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Homework_02_1013

# Homework_02_1013 - b A new measuring device whose...

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Homework #2 (due on Oct. 13) 1. The Kilogram is now weighed five times on a different scale. The measurements are as follows, in unit of micrograms above 1 kg: 25.6, 26.8, 26.2, 26.8, 25.4. a. Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not. b. Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not. 2. Assume that X and Y are independent measurements with uncertainties σ X = 0.2 and σ Y = 0.4. Find the uncertainties in the following quantities. a. 3 X b. X Y c. 2 X + 3 Y

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3. The length of a component is to be estimated through repeated measurement. a. Ten independent measurements are made with an instrument whose uncertainty is 0.05 m. Let denote the average of these measurements. Find the uncertainty in
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Unformatted text preview: . b. A new measuring device, whose uncertainty is only 0.02 m, becomes available. Five independent measurements are made with this device. Let denote the average of these measurements. Find the uncertainty in . c. In order to decrease the uncertainty still further, it is decided to combine the estimates and . One engineer suggests estimating the length with (1/2) + (1/2) . A second engineer argues that since . is based on 10 measurements, while is based on only five, a better estimate is (10/15) + (5/15) . Find the uncertainty in each of these estimates. Which is smaller? d. Find the value c such that the weighted average c +(1-c ) has minimum uncertainty. Find the uncertainty in this weighted average. X X Y Y Y Y Y Y Y X X X X X...
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