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course Phy 232
7/19/134:13
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
The triply reduced ruler because it is more accurate if you can read it to each mark clearly.
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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
Take into consideration whether smaller marks could be more precise than the actual sized 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
The answer would still be that the triply reduced ruler would be better. If not the answer would have been that the triply reduced ruler would be worse since you cant clearly see each mark.
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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
You have to take into consideration the difference between clear and unclearly marked ruler. Then consider the previous question.
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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
Because the distance is small I would use the smaller ruler to be more precise and give a better read on the distance.
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· Explain what factors you considered and how they influence your final answer.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
Since its only a small distance the regular sized ruler would only give little precision to the true size since it measures in centimeters.
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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
About a .2 centimeter error for each reading. This is because of eyes and not measuring from the true point of the water level. With each difference it would increase by about double the amount.
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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 graphs would become more an dmore uncertain and the points would become less in patter.
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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 would be pretty reliable with only small amounts of error.
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· Answer the same for the second-difference graph.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
It would be somewhat reliable but with larger possibility of error.
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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 would tell you the average velocity vs time and the second would tell you acceleration vs time.
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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
10%
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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 thought about the experiments and how they were conducted and what the results looked like. Then took that into consideration when answering each question.
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&#This looks good. Let me know if you have any questions. &#