Final answer:
To calculate the corrected length of the horizontal length, we need to consider the effect of temperature and pull on the steel tape. The temperature correction is -0.0276m due to a temperature change of -8°C, and the pull correction is 0.06m due to a pull of 100N. Subtracting these corrections from the measured length of 29.859m gives a corrected length of the horizontal length of 29.8464m.
Step-by-step explanation:
To calculate the corrected length of the horizontal length, we need to consider the effect of temperature and pull on the steel tape. Firstly, let's calculate the correction due to temperature. The change in length of the tape due to temperature is given by the formula ΔL = LαΔT, where L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature. In this case, L = 30m, α = 1.15 * 10^(-5)/°C, ΔT = 12°C - 20°C = -8°C. Substituting these values into the formula, we get ΔL = 30m * (1.15 * 10^(-5)/°C) * (-8°C) = -0.0276m. Therefore, the temperature correction is -0.0276m.
Next, let's calculate the correction due to pull. The change in length of the tape due to pull is given by the formula ΔL = (P / Ae) * L, where P is the pull applied, A is the cross-sectional area of the tape, e is the modulus of elasticity, and L is the original length. In this case, P = 100N, A = 2.5mm² = 2.5 * 10^(-6)m², e = 2.0 * 10^5N/mm² = 2.0 * 10^11N/m², and L = 30m. Substituting these values into the formula, we get ΔL = (100N / (2.5 * 10^(-6)m² * 2.0 * 10^11N/m²)) * 30m = 0.06m. Therefore, the pull correction is 0.06m.
The corrected length of the horizontal length is obtained by subtracting the temperature correction and the pull correction from the measured length. In this case, the measured length is 29.859m, the temperature correction is -0.0276m, and the pull correction is 0.06m. Substituting these values into the formula, we get the corrected length of the horizontal length as 29.859m - (-0.0276m) - 0.06m = 29.8464m.