Solution:

$m = 250 \ kg$

$h = 60 \ cm = 0.6 \ m$

$d = 60 \ cm = 0.6 \ m$

$I_w = 1 \ kg – m^2$

$W_E = 6 \ W_w$

$G = \frac{W_E}{W_w} = 6$

$I_E = 0.175 \ kg-m^2$

$V = 80 \ km/hr = 22.22 \ m/s$

$R = 50 \ m$

other type : for $I_w = \frac{mr^2}{2}$

$w_w = \frac{v}{r} = \frac{22.22}{0.3} = 74.067$ rad/sec

$W_w = \frac{v}{R} = \frac{22.22}{50} = 0.444$ rad/sec

$\therefore$ $C = 74.06 \times \ 0.44 \ \times \ cos \ \theta \ [ 2 \times 1 + 0.175 \times 6]$

$C = 99.3885 \ cos \ \theta$

$\sum \ M_o = 0 \curvearrowright +$

$M_g \ (h \ sin \ \theta) - F_c \ (h \ cos \ \theta) - c = 0$

$Fc = \frac{mv^2}{R} = \frac{250 \times 22.22^2}{50} = 2468.642 \ N$

$\therefore$ $250 \ \times \ 9.81 \ (6.6 \ sin \ \theta) \ – \ 2468.64 \ (0.6 \ cos \ \theta) – 99.3885 \ cos \ \theta = 0$

$1471.5 \ sin \ \theta \ – 1481.184 \ cos \ \theta \ – 99.3885 \ cos \ \theta \ = \ 0$

$\therefore$ $\theta \ = \ 47.04°$ . . . .(Angle of heel)

$\therefore C = 99.385 \ cos (47.04) = 67.73 N-m$