A motor is connected to a pump with $1\mathrm{.}5$ in Pump

diameter shaft spining at $500$ rpm$.$ If the shaft coupling uses a $1"$ long x $0\mathrm{.}375"$ square key, what is the maximum size motor that can be used for a FoS of $2.$ Motors are only available in $1$ hp increments.

The key is made from $1020$ cold rolled steel and the shaft is made from $4130$ steel quench and tempered at $1200$ deg F$.($Used book values for material properties$)$

If applicable, use von Mises equivalent stresses.

Will the key shear or yield first? $($shear$,$ yield, same time, or cannot be determined$)$

What magnitude of force will cause the key to fail in shear?

What magnitude of force will cause the key to yield $($bearing failure$)?$

What magnitude of torque will cause key failure?

What horsepower motor should be used?

What is the yielding FoS for the shaft at the key seat using the selected motor?