For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to σ

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For some viscoelastic polymers that are subjected to stress
relaxation tests, the stress decays with time according to
σ(t)=σ(0)exp(−t/τ)
where σ(t) and σ(0)
represents the time-dependent and initial (i.e., time =0) stresses,
respectively,
and t and τ denote elapsed
time and the relaxation time; τ is a
time-independent constant characteristic of the material. A
specimen of some viscoelastic polymer with the stress relaxation
that obeys Equation 15.10, was suddenly pulled in a tension to
a measured strain of 0.7; the stress necessary to maintain
this constant strain was measured as a function of time.
Determine Er(8) for this material if the
initial stress level was 2.53 MPa (367 psi), which
dropped to 1.76 MPa (255 psi)
after 50 s.
A. Solving for stress according to Equation
15.10 first requires
determining t and σ. From the data
provided in the problem, calculate τ, in seconds.
B.Determine σ(8) (the stress level
at 8 seconds) in MPa.
C. What is Er(8) in MPa (the value
of E at 8 seconds)?