$1)$ A $3-$hp DC motor has the following nameplate information: $150$ V$,1400$rpm$,18$ A$,,$ and $.$ The field is shunt connected, and the $18$ A includes the field current. Assume rotational losses are constant. $[40$ pts$]$

a$.$ Find the efficiency of the motor at nameplate operation $($include the field in your calculations$).$

b$.$ Find the rotational losses at nameplate operation.

c$.$ Find the required current for a developed power of $1\mathrm{.}5$ hp with $.$

d$.$ Find the output power if the developed power is $1\mathrm{.}5$ hp with $.$

e$.$ Find the shaft speed if the developed power is $1\mathrm{.}5$ hp with $.$

f$.$ A deranged Mouse chews through part of the field winding so that the field current drops and the field flux drops to $40\%$ of its former value, find the shaft speed if the developed power is still $1\mathrm{.}5$ hp with $.$

g$.$ Find the load torque if the developed power is still $1\mathrm{.}5$ hp with $.$