Answer
$k=91N/m$
Work Step by Step
According to the conservation of energy, all energy must be conserved. In this case, kinetic energy is converted to elastic potential energy. This means that $$\frac{1}{2}k\Delta x^2=\frac{1}{2}mv^2$$ Solving for force constant $k$ yields $$k=\frac{mv^2}{\Delta x^2}$$ Substituting known values of $m=1.8kg$, $v=2.2m/s$, and $\Delta x=0.31m$ yields a force constant of $$k=\frac{(1.8kg)(2.2m/s)^2}{(0.31m)^2}=91N/m$$
