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Answer :
Final answer:
The magnitude of force F1 needed to keep the block in static equilibrium is found to be 74.43 N, which is calculated using the Pythagorean theorem applied to the northward and westward forces given in the free-body diagram.
Explanation:
To determine the magnitude of the force F1 needed to keep a block in static equilibrium, one must ensure that the net force acting on the block is zero. According to the given information, there is a northward force of 64 N and a westward force of 38 N. Using the Pythagorean theorem, the magnitude of the resultant force can be calculated as √(64^2 + 38^2) N, which simplifies to √(4096 + 1444) N = √5540 N, resulting in approximately 74.43 N. Since the block is in static equilibrium, the force F1 must be equal in magnitude and opposite in direction to this resultant force, thus F1 will also be 74.43 N.
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