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course Phy 121
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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cm_s
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Which is longer, one cm_s or two cm_t?
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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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3.65
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How many cm_t would a measurement of 3 cm be?
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3*3.65=10.95
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How many cm would a measurement of 13 cm_t be?
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13/3.65=3.56
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Does it depend on where on the ruler the measurement is made?
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Yes, because of the potential optical distortion.
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How many cm_s make a cm_t?
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2.54
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How many cm_s would a measurement of 5 cm_d be?
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1cm_s=2.70cm_d
5cm_d/ 2.70=1.85cm_s
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How many cm_d would a measurement of 11 cm_t be?
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1cm_d=2.10cm_t
11cm_t/2.10=5.23cm_d
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Does it depend on where on the ruler the measurement is made?
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No, unless there is distortion in the image of the ruler.
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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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no, measuring on the triply-reduced ruler, it is impossible to discern out to hundredths place accurately, so adding it in your measurement is misleading.
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To how many significant figures are you pretty sure you could answer these questions. Explain.
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two, any more and it becomes a guessing game as two where the mark is on the ruler.
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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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four, on any ruler, four significant figures would not be able to be determined accurately.
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&#Your work on this lab exercise looks good. Let me know if you have any questions. &#