Only Solve the second problem. The first problem is only provided for the data.

During a tensile test in which the starting gage length $=100\mathrm{.}0$ mm and the cross$-$sectional

area $=150$ mm$2.$ During testing, the following force and gage length data are collected: $(1)17,790$ N

at $100\mathrm{.}2$ mm$,(2)23,040$ N at $103\mathrm{.}5$ mm$,(3)27,370$ N at $110\mathrm{.}5$ mm$,(4)30,910$ N at $122\mathrm{.}0$ mm$,(5)$

$27,400$ N at $130\mathrm{.}0$ mm$,$ and $(6)20,460$ N at $135\mathrm{.}1$ mm$.$ The final data point $(6)$ occurred immediately

prior to failure. Yielding occurred at a load of $19,390$ N $(0\mathrm{.}2\%$ offset value$),$ and the maximum load

occurred at point $4.($a$)$ Plot the engineering and true stress$-$strain on the same plot based on the

provided test data $(10$ pts$).$ Determine $($b$)$ yield strength, $($c$)$ modulus of elasticity, $($d$)$ tensile

strength, and $($e$)$ percent elongation $(7$ pts per section$).$

$3\mathrm{.}4(24$ pts$)$ Determine the strength coefficient $($K$)$ and the strain$-$hardening exponent $($n$)$ in the flow

curve equation $($ $=$ Kn$)$ by two methods: $($a$)$ fitting a power$-$law model to the data provided in the

previous problem $(10$ pts$),$ and $($b$)$ selecting two points from the provided data and solving the system

of coupled algebraic equations $($Equation $1$: $1=$ K$1$n and Equation $2$: $2=$ K$2$n where $($i$,$ i$)$ are

points provided in the previous problem$)$ for the $2$ unknowns K and n$.($c$)$ Why are the answers

different and what answer is more accurate?