Problem 527 and Problem 528 | Friction

$\Sigma F_H = 0$

$N_A \cos 15^\circ = N_B \cos 75^\circ$

$N_A = 0.2679N_B$
 

$\Sigma F_V = 0$

$N_A \sin 15^\circ + N_B \sin 75^\circ = 30$

$(0.2679N_B) \sin 15^\circ + N_B \sin 75^\circ = 30$

$1.0353N_B = 30$

$N_B = 28.98 \, \text{ kN}$
 

$N_A = 0.2679(28.98)$

$N_A = 7.76 \, \text{ kN}$
 

$\mu = \tan 15^\circ = 0.2679$
 

$f_A = \mu N_A = 0.2679(7.76)$

$f_A = 2.08 \, \text{ kN}$
 

$f_B = \mu N_B = 0.2679(28.98)$

$f_B = 7.76 \, \text{ kN}$
 

Required couple
$C = \Sigma M_{center}$

$C = 1.5(f_A + f_B) = 1.5(2.08 + 7.76)$

$C = 14.76 \, \text{ kN}\cdot\text{m}$           answer

 

 

$1.5F = 1.5f_A + 1.5f_B$

$F = f_A + f_B$

$F = 2.08 + 7.76$

$F = 9.84 \, \text{ kN}$           answer