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course PHY 121
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
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Which is longer, one cm_s or two cm_t?
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one cm_S
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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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4
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How many cm_t would a measurement of 3 cm be?
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5.5
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How many cm would a measurement of 13 cm_t be?
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4.3
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Does it depend on where on the ruler the measurement is made?
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Yes.
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How many cm_s make a cm_t?
0.5
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How many cm_s would a measurement of 5 cm_d be?
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4.3
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How many cm_d would a measurement of 11 cm_t be?
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5
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Does it depend on where on the ruler the measurement is made?
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yes.
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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.
Yes. I used the number of significant figures stated or less.
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To how many significant figures are you pretty sure you could answer these questions. Explain.
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2. You can easily tell this on the rulers.
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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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1. It wouldn’t be accurate.
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&#Good work on this lab exercise. Let me know if you have questions. &#