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The elastic cords used for bungee jumping are designed to endure large strains. Consider a bungee cord that stretches to a maximum length 3.85 times the original length. There are different ways to report this extensional deformation. Calculate how 'wrong' the engineering strain is compared to the true strain by evaluating the ratio:

εtrue / εengr = __________

Respuesta :

Answer:

(εtrue/εengr) = (1.3481/2.85) = 0.473

This shows that the engineering strain is truly a bit far off the true strain.

Explanation:

εengr

Engineering strain is a measure of how much a material deforms under a particular load. It is the amount of deformation in the direction of the applied force divided by the initial length of the material.

ε(engineering) = ΔL/L₀

Lf = final length = 3.85 L₀

L₀ = original length = L₀

ΔL = Lf - L₀ = 3.85 L₀ - L₀ = 2.85 L₀

ε(engineering) = ΔL/L₀ = (2.85L₀)/L₀ = 2.85

εtrue

True Strain measures instantaneous deformation. It is obtained mathematically by integrating strain over small time periods and Running them up. Hence,

ε(true) = In (Lf/L₀)

Lf = 3.85L₀

L₀ = L₀

ε(true) = In (Lf/L₀) = In (3.85L₀/L₀) = In 3.85 = 1.3481

(εtrue/εengr) = (1.3481/2.85) = 0.473

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