$8\mathrm{.}18$ Obtain a large common nail $($flat head$).$ Measure the head diameter and thickness, as well as the diameter of the nail shank. $($a$)$ What stock length must project out of the die in order to provide sufficient material to produce the nail? $($b$)$ Using appropriate values for strength coefficient and strain hardening exponent for the metal out of which the nail is made $($Table $3\mathrm{.}4),$ compute the maximum force in the heading operation to form the head.