# 251 Two forces producing a couple and a force

**Problem 251**

A vertical force P at A and another vertical force F at B in Fig. P-251 produce a resultant of 100 lb down at D and a counterclockwise couple C of 200 lb·ft. Find the magnitude and direction of forces P and F.

**Solution 251**

$M_B = 7R + C$

$3P = 7(100) + 200$

$P = 300 \, \text{ lb downward}$ *answer*

$\Sigma F_V = R$

$P - F = 100$

$300 - F = 100$

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