A solid circular has a notch turned into it as shown below. The nominal outside

diameter is $2\mathrm{.}25"$ and the notch diameter needs to be $\mathrm{.}25"$ less than the nominal to

accommodate a mechanical element. The radius of the notch needs to be $0\mathrm{.}25".$

The shaft experiences a tension load of $100,000$ lb and torsional load of $10,000$ ft$-$lb$.$

The shaft is made of steel with a yield strength of $150,000$ psi. The shaft design

needs a safety factor of at least $2.$ Will the current shaft meet the design criteria? If

not, propose a new nominal shaft diameter that meets the design requirements but

is not excessively large. $(20$ points$)$