triply reduced ruler because we'd have to multiply by the scale factor which may not be accurate either. confidence assessment: 2
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12:23:04 Later in the course you will observe how the depth of water in a uniform cylinder changes as a function of time, when water flows from a hole near the bottom of the cylinder. Suppose these measurements are made by taping a triply-reduced ruler to the side of a transparent cylinder, and observing the depth of the water at regular 3-second intervals. {}{}The resulting data would consist of a table of water depth vs. clock times, with clock times 0, 3, 6, 9, 12, ... seconds. As depth decreases the water flows from the hole more and more slowly, so the depth changes less and less quickly with respect to clock time. {}{}Experimental uncertainties would occur due to the optical distortion of the copied rulers, due to the the spacing between marks on the rulers, due to limitations on your ability to read the ruler (your eyes are only so good), due to timing errors, and due to other possible factors. {}{}Suppose that depth changes vary from 5 cm to 2 cm over the first six 3-second intervals. {}{}Assume also that the timing was very precise, so that there were no significant uncertainties due to timing. Based on what you have learned in experiments done in Assignments 0 and 1, without doing extensive mathematical analysis, estimate how much uncertainty would be expected in the observed depths, and briefly explain the basis for your estimates. Speculate also on how much uncertainty would result in first-difference calculations done with the depth vs. clock time data, and how much in second-difference calculations. {}{}How would these uncertainties affect a graph of first difference vs. midpoint clock time, and on a graph of second difference vs. midpoint clock time? {}How reliably do you think the first-difference graph would predict the actual behavior of the first difference? {}Answer the same for the second-difference graph. {}{}What do you think the first difference tells you about the system? What about the second difference?
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RESPONSE --> I think there would be a lot of uncertainty. I don't know a numerical guestimate of how much, but since I know that the triply-reduced ruler is very off and the distortion seems to increase as you continue measuring. with each measurement taken as the water depth decreases, the more inaccurate your reading will be. The first difference calculations, I don't think, will add on that much more uncertainty, but the graph of the results will more than likely show those uncertainties obtained by the ruler. The second-difference calculations will magnify the uncertainties and will probably magnify them to a point where the trend on the graph isn't nearly as noticable as it was at first, just like in the experiment we did previously. Each time the difference quotient is done, the more magnified the uncertainties become. I think the first difference graph will predict the actual behavior pretty well because the uncertainties shouldn't be as evident yet. However, for the second difference, I do not expect the graph to be reliable at all. The uncertainties will prevent a clear trend from being evident. The first difference will tell us the velocity and the second will tell us the acceleration. confidence assessment: 2
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12:25:25 Suppose the actual second-difference behavior of the depth vs. clock time is in fact linear. How nearly do you think you could estimate the slope of that graph from data taken as indicated above (e.g., within 1% of the correct slope, within 10%, within 30%, or would no slope be apparent in the second-difference graph)? Again no extensive analysis is expected, but give a brief synopsis of how you considered various effects in arriving at your estimate.
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RESPONSE --> I don't think there will be an apparent trend for the second difference graph. If there happened to be one, however, I would say within 30% because there is so much uncertainty. If the uncertainties were reduced by 1/3 like they were in the previous experiment I'd be able to say 10%. confidence assessment: 2
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