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Find forces P and Q such that resultant of given system is zero.
written 8.4 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 4.5 years ago

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engineering mechanics
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written 8.4 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 8.4 years ago

$$R_x= Σ F_x ( → +ve ) $$ $$ =40 \cos 60+Q \cos 20-30$$

Since, resultant of given system is zero

$∴R_x=0 \\ ∴Q \cos 20=30-40 \cos 60=30-20=10 \\ ∴Q=\dfrac {10}{\cos 20}=10.642N \\ R_y= Σ F_y ( ↑ +ve ) \\ =50+40 \sin 60-P-Q \sin ⁡20 \\ ∴ R_y=0 \\ ∴0=50+40 \sin 60-P-10.642 \sin 20 \\ ∴P=81N$

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