PROBLEM $2$: Solve the Example $17\mathrm{.}3$ in Kim's textbook by hand. Show only the first iteration by hand.

EXAMPLE $17\mathrm{.}3$: A caliper disk brake is used to arrest a machine shaft over $20$ seconds,

resulting in $10$ Btu of kinetic energy loss. The ventilation of the brake provides a mean

air speed of $20f\frac{t}{s}.$ The equivalent rotary inertia of the brake is $200l{b}_m-in-s.$ The rotor

has a weight of $2l{b}_m$ and a specific heat capacity of $0\mathrm{.}108Bt\frac{u}{l{b}_m-F}.$ The surface area

of the brake is $50i{n}^2.$ Find $T_{\text{m}\text{a}\text{x}}$ for the operation.