Answer
(a) $200\frac{N}{m}$
(b) $0.92cm$
Work Step by Step
(a) We can find the required force constant as
$U=\frac{1}{2}Kx^2$
This can be rearranged as:
$K=\frac{2U}{x^2}$
We plug in the known values to obtain:
$K=\frac{2(0.0025)}{0.0050}$
$K=200\frac{N}{m}$
(b) We can find the required compression as follows:
$U=\frac{1}{2}Kx^2$
This simplifies to:
$x=\sqrt{\frac{2U}{K}}$
We plug in the known values to obtain:
$x=\sqrt{\frac{2(0.0048)}{200}}=0.92cm$
