Answer
a) $k=7238$ lb/in. b) $W=2714$ in/lb
Work Step by Step
a. Hooke's Law states that $F=k x$
or,$k=\dfrac{F}{x}=\dfrac{21714}{3}=7238$ lb/in.
$\implies F=7238 x$
b. i) Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
This implies that
$W=\int_0^{0.5} 7238 x dx=7238[ \dfrac{x^2}{2}]_0^{0.5}$
or, $3619[ (0.5)^2-0] =904.75 N-m$
ii) Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
This implies that
$W=\int_{0.5}^1 7238 x dx=7238[ \dfrac{x^2}{2}]_{0.5}^1$
so, $3619[1- (0.5)^2] =2714 in/lb$
