Moment Balance: see-saw

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Question 1

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15 ft long rigid beam $ABC$ pivots on a frictionless pin at $B$ . Segment $AB$ is 7 ft long.

Determine the magnitude of force $\mathbf{C}$ required for rotational equilibrium if the magnitude of force $\mathbf{A}$ is 400 lbs.

$C=$ Expected answer:

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Given:

$d_1 = \var{AB}, d_2 = L - d_1 = \var{L-AB},$

$A = \var{FA}, \theta = \var{if(theta < 90, theta, 180-theta)}°$

For rotational equilibrium:

$\sum M_B = 0$

$A \; d_1 = C \sin \theta \; d_2$

$C = \dfrac{A d_1}{d_2 \sin \theta} = \var{siground(FC,5)}$

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