Two horizontal wires are joined end to end, each with a diameter of $2\mathrm{.}000$ mm$.$ The two joined wires are connected to fixed points a total distance of $4\mathrm{.}00000$ m apart. When both wires are at a temperature of $45\mathrm{.}0$C$,$ each wire has an unstretched length of $2\mathrm{.}00000$ m$,$ and the tension in each is negligible. The first wire is made of copper and extends from

x $=2\mathrm{.}00000$ m

to

x $=0,$

and the second is made of brass and extends from

x $=0$

to x $=2\mathrm{.}00000$ m$.$ The temperature of both wires is then lowered to $18\mathrm{.}0$C$,$ and the wires stay joined together as they cool.

The copper wire is composed of an alloy that has an average coefficient of linear expansion of

$1\mathrm{.}70105($C$)1$

and a Young's modulus of

$1\mathrm{.}101011$ N$/$m$2.$

The brass wire is composed of an alloy that has an average coefficient of linear expansion of

$1\mathrm{.}90105($C$)1$

and a Young's modulus of

$9\mathrm{.}101010$ N$/$m$2.$

$($Due to the nature of this problem, do not use rounded intermediate values$$including answers submitted in WebAssign$$in your calculations.$)$

$($a$)$

At the final, lower temperature, what is the x$-$coordinate $($in m$)$ of the junction between the wires?

m

$($b$)$

At the final, lower temperature, what is the tension $($in N$)$ in the wire?

N