Static equilibrium occurs when an object is at rest and all the forces acting on it are balanced, meaning the net force is zero. In the case of pushing a box, the situation involves both your applied force and the frictional force opposing the motion.
As you begin to decrease the force you're exerting on the box while pushing it, the following will occur:
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Initially: When your applied force is greater than the frictional force, the box will accelerate in the direction of the applied force.
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Decreasing Force: As you gradually decrease your applied force, the box will continue to move as long as the applied force remains greater than the frictional force.
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Reaching Equilibrium: The box will reach static equilibrium when your applied force is reduced to the point where it equals the frictional force acting on the box. At this moment, the box will stop moving and remain at rest, assuming that it was pushed to move at first. If it was already in motion, it will continue moving until the force equals friction, but it will eventually stop if the net force acting on it becomes zero.
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Final Condition: The box is in static equilibrium when the forces are balanced, which means your applied force has decreased to match the maximum static frictional force (if it is stationary) or the kinetic frictional force (if it is sliding but being brought to rest).
In summary, the box will reach static equilibrium when the force you exert on it equals the force of friction opposing the movement, resulting in a net force of zero.