# 232 Moment of a force about points O and B

**Problem 232**

In Fig. P-231, the moment of a certain force F is 180 ft·lb clockwise about O and 90 ft·lb counterclockwise about B. If its moment about A is zero, determine the force.

**Solution 232**

Moment about O

$M_O = 180$

$M_O = 180$

$xF_y = 180$

Moment about B

$M_B = 90$

$(6 - x)F_y = 90$

$6F_y - xF_y = 90$

Substitute xF_{y} = 180 to the above equation

$6F_y - 180 = 90$

$6F_y = 270$

$F_y = 45 \, \text{ lb}$

$xF_y = 180$

$x(45) = 180$

$x = 4 \, \text{ ft}$

$\tan \theta_x = \dfrac{3}{x}$

$\tan \theta_x = \dfrac{3}{4}$

$\theta_x = 36.87^\circ$

$\sin \theta_x = \dfrac{F_y}{F}$

$F = \dfrac{F_y}{\sin \theta_x} = \dfrac{45}{\sin 36.87^\circ}$

$F = 75 \text{ lb}$

Thus, F = 75 lb downward to the right at θ_{x} = 36.87° and x-intercept at (4, 0). *answer*

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