course Phy 201
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• At each level of reduction, on the average, by what factor would you multiply or divide a measurement made by one of the ruler copies in order to express the measurement in standard centimeters?
o For each ruler I only measured to 10 centimeters. To measure accurately I used a standard centimeter ruler along with each of the copied rulers to see the difference in each.
o Ruler Copy: Suppose to be: Actual size:
o Full 10 cm 9.85 cm
o Single 10 cm 6.2 cm
o Double 10 cm 1.2 cm
o Triple 10 cm 0.7 cm
Therefore, for each ruler I took the actual size divided by what it was supposed to be.
9.85cm/ 10cm = 0.985
The same strategy applies to each ruler copy.
• To measure the length of an object with one of the rulers you would find the difference in the positions of its two ends, and multiply this by the conversion factor you determined in the first step. This would give you the measurement in standard centimeters.
o Ruler Copy: Suppose to be: Actual size: % Smaller:
o Full 10 cm 9.85 cm 1.5
o Single 10 cm 6.2 cm 38
o Double 10 cm 1.2 cm 88
o Triple 10 cm 0.7 cm 93
Therefore, for each ruler I took the actual size divided by what it was supposed to be and multiplied by 100. For example,
9.85cm/ 10cm = 0.985 * 100 = 98.5%
Next I subtract the number obtained from 100,
100% – 98.5% = 1.5%
This means that the full size ruler is 1.5% smaller than the actual size of a standard ruler measured in centimeters. The same strategy applies to each ruler copy.
If you were to cut out a paper rectangle with dimensions about 1.2 cm by 8 cm, and in this manner measure the length of each of its edges as precisely as possible, using rulers at each level of reduction, which level of reduction would give you the most accurate results and which the least, and why?
The full sized ruler would give the most accurate results because it has an uncertainty of only 1.5% which is obviously the lowest percentage among all of the rulers. The least accurate ruler copy is the triply reduced copy. The copy has a distortion of 93% from what a normal centimeter reads.
Would your answer be the same for all measurements? Why or why not?
Yes the answer would be the same for all measurements because the copies do not change. It doesn’t matter what you are measuring; the full size will always be the most accurate of the copies and the triply reduced copy will always be the least accurate.
What do you think would be the percent error for a length measurement at each level of reduction?
o Ruler Copy: Suppose to be: Actual size: % Smaller:
o Full 10 cm 9.85 cm 1.5
o Single 10 cm 6.2 cm 38
o Double 10 cm 1.2 cm 88
o Triple 10 cm 0.7 cm 93
What do you think would be the percent error for a width measurement at each level of reduction?
Ruler Copy: Percent error:
Full 30 %
Single 56%
Double 72%
Triple 79%
• If you actually cut out the rectangle, you would be unable to cut a perfect rectangle. Specifically, focus on the difference between your two width measurements.
At which level of reduction would you expect your data to give you the most precise indication of this difference, and why?
According to my data, the full sized copy would give a more precise indication of the difference of my triangle because it has the least amount of percentage of reduction; 30%.
• Due to optical distortions, measurements made in one area of a given copy might differ from measurements made in another area.
For which level of reduction do you observe the most optical distortion between different locations of the page?
I think the triply reduced copy gives the most optical distortion between different locations on the page because it is so much smaller. For someone with bad eyes it almost appears that the tiny centimeters ticks on the page are all running together.
What is the maximum percent error you would expect between the same measurement made at different locations on this page?
I would say about 1% error because that is the average amount of percent error for most distortions. Most people can read the centimeter ticks within at least .1 higher or .1 lower of the reading.
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