Question #232885

A 50 m steel tape is of standard length under a pull of 5.5 kg when supported throughout its entire length. the tape weighs 0.05 kg/m, has a cross sectional area of 0.04 sq.cm and being made steel, it's modulus of elasticity is 2.10x10^6 kg/cm2. this tape was used in the field to measure a distance that was determined to be 458.650 m. at the time the measurement was made, the constant pull applied was 8 kg with the tape supported only at its end points. determine the correct length of the line.

Expert's answer

l = Length of tape = 50 m

L = Length of measurement = 458.650 m

P_{m} = Pull at the time of measurement = 8 kg

P_{o} = Pull at the time of s tan dardization = 5. 5 kg

w = Weight of tape = 0.05 kglm

A = Cross — sectional area of tape = 0.04 cm^{2}

E = Modulus of Elasticity = 2. 1 x 106 Kg/cm^{2 }

**To find **

**Correction measure line;**

C_{p} = Correction measure line due to tension

C_{p=}(P_{m}—P_{o})L/AE

C_{p} = AE (8 — 5.5)x458.650/0.04x2.10x10^{6}

*C*_{p}* = 0.014 m (+ve)*

Length of one tape is 50 m, so for measurement of 458. 650 in distance,

9 tapes + 8. 650 m = 9 x 50 + 8.650 = 458. 650 m

l_{r}= Remaining length = 8. 650 m

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