A square plastic bar $($length Lp $,$ side dimension $sp=193mm)$ is inserted inside a

hollow, square, cast iron tube $($length $Lc=400mm,$ side $sc=200mm,$ and thickness

$tc=3mm$

a$)$ What is the required initial length Lp of the plastic bar so that, when it is

compressed by some force $P,$ the final length of bar and tube are equal to length Lc

and, at the same time, the gap between plastic bar and cast iron tube is closed?

b$)$ Compare initial and final volumes for plastic bar.

Assume that $Ec=170$GPa,$Ep=2\mathrm{.}1$GPa,$vc=0\mathrm{.}3,$ and $vp=0\mathrm{.}4$