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Measurement Methods of Distances

Problem 1:

Four measurements of a distance were recorded as 352.45, 352.04, 351.89, and 353.12m., and given weights are 2, 5, 1, and 6, respectively. Determine the weighted mean.

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Problem 2:

A student recorded the following repeated paces of a given line: 456, 448, 462, 447, 452, and 455. If his pace factor is 0.628m/pace, what is the approximate length of the line in meters?

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$$Ave. Pace = \frac{456+448+462+447+452+455}{6}=453.33 \ paces$$
$$Length\ of\ line = 453.333(0.628)=284.69m$$

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Problem 3:

A line was determined to be 2395.25m when measured with a 30-m steel tape supported throughout its length under the pull of 4kg at a mean temperature of 35ºC. The tape used is of standard length at 20ºC under a pull of 5kg. The cross sectional area of the tape is 0.03 sq. cm. Coefficient of thermal expansion is 1.16x10-5/ºC. Modulus of elasticity of the tape is 2x106kg/cm2.
a. Determine the error due to change in temperature
b. Determine the error due to tension
c. Determine the corrected length of the line

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Problem 4:

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Problem 5:

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Problem 6:

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Problem 7:

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Problem 8:

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