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Answer :
Final answer:
To keep the beam and the 120N object at equilibrium, a vertical force of 90N must be applied 4m from the pivot, according to the principle of moments.
Explanation:
To calculate the magnitude F of the force required to keep the beam horizontal and at rest, we must consider the principle of moments. This principle states that, for an object to be in equilibrium, the sum of the clockwise moments about a pivot must be equal to the sum of the anticlockwise moments. In this scenario, the weight of the object creates a clockwise moment, whereas the force F we need to find will create an anticlockwise moment to balance it out.
The moment due to the object's weight is its force times the perpendicular distance from the pivot, which is 120N × 3m = 360Nm. The force F creates a moment of F × 4m. For equilibrium:
120N × 3m = F × 4m
360Nm = F × 4m
F = 360Nm / 4m = 90N
Therefore, the correct magnitude of the vertical force F is 90N (option c).
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