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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 \((\theta)\) of the force \(F\) with respect to the x-axis should be

1. \(F=56.389\,\text{kN}\) and \(\theta=28.28^\circ\)
2. \(F=-56.389\,\text{kN}\) and \(\theta=-28.28^\circ\)
3. \(F=9.055\,\text{kN}\) and \(\theta=1.414^\circ\)
4. \(F=-9.055\,\text{kN}\) and \(\theta=-1.414^\circ\)

Correct answer: \(F=56.389\,\text{kN}\) and \(\theta=28.28^\circ\)

Solution

To lift the box without swinging, the applied force must balance the weight while maintaining the required line of action. Using coplanar equilibrium and the geometry from the figure gives the force magnitude and angle as stated.

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