- 2074 Chaitra · 4 marks
Find forces P and Q for equilibrium
Short answer
From ΣFy=0: P sin60° = 25 kN, so P = 28.87 kN. From ΣFx=0: Q = 30 + P cos60° = 44.43 kN.
Determine the values of the unknown forces P and Q for the system of forces to be in equilibrium. [Figure: concurrent forces: 30 kN acting to the left, Q acting to the right, 25 kN acting downward, and P acting up-left at 60° as marked.]
Reading of the figure: four concurrent forces: 30 kN to the left, Q to the right, 25 kN downward, and P acting up and to the left at 60° to the horizontal (the 60° is marked between P and the horizontal axis).
Equilibrium equations
ΣFy = 0 (up positive): P sin 60° − 25 = 0 P = 25 / 0.8660 = 28.87 kN
ΣFx = 0 (right positive): Q − 30 − P cos 60° = 0 Q = 30 + 28.87 × 0.5 = 30 + 14.43 = 44.43 kN
Answer: P = 28.87 kN, Q = 44.43 kN.
✓ Answer checked by Claude Opus 5.5 (high effort)
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