$[45\%]$ Two steel stay cables $(E=207$GPa,${}_y=180$MPa $),$ each with a $10$ mm diameter will be used to locate and secure a sailboat mast. Each cable will be tensioned with a $5,000$ N tensile load.

$($a$)$ If each cable is $6$ m long how much will each stretch when under tension? Ignore cable weight.

$($b$)$ Determine if the cable will plastically deform when under tension.

$($c$)$ If a cable plastically deforms, it will loose its tension and weaken the mast. Calculate the maximum load that the cable can accept before plastically deforming.