$7-66.$ The boom is supported by the winch cable that has a diameter of $0\mathrm{.}25$ in $.$ and an allowable normal stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=24$ksi. Determine the greatest weight of the crate that can be supported without causing the cable to fail if $=30.$ Neglect the size of the winch.

$7-67.$ The boom is supported by the winch cable that has an allowable normal stress of ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=24$ksi. If it supports the $5000$ lb crate when $=20,$ determine the smallest diameter of the cable to the nearest $\frac{1}{16}$ in$.$