243 Finding the magnitude and position of the missing force

Sum of vertical forces
$R = \Sigma F_v$

$13.6 = 18 - F + 27$

$F = 31.4 \, \text{ kg}$       downward
 

 

Moment about point A
$Rd = \Sigma Fx$

$13.6(3) = 18(0.6) - 31.4x + 27(4)$

$x = 2.48 \, \text{ m}$
 

Thus, F = 31.4 kg downward at 2.48 m to the right of left support.       answer