# 242 Finding the unknown two forces with given resultant

**Problem 242**

Find the value of P and F so that the four forces shown in Fig. P-242 produce an upward resultant of 300 lb acting at 4 ft from the left end of the bar.

**Solution 242**

Sum of vertical forces

$R = \Sigma F_v$

$R = \Sigma F_v$

$300 = -100 + P - F + 200$

$P = 200 + F$

Moment about point A

$Rd = \Sigma Fx$

$300(4) = -100(0) + P(2) - F(5) + 200(7)$

$1200 = 2P - 5F + 1400$

$2P - 5F + 200 = 0$

$2(200 + F) - 5F + 200 = 0$

$400 + 2F - 5F + 200 = 0$

$600 = 3F$

$F = 200 \, \text{ lb}$ *answer*

$P = 200 + 200$

$P = 400 \, \text{ lb}$ *answer*