- 2069 Chaitra · 4 marks
Find F1 and F2 for equilibrium
Short answer
From ΣFy=0: F1 sin40° = 75 kN ⇒ F1 = 116.68 kN. From ΣFx=0: F2 + F1 cos40° − 20 = 0 ⇒ F2 = −69.38 kN, meaning F2 acts to the left.
Determine the value of F1 and F2 if the forces shown in figure below are in equilibrium. [Figure: concurrent forces at O: 20 kN to the left, F2 to the right, 75 kN downward, F1 upward at 40° to the horizontal.]
Reading of the figure: concurrent forces at O: 20 kN to the left, 75 kN downward, F₂ along the x axis (drawn to the right), and F₁ pointing up and to the right at 40° to the horizontal.
For equilibrium ΣFx = 0 and ΣFy = 0.
ΣFy = 0
F₁ sin 40° − 75 = 0 F₁ = 75 / 0.6428 = 116.68 kN
ΣFx = 0 (right positive)
F₂ + F₁ cos 40° − 20 = 0 F₂ = 20 − 116.68 × 0.7660 = 20 − 89.38 = −69.38 kN
The negative sign means F₂ really acts to the left, opposite to the direction drawn in the figure.
Answer: F₁ = 116.68 kN (up-right at 40°), F₂ = 69.38 kN directed to the left.
✓ Answer checked by Claude Opus 5.5 (high effort)
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