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course Phy 232
7/2 10am
Question: 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?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
Using the actual length of the pencil will most likely be closer to the actual length of the pencil.
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· What factors do you have to consider in order to answer this question and how do they weigh into your final answer?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
I considered the fact that the actual ruler will be more exact, and using a triply reduced ruler makes more room for error since the number might not be as precise as it would be using the regular ruler.
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Question: Answer the same questions as before, except assume that the triply-reduced ruler has no optical distortion, and that you also know the scale factor accurate to 4 significant figures.
· Which result is likely to be closer to the actual length of the pencil?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
Assuming that the triply-reedcued ruler has no distortion and the scale factor is accurate to four significant figures, both methods could produce a close measure to the actual length of the pencil, but the triply reduced scale might be more precise.
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· What factors do you have to consider in order to answer this question and how do they weigh into your final answer?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
I took into account the fact that the regular ruler could only be so precise, and if the triply reduced ruler had a scale factor accurate to four significant figures, then that method might actually produce a more precise estimate.
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Question: 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?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
If the triply reduced ruler like the one in the question above (no distortion/scale factor accurate to four sig figs) then the triply reduced will give you the more accurate length. However, if there is distortion, then the regular ruler will give a more accurate length.
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· Explain what factors you considered and how they influence your final answer.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
I considered the distortion, and how great it would be if the triply ruler was used. If the distortion is high, then it will not be as accurate as the ruler. If the distortion is low, it might be more accurate.
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Question: 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 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 through Assignment 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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
I believe that the uncertainty would range between 1-2 significant figures. Especially if there is distortion because of the ruler, the depths might not be entirely accurate. The uncertainty in measurements because of the distortion would lead me to believe that the accuracy is good up to a fwe significant figures. Also, there would be more uncertainty in first difference calculations, because as you take more and more differences the numbers will get more and more unprecise if the original numbers were unprecise.
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· How would these uncertainties affect a graph of first difference vs. midpoint clock time, and how would they affect a graph of second difference vs. midpoint clock time?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
The uncertainties will cause the graph to slightly different form expected for the first difference, but the second difference would be even more less precise. It might have jagged lines if the first difference is not very accurate.
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· How reliably do you think the first-difference graph would predict the actual behavior of the first difference?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
It will be close to the actual behavior of the first difference, but there will still be points above and below the best fit line.
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· Answer the same for the second-difference graph.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
The second difference graph will not very well predict the actual behavior of the second difference, especially if the first difference is significantly unaccurate.
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· What do you think the first difference tells you about the system? What about the second difference?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
The first difference tells you the difference between each depth. The second difference shows you the distance to the midpoint value between the first differences.
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Question: 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)?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
If the actual second difference behavior of the depth vs. clock time is linear, then i feel like I could estimate the slope of the graph within 1% of the correct slope, since it is linear and it is easier to determine the slope of a linear line.
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Again no extensive analysis is expected, but give a brief synopsis of how you considered various effects in arriving at your estimate.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
I considered the fact that if it was linear, then the data would all be fairly accurate, and if I used my skills of determining the slope of a linear line I feel as though I could get very close to the actual slope.
&#Good responses. Let me know if you have questions. &#