Answer
(a) $1.8cm$
(b) $14\frac{N}{m}$
Work Step by Step
(b) We can find the force constant as follows:
$U=\frac{1}{2}Kx^2$
$\implies U=\frac{1}{2}K(-\frac{F}{K})^2$ because $x=-\frac{F}{K}$
$U=\frac{F^2}{2K}$
This can be rearranged as:
$K=\frac{F^2}{2U}$
We plug in the known values to obtain:
$K=\frac{(0.25)^2}{2(0.0022)}$
$K=14\frac{N}{m}$
(a) Now we can find the required distance as
$x=\frac{F}{K}$
We plug in the known values to obtain:
$x=\frac{0.25}{14}$
$x=0.018m=1.8cm$
