Chapter 17, Problem 5P

In solving problems and examining examples, you probably have noticed some recurring forms:

w = 12γbt = (12γt)b = a₁b

(F₁)_a = F_abC_pC_v = (F_aC_pC_v)b = a₀b

$F_c=\frac{w{V}^2}{g}=\frac{a_{1}b}{32.174}{\left(\frac{V}{60}\right)}^2=a_{2}b$

(F₁)_a – F₂ = 2T/d = 33 000H_d/V = 33 000 H_nomK_sn_d/V

F₂ = (F₁)_a –[(F₁)_a – F₂] = a₀b – 2T/d

$f\varphi =\text{ ln}\frac{{(F_1)}_a-F_c}{F_2-F_c}=\ln \frac{\left(a_0-a_2\right)b}{\left(a_0-a_2\right)b-2T/d}$

Show that

$b=\frac{1}{a_0-a_2}\frac{33000H_d}{V}\frac{\exp \left(f\varphi \right)}{\exp \left(f\varphi \right)-1}$