Final answer:
The true stress required to elongate the metal specimen from 48.0 mm to 57.4 mm is calculated using the strain-hardening equation with the given exponent and stress values, considering the changes in strain for each elongation.
Step-by-step explanation:
To find the true stress necessary to plastically elongate the specimen from a length of 48.0 mm to 57.4 mm, we need to use the strain-hardening equation which is given by:
\(\sigma = K \cdot \epsilon^n\)
where \(\sigma\) is the true stress, \(K\) is the strength coefficient, \(\epsilon\) is the true strain, and \(n\) is the strain-hardening exponent (which is given as 0.2).
First, we calculate the true strain for the given elongation from 48.0 mm to 53.5 mm using the formula:
\(\epsilon = \ln(\frac{L_f}{L_0})\)
We then can determine the strength coefficient \(K\) from the initial true stress of 368 MPa. With the known values, we rearrange the formula to solve for \(K\):
\(K = \frac{\sigma}{\epsilon^n}\)
After calculating \(K\), we then find the true strain for the elongation from 48.0 mm to 57.4 mm and finally calculate the new true stress using the same strain-hardening equation for this new strain.
This problem involves the concepts of material science and mechanical engineering, predominantly pertaining to the material behavior under tensile testing, which aligns with advanced engineering studies at the college level.