Question

A steel tape of nominal length 30m was suspended between supports to measure the length of a line. The measured length of the line along a slope of angle 3◦50’ is 29.859m. The mean temperature during the measurement was 12 ◦C and the pull applied was 100 N. If standard length of the tape is 30.005m at 20 ◦C, and the standard pull is 45.0 N, calculate the corrected length of Horizontal length. Take the weight of the tape ω=0.15N/m , its crosssectional area A=2.5mm2, α=1.15*10-5/◦ C and E= 2.0*105 N/mm².

What is the tension in the tape during the measurement?

a. 45.0 N
b. 55.0 N
c. 100 N
d. 75.0 N

Answer 1

To calculate the corrected length of the horizontal length, we need to consider the effects of temperature and tension. The corrected length is obtained by subtracting the change in length due to temperature and tension from the measured length. The tension in the tape during the measurement is 100N.

Step-by-step explanation:

To calculate the corrected length of the horizontal length, we need to consider the effects of temperature and tension. First, let's calculate the change in length due to temperature. The formula to calculate the change in length due to temperature change is:

ΔL = L0 × α × ΔT

Where ΔL is the change in length, L0 is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature. In this case, the original length is 30.005m, the coefficient of linear expansion is 1.15x10-5/°C, and the change in temperature is 12°C. Plugging in these values, we get:

ΔL = 30.005 × 1.15x10-5/°C × 12°C = 0.00474m

Next, let's calculate the change in length due to tension. The formula to calculate the change in length due to tension is:

ΔL = F × L0 / (A × E)

Where ΔL is the change in length, F is the tension, L0 is the original length, A is the cross-sectional area, and E is the elastic modulus. In this case, the tension is 100N, the original length is 30.005m, the cross-sectional area is 2.5mm2, and the elastic modulus is 2.0x105 N/mm2. Plugging in these values, we get:

ΔL = 100N × 30.005m / (2.5mm2 × 2.0x105 N/mm2) = 0.0030003m

To obtain the corrected length of the horizontal length, we subtract the sum of the change in length due to temperature and the change in length due to tension from the measured length:

Corrected Length = Measured Length - (ΔLtemperature + ΔLtension) = 29.859m - (0.00474m + 0.0030003m) = 29.8512597m

Therefore, the corrected length of the horizontal length is approximately 29.8513m.

The tension in the tape during the measurement is 100N.