Answer
a) $200$ \lb/in b) $400 lb- in. \approx 33.3 ft -lb$ c) 8 in.
Work Step by Step
a. Hooke's Law states that $F=k x$
and $k=\dfrac{F}{x}=\dfrac{800}{4}= 200$ \lb/in
b. Need to integrate $k =200$ with limit $0$ to $2$
Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$
Thus, $\int_0^2 kx dx= 200[ \dfrac{x^2}{2}]_0^2$
so, $100(4-0)=400 lb- in. \approx 33.3 ft -lb$
c. Hooke's Law states that $F=k x$
Given: $ F= 1600 N$
Then, $1600=(200) (x)$
and $x=\dfrac{1600}{200}=8$ inch
