Tape correction for pull — a 30 m standard steel tape (cross-section 15 mm × 1.0 mm) was standardized at 25°C under 30 kg pull. The base line was measured at the same temperature but with a 40 kg pull. Given E = 2.2 × 10^6 kg/cm^2, compute the pull (tension) correction to apply to the measured length.

Introduction / Context:A steel tape elongates when subjected to higher pull than its standardization tension. If not corrected, the measured distance will be underestimated, because each laid tape length is slightly longer than nominal. The pull correction quantifies this elastic extension using Hooke’s law.

Given Data / Assumptions:

• Tape length, L = 30 m = 3000 cm.
• Cross-section area, A = 15 mm^2 = 0.15 cm^2.
• Standard pull, P0 = 30 kg; field pull, P = 40 kg → ΔP = P − P0 = 10 kg.
• Modulus of elasticity, E = 2.2 × 10^6 kg/cm^2.
• Temperature is unchanged (no thermal correction).

Concept / Approach:Elastic extension ΔL under axial force follows ΔL = (ΔP * L) / (A * E), in consistent units. A positive ΔP means the tape is longer than standard, so the correction to the measured length is additive by +ΔL per tape length used.

Step-by-Step Solution:

Verification / Alternative check:Sensitivity: If the pull were less than standard, the correction would be negative (tape shorter). Magnitude scales linearly with ΔP and L, and inversely with A and E.

Why Other Options Are Wrong:

• + 0.0909 m: Off by a factor of 100 (centimetre vs metre conversion error).
• - 0.000909 m: Wrong sign; higher pull increases tape length.
• None of these: Incorrect, as + 0.000909 m is correct.

Common Pitfalls:Unit mistakes between mm^2 and cm^2, and forgetting that correction is added when the tape is longer than standard.

Final Answer:+ 0.000909 m