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course Phy 121
9/10 9:18 pm???For our titles are spaces a forbidden symbol? I keep using underscores but I won't if I don't have to???
Note that the top copy is upside down and backwards. Orient your copy the same way and in small letters near the top of the page, but positioned so as not to interfere with any of the marks on the ruler, write the word 'top'.
We will refer to the four levels of reduction sizes as 'full-sized;, 'singly-reduced', 'double reduced' and 'triply reduced'. In addition to the 'full-sized' copy shown above, there is one sheet of 'singly-reduced' rulers, and another sheet containing both 'doubly-reduced' and 'triply-reduced' rulers.
Even the full-sized copies are not perfect. The copier uses lenses, and no lens can be perfect. There are slight distortions in the copies, and in this experiment we 'map out' these distortions.
The singly-reduced copy looks similar, but the rulers are reduced. This means that the marks on the page are closer together, and they can therefore measure lengths with more precision than the singly-reduced rulers. However in order to measure with equivalent accuracy we will need to map out and correct for any distortions arising from the copying process.
The goals of this experiment are as stated above:
Understand how the different rulers have different degrees of precision and accuracy for different measurements.
Determine as accurately as possible any optical distortions in the copies. Related questions you should keep in mind and answer:
What is the margin of error in your placement of the markings?
Within what limits of accuracy can you place and measure the distance between two markings at each level of reduction?
Can optical distortion be detected within this margin of error?
If you have a ruler whose smallest division is a millimeter, then the position of a point on the ruler would be measured accurate to a millimeter, and you would also make your best estimate of where that point lies between the marking (e.g., a point between the 3.8 and 3.9 cm markings might lie halfway between those markings, in which case you would estimate the position as 3.85 cm; or it might lie closer to one marking than the other, so you might have an estimate of 3.82 cm or 3.86 cm; you should try to estimate the position between the smallest mark to the nearest tenth of that distance).
We'll make the following conventions for our units of measurement:
Let 'cm' stand for centimeters as measured with the full-sized ruler.
Let 'cm_s' stand for centimeters as measured with the singly-reduced ruler.
Let 'cm_d' stand for centimeters as measured with the doubly-reduced ruler.
Let 'cm_t' stand for centimeters as measured with the triply-reduced ruler.
Answer the following:
Which is longer, one cm_d or one cm_s?
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One cm_s is longer
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Spaces are legal, but I believe the programs change spaces in titles to underscores.
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Which is longer, one cm_s or two cm_t?
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One cm_s is longer
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It is likely that your answers to the following will be in the form of decimal numbers. Give your results to three significant figures:
How many cm_t make a cm?
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3.8 cm_t make a cm
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How many cm_t would a measurement of 3 cm be?
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Doing the math it would be 3 * 3.8 cm_t = 11.4 cm_t. When I measured I got 11.3 cm_t
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How many cm would a measurement of 13 cm_t be?
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Doing the math it would be 13cm_t * 1 cm/ 3.8cm_t = 3.42 cm. When I measured I got 3.5 cm
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Does it depend on where on the ruler the measurement is made?
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Yes it does matter. When I measured the 1 cm from the 10 cm_t I got 1 cm = 3.8 cm_t. When I measured it at the 40 cm_t I got 1 cm = 3.7 cm_t.
When I measured 3cm at the 10 cm_t I got 11.3 cm_t. When I meausred it at the 40cm_t I got 1 cm = 11.0 cm_t. There is some distortion going on.
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How many cm_s make a cm_t?
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0.41 cm_s
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How many cm_s would a measurement of 5 cm_d be?
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3.2 cm_s
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How many cm_d would a measurement of 11 cm_t be?
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7.2 cm_d
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Does it depend on where on the ruler the measurement is made?
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Yes, for example when meauseign the 11 cm_t when I measured at from 10 cm_t I got 7.2 cm_d, but when I measured at 30 cm_t I got closer to 7.3 cm_d
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Now answer the following questions about significant figures, including a brief but concise explanation.
Do you think all the significant figures in your result are appropriate? Explain.
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I really had a hard time with this experiment. On anything smaller than the cm ruler, I found it very difficult to determine where any .1 was. On the cm_d and cm_t rulers I felt as if I was looking at some optical illusion. The .3 and .4 lines almost seemed to be moving and then I would get white spots in my eyes. I was not able to come anywhere close to estimating to the .001 and I felt very little confidence even with the .1. My eyes are just not that good.
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Good note. Obviously eyesight is a limiting factor here and has an effect on which ruler will give you the best results.
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To how many significant figures are you pretty sure you could answer these questions. Explain.
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To be honest I don't think I could do any better than 2 significant figures
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What is the smallest number of significant figures for which the last figure would be completely meaningless? Explain
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At three significant figures the last number would be rather meaningless. Especially on any of the rulers smaller than cm. I kept having to blink, my eyes got sore and I felt a little dizzy looking at them.
There were some other questions listed above and I do not know where to answer them, so I will address them here:
What is the margin of error in your placement of the markings?
For anything less than the cm rulers, I would have to say my margin of error was +/- .1 For the cm ruler I could manage +/- .05
Within what limits of accuracy can you place and measure the distance between two markings at each level of reduction?
At anything less than cm I was only able to be accurate to .1
Can optical distortion be detected within this margin of error?
When I said that there seemed to be distortion, all my examples were within 0.1 so no, I at least cannot detect it within the margin of error.
I hope no one's life ever depends on me having to read these rulers.
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If it ever does, consider using a magnifying glass. My eyes are pretty good, but I need the magnifying glass and reading glasses to make clear distinctions on the triply reduced rulers.
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