Consider the three forces acting at O and in equilibrium as shown in the figure....

Consider the three forces acting at O and in equilibrium as shown in the figure. Which of the following equations is/are CORRECT?

I. P\(_1\) cos \(\theta_1\) = p\(_1\) cos \(\theta_2\)

II. P\(_3\) = P\(_1\) cos \(\theta_4\) + P\(_2 cos_2\)

III. P\(_1 \sin \theta_1 = P_2 \sin \theta_2\)

resolving \(P_1\), \(P_2\) and \(P_3\) into x and y component

\(P_x\) = \(P_1 Cos\theta_1\)

\(P_y\) = \(P_1Sin\theta_1\)

\(P_x\) = \(P_2Cos\theta_2\)

\(P_y\) = \(-P_2Sin \theta_2\)

\(P_x\) = \(- P_3Cos \theta0\)

therefore

total \(P_x\) = \(P_1 Cos\theta_1\) + \(P_2Cos \theta_2\) + \(- P_3Cos \theta0\) = 0

total \(P_y\) = \(P_1Sin\theta_1\) + \(-P_2Sin \theta_2\) = 0

so that \(P_1Sin\theta_1\) = \(P_2Sin \theta_2\)

\( P_3Cos \theta0\) = \(P_1 Cos\theta_1\) + \(P_2Cos \theta_2\)

There is an explanation video available below.

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