Question

The tensile load (F) in Newton (N) and the elongation (e) in cm of a yarn are related as follows \[ F = 2e^2 + e \] If the breaking elongation of the yarn is 10 cm, then the work of rupture (N·m) of yarn (rounded off to 2 decimal places) is ________________.

Hint:

Work of rupture is the product of the tensile load at the breaking elongation and the elongation itself.

Answer 1

Correct Answer: 7.1

The work of rupture is given by the tensile load at the breaking elongation. Substitute the given elongation \( e = 10 \) cm into the equation for \( F \): \[ F = 2(10)^2 + 10 = 2(100) + 10 = 200 + 10 = 210 \text{ N} \] Thus, the work of rupture is: \[ \text{Work of rupture} = F \times e = 210 \times 10 = 2100 \text{ N·cm} = 21 \text{ N·m} \] Final Answer: 21.00 N·m