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course Phy 121
In your standard lab kit you will find several sheets of plain white paper, which you should not discard. In general, never discard anything in your kit.In your initial lab material package (the one you were sent for free in response to submitting your address), as well as in the standard lab materials package (the one you paid the bookstore for), you will also find copies of meter sticks. Some will be full-sized, some will be reduced. There are three levels of reduction.
If you are working ahead and don't yet have your Standard Kit, if there has been a delay in the availability of Standard Kits, or if the paper copies have been left out of your kit, you can download and print these images. The best quality image files are nearly 10 mB each at this point, so if you have a dial-up connection allow sufficient time to download them, and consider using the smaller images listed under Acceptable Resolution. If your connection allows you to reliably download larger files, those under Best Resolution are a little sharper; this is especially so for the doubly-reduced document.
If you choose to print out the documents, you might need to click on 'Scale to Fit' in order to get the document at its intended size. The details for versions of XP and Vista (current as of July 2008): Right-click on the link, choose Print, click on Preferences, click on the Layout tab and check the Scale to Fit option.
Acceptable Resolution will be found in the following:
full-sized (260 kB)
singly-reduced (786 kB)
doubly-reduced (1.5 mB)
Best Resolution Files
fill-sized copy (8 mB)
singly-reduced copy (8 mB)
doubly-reduced copy (8 mB)
The full-sized copy looks like this:
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 because it has only been reduced one time. A double reduction means that the reduction process has been done twice(the once original sized image has been shrunk to a smaller size, then the smaller size was shrunk again). Though, technically, one cm is one cm, so it doesn't matter what our reduction scale is we haven't reinvented a system of measurement and are calling it a centimeter. A centimeter is a centimeter.
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Which is longer, one cm_s or two cm_t?
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One cm_s is longer because it has only been reduced one time, but as stated above, a cm is a cm. We haven't reinvented how long a cm is.
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We have defined the cm_s, cm_d and cm_t. None of these units is a centimeter.
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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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There are approximately 3.70cm_t in one cm.
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How many cm_t would a measurement of 3 cm be?
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According to my metric tape measure, 1cm measures out to be 3.7cm_t. So, 3 x 3.7 = 11.1cm_t.
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How many cm would a measurement of 13 cm_t be?
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If 1.00cm = 3.70cm_t, then 13.0cm_t/3.70cm_t=3.50
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Does it depend on where on the ruler the measurement is made?
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No, it doesn't matter where on the ruler the measurement is made. But beginning a measurement away from a simple reference point(like 0, 1, 2 etc) makes recording the measurement more difficult, but the measurement is the same across the measuring device.
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How many cm_s make a cm_t?
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There are approximately 0.569cm_s in one cm_t. A cm_s is longer than a cm_t, hence the fractional amount.
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How many cm_s would a measurement of 5 cm_d be?
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There are approximately 41mm in 1cm_d and 65mm in 1cm_s. 5.00 x 41.0 = 205mm. 205 / 65.0 = 3.15cm_s.
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How many cm_d would a measurement of 11 cm_t be?
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One cm_t is 27.0mm long. One cm_d is 41.0mm long. 27.0 * 11.0 = 297mm / 41.0mm = 7.24cm_d.
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Does it depend on where on the ruler the measurement is made?
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When dealing with the double and triple images, the millimeter marks are very small and close together so I'd be trying to keep the starting point of the reference as close to a power of 10 as possible. Becoming very precise.
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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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The sig figs are appropriate because as we started using the more precise rulers, the more sig figs would be needed because by using a more precise measuring devise we can be more accurate with our measurements.
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To how many significant figures are you pretty sure you could answer these questions. Explain.
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Without the use of a magnifying glass, I could accurately measure up to one sig fig. After that, the lines start running together.
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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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Well, in analytical chemistry I was taught that sig figs were only useful up to the calibration of the measuring device. In other words, If my analytical balance was only precise to two digits, then it would be pointless to try to find a third digit.
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Very good example.
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&#Good responses. See my notes and let me know if you have questions. &#