A 100m tape is 12mm wide and 0.80mm thick. If the tape is correct under a pull of 54N. Compute the percentage error made by using a pull of 68N. E=200,000MPa

Answer 1

L= 100 m

Tape area = 12mm x 0.8 mm = 9.6 mm²

Tape is correct under 54 N , when tape is pulled to 68 N it elongates for the difference in force applied

force applied = 68 - 54 = 14 N

Stress in tape = σ = F / A = 14 N / 9.6 mm² = 1.46 N/ mm²

Strain in tape = ε = σ / E = 1.46 N / mm² / 200000 Mpa

ε = 1.46 N / mm² ( mm² / ( 10^-3)² m²) / 200000 x 10⁶ N / m²

= 1.46 x 10⁶ N/ m² / 200000 X 10⁶ N / m²

= 7.3 x 10^-6 mm / mm

The elongation due to the difference in forces:

ΔL = ε x L = 7.3 x 10^-6 x 100 m = 7.3 x 10^-4 m

Percent error = (7.3 x 10^-4 m / 100 m) x 100 %

= 7.3 x 10^-4 %