course Phy 232 This assignment proved slightly more difficult because I was having trouble visualizing and calculating things without actual data. I find it easier to interpret things when I can see data. ߦ[݄DIS{assignment #001
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10:29:27 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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10:36:39 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 --> The original ruler will probably be closer to the actual length of the pencil because it will be harder to read the triply-reduced ruler and get accurate results. Also, anything that you do that has less calculations is usually more accurate, especially in measurements. The factors that help me decide which will be more accurate is looking at which is easier to read with the human eye, and also seeing which one has less caculations. confidence assessment: 3
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10:37:22 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 --> The triply-reduced ruler then would be more accurate because you can read it accurately to 4 sig figs, and it is easy to read. confidence assessment: 3
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10:46:33 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 first go through the data from the experiment before and make sure that I got more accurate results from the one that I wanted to use for this experiment. I think that the triply-reduced ruler would be more accurate becuase I could read it to 4 sig figs accurately. I would look at the factors of the experiment and make sure that, that ruler was th emost accurate. confidence assessment: 3
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10:56:41 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 --> First, I would graph and look at the trends in the data to see if it was decreasing at a decreasing rate like predicted. Since the depth changes varied from 5 cm to 2 cm over the first six 3-second intervals, we are looking at a (5-2)/(6*3)= 1/6 = 0.17 rate of change overall. I don't really know how I could quantify these numbers anymore. By taking the first and second derivative of this equation we would be looking at more and more error and uncertainty the further out we go. These uncertainties would make the graph more and more jagged as we went from the first-difference to the second-difference calculations. The first difference tells me the velocity as the tank empties and the second difference tells me the acceleration (or deacceleration) that the water experiences as it drains. confidence assessment: 2
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10:59:03 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 --> If the second-difference graph showed a linear trend, then the slope of that graph would be estimated with numbers that are not entirely considered accurate. Thist would throw off the calculation slightly. I am not sure of the exact percentage because I would need to see the data, but probably find it within 10% or so. confidence assessment: 2
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