Answer
(a) 0.051 m
(b) 4.7 J
Work Step by Step
(a) We can apply the equation $F=kx$ into the spring to find the displacement of the spring.
$F=kx-(1)$
Also we can write,
$F=pressure\times area=PA-(2)$
(2)=>(1),
$PA=kx=>x=\frac{PA}{k}$ ; Let's plug known values into this equation.
$x=\frac{(1.013\times10^{5}N/m^{2})\pi(0.024\space m)^{2}}{3600\space N/m}\approx0.051\space m$
(b) Let's apply the equation $W=\frac{1}{2}kx^{2}$ to find the work done by the atmospheric pressure.
$W=\frac{1}{2}kx^{2}$ ; Let's plug known values into this equation.
$W=\frac{1}{2}(3600\space N/m)(0.051\space m)^{2}\approx4.7\space J$
