The speed-torque characteristic of an induction motor has been empirically determined as follows:
$$
\begin{array}{l|lllll}
\text { Speed (r/min) } & 1,470 & 1,440 & 1,410 & 1,300 & 1,100 \\
\hline \text { Torque (N-m) } & 3 & 6 & 9 & 13 & 15 \\
\text { Speed (r/min) } & 900 & 750 & 350 & 0 & \\
\hline \text { Torque (N-m) } & 13 & 11 & 7 & 5 &
\end{array}
$$
The motor will drive a load requiring a starting torque of $4 \mathrm{~N}-\mathrm{m}$ and increase linearly with speed to $8 \mathrm{~N}-\mathrm{m}$ at $1,500 \mathrm{r} / \mathrm{min}$.
a. Find the steady-state operating point of the motor.
b. Equation 15.68 predicts that the motor speed can be regulated in the face of changes in load torque by adjusting the stator voltage. Find the change in voltage required to maintain the speed at the operating point of part a if the load torque increases to $10 \mathrm{~N}-\mathrm{m}$.