Answer
(a) $1.2cm$
(b) $2.3cm$
Work Step by Step
(a) We know that
$K=-\frac{F}{x}$
$\implies K=-\frac{4.1}{0.014}=290\frac{N}{m}$
We can find the required stretch of the spring as
$U=\frac{1}{2}Kx^2$
This simplifies to:
$x=\sqrt{\frac{2U}{K}}$
We plug in the known values to obtain:
$x=\sqrt{\frac{2(0.020)}{290}}$
$x=1.2cm$
(b) We can find the required stretch as follows:
$x=\sqrt{\frac{2U}{K}}$
We plug in the known values to obtain:
$x=\sqrt{\frac{2(0.080)}{290}}$
$x=2.3cm$
