A box of weight 100 kN shown in the figure is to be lifted

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A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction (q) of the force (F) with respect to x-axis should be

1. F = 56.389 kN and θ = 28.28°
2. F = – 56.389 kN and θ = – 28.28°
3. F = 9.055 kN and θ = 1.414°
4. F = – 9.055 kN and θ = – 1.414°

Correct Option: A

For no swing, resultant, force along horizontal should be zero
F_H = 90 cos 30° – (40 cos 45° + F cos θ) = 0
∴ F cos θ = 49.658
Find F cos θ values from the given F and θ values in options to find the nearest answer.
In option (a)
F cos θ = 56.389 × cos (28.28°)
= 49.65 kN