# 243 Finding the magnitude and position of the missing force

**Problem 243**

The resultant of three parallel loads (one is missing in Fig. P-243) is 13.6 kg acting up at 3 m to the right of A. Compute the magnitude and position of the missing load.

**Solution 243**

Sum of vertical forces

$R = \Sigma F_v$

$R = \Sigma F_v$

$13.6 = 18 - F + 27$

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

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