Question #231191

A line is recorded as 472.90 m. long. It is measured with a 0.65 kg. tape which is 30.005 m. long at 20

Expert's answer

*Here is your complete and exact question: *

*A line is recorded as 472.90 m long. It is measured with a 0.65 kg tape which is 30.005m long at 20°C under a 50 N pull supported at both ends. During measurement the temperature is 5°C and the tape is suspended under a 75 N pull. The line is measured of 3% grade. What is the true horizontal distance? E = 200 GPa, cross-sectional are of tape is 3 mm² and coefficient of linear expansion is 0.0000116 m/°C.*

given data

Length of measurement (L) = 472.90 m

Designated length of tape (l) = 30.005 m

Weight of tape (W) = 0.65 kg

Temperature at the time of Standardization (T_{o})= 20°C

Pull at the time of Standardization (P_{o}) = 50 N

Temperature at the time of measurement (T_{M})= 5°C

Pull at the time of measurement (P_{m})=75N

Gradient at which line is measured = 3%

Coefficient of linear expansion () 0.0000116 m/°C

Cross sectional area of tape (A) = 3 mm2

E = 200 GPa

To determine:

True horizontal distance of line.

To find the True horizontal distance of line, corrections are needed to be applied as follows:

1. Correction due to standardization (or correction due to absolute length)

**(b)Total error to be corrected for inclined distance:**

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