$[5](20$ points$)$ The $40-$ft$-$long A$-36$ steel rails on a train track are laid with a small gap between them to allow for thermal expansion. The thermal expansion coefficient of A$-36$ steel is $6\mathrm{.}60\frac{{10}^{-6}}{}F$ and its modulus of elasticity is $29({10}^3)ksi.$

$(1)$ Determine the required gap $$ so that the rails just touch one another when the temperature is increased from $T_1=20F$ to $T_2=90F.$

$(2)$ After this gap as determined from Question $(1)$ is constructed in this project, what would be the axial force in the rails if the temperature rises to $T_3=110F($from $($:$T_1=20F\}.$ The cross$-$sectional area of each rail is $5i{n}^2.$