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course PHY 231
cm_f = centimeters fullcm_s = centimeters singly reduced
cm_d = centimeters doubly reduced
cm_t = centimeters triply reduced
h = hypotenuse
b = base
a = adjacent
Measurements for triangle:
Cm_f = 10.2 h, 8.3 b, 7 a
Cm_s = 17.2 h, 13.5 b, 11.5 a
Cm_d = 26.3 h, 20.6 b, 17.5 a
Cm_t = 40 h , 30 b, 25 a
The greatest percent error most likely is in the adjacent side therefore I will assume that the hypotenuse and the base are accurate in order to calculate the adjacent side and its error.
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Very good idea.
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Cm_f: (10.2)^2 - (8.3)^2 = a^2
104.04 - 68.89 = a^2
35.15 = a^2
a is approximately 6.cm_f has an inaccuracy of + - 1 cm.
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You've measured to the tenth of a centimeter, so it is appropriate to calculate a to the tenth of a centimeter.
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cm_s: 17.2^2 - 13.5^2 = a^2
295.84 - 182.25 = a^ 2
113.59 = a^2
a is approximately 10.5 cm. cm_s has an inaccuracy of +- 1 cm.
cm_d: 26.3^2 - 20.6^2 = a^2
691.7 - 424.4 = a^2
267.33 = a^2
a is approximately 16.3 cm. cm_d has an inaccuracy of +- .7 cm.
cm_t: 40^2 - 30^2 = a^2
1600- 900 = a^2
700 = a^2
a is approximately 26.4 cm. cm_t has an inaccuracy of +-1.4 cm.
I predicted that the accuracy would increase with each reduction. I could conclude this prediction as true if I was not limited by my eyesight or the distortion of the ruler. The accuracy did increase until the triple reduced ruler measurement where rounded recordings had to be made.
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This is frequently the case. In most investigations I've found that the doubly-reduced ruler gives the most consistent results.
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Self-critique (if necessary):
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Self-critique rating:
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If the legs are measured accurate to within 0.1 cm, then the results should be consistent to within +- 0.1 cm.
Obviously you know how to measure with and read a ruler, and you calculations are good. But the level of inconsistency revealed by your analysis is hard to explain.
Did you use the triangle provided in class?
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