course PHY 232 After the final question I answered, the application closed. I reopened the file and the same thing happened. Let me know if there was something wrong with my file and there are more questions to answer or if there are any other problems. Thanks! 19:13:23Most 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 --> okay!
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19:21:37 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 --> Measuring something with an origional ruler will provide a more accurate length. There are many factors that influence the measurements. The first one is the scale factor. Since the scale factor was calculated from observation, there is more opportunity for error. Secondly, a pencil is a long object that measures multiple full centimeters long. Thirdly, the tripply reduced ruler has distortion that will have a negative impact on accurately measuring the length. confidence assessment: 2
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19:23:30 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 --> If the triply-reduced ruler has no optical distortion and the scale factor is very accurate, measuring with the triply-reduced ruler would be more accurate because each marking on the ruler would be clear, allowing the person measuring the object to be able to have less uncertainty. confidence assessment: 2
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19:24:58 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 --> The tripply reduced ruler would be more accurate since a small distance is being measured. confidence assessment: 2
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19:25:17 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 --> There should be about 1.195 of uncertainty. This number would be calculated by adding all of the measured distances together and then dividing by the total number of data points (5 in this case). Then, the (mean) average deviation is calculated from the mean. Next all of the deviations are squared and then added together. Finally, to calculate the standard deviation, or uncertainty, the sum of the equared deviations is divided by one less than the total number of data points (4 in this case). The uncertainty in first-difference calculations will be less than in second-difference calculations. The first-difference is the slope of the position vs. time graph and the second-difference is the slope of that. It is easier to see a trend of decreasing distance than to calculate the rate of the rate of decreasing (second-difference). This can be seen on a graph. The origional graph will have a curved, decreasing slope. Each point should be pretty close to the best-fit line. The first-difference graph will be a straight increasing line found on the negavite y axis. The best-fit line for these points will most likely not go through most or many of the data points. Finally, the sedond-derivative graph will have data points that are even more spread out. The best-fit line could easily not go through any of the points. The first diference graph tells you by how much the water is leaving the cylinder, or the rate of change. The second derivative is showing the rate of that, or the rate of by how much the water is leaving. confidence assessment: 3
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19:25:25 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 --> If the first-difference graph is a linear line, the second-difference graph should be a horizontal line because the second-difference is the slope of the first-difference. A linear line has a constant slope and this constant number will be the y-coordinate for all y-values for the second-difference graph. confidence assessment: 2
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