Problem 541 | Friction on Wedges

From the FBD of the block to the right
$\Sigma F_V = 0$

$R_1 \cos 15^\circ = R_2 \sin 15^\circ + 200$

$R_1 = 0.2679R_2 + 207.06$
 

$\Sigma F_H = 0$

$R_2 \cos 15^\circ = R_1 \sin 15^\circ + 50$

$R_2 \cos 15^\circ = (0.2679R_2 + 207.06) \sin 15^\circ + 50$

$0.8966R_2 = 103.59$

$R_2 = 115.54 \, \text{ kN}$
 

 

From the FBD of the wedge to the left
$\Sigma F_H = 0$

$R_3 \cos 30^\circ = R_2 \cos 15^\circ$

$R_3 \cos 30^\circ = 115.54 \cos 15^\circ$

$R_3 = 128.87 \, \text{ kN}$
 

$\Sigma F_V = 0$

$P = R_2 \sin 15^\circ + R_3 \sin 30^\circ$

$P = 115.54 \sin 15^\circ + 128.87 \sin 30^\circ$

$P = 94.34 \, \text{ kN}$           answer