Question

A 14.0-cm-long polymer sample is stretched with a constant tensile load of 15.0 kPa, it stretches to a total length of 30 cm in 200 s. After removing the load, the sample recovers only to 24 cm. (a) Assuming that the mechanical behavior of the polymer can be treated as a Maxwell element, estimate the time it would take for an identical (untested) sample to relax to 0.6 its original stress when a constant elongation of 71.4% is applied. (b) If the sample in (a) is stretched at a constant rate of 0.2 mm/s, what will be the stress at (a) 1.5 min and (b) 4 min?

          A 14.0-cm-long polymer sample is stretched with a constant tensile load of 15.0 kPa, it stretches to a total length of 30 cm in 200 s. After removing the load, the sample recovers only to 24 cm.
(a) Assuming that the mechanical behavior of the polymer can be treated as a Maxwell element, estimate the time it would take for an identical (untested) sample to relax to 0.6 its original stress when a constant elongation of 71.4% is applied.
(b) If the sample in (a) is stretched at a constant rate of 0.2 mm/s, what will be the stress at (a) 1.5 min and (b) 4 min?

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A 14.0-cm-long polymer sample is stretched with a constant tensile load of 15.0 kPa, it stretches to a total length of 30 cm in 200 s. After removing the load, the sample recovers only to 24 cm.
(a) Assuming that the mechanical behavior of the polymer can be treated as a Maxwell element, estimate the time it would take for an identical (untested) sample to relax to 0.6 its original stress when a constant elongation of 71.4% is applied.
(b) If the sample in (a) is stretched at a constant rate of 0.2 mm/s, what will be the stress at (a) 1.5 min and (b) 4 min?

Added by Dana N.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

06/16/2023

Step 1

We can use the data given in the problem to find σ_0 and τ: σ_0 = F/A = 15.0 kPa A = (14.0/100)^2 * π/4 = 1.54E-3 m^2 F = σ_0 * A = 23.1 N ε = (L - L_0)/L_0 = (30 - 14)/14 = 1.14 t = 200 s Using these values, we can solve for τ: τ = t / ln(1/(1-ε)) = 200 / Show more…

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