Final Answer:
The scale reads 3.40s after the first drop of water reaches the bucket is approximately 0.034 N.
Step-by-step explanation:
When the first drop of water reaches the bucket, the scale's reading of approximately 0.034 N signifies the force exerted by the water on the bucket. This force is essentially the weight of the water, calculated using the formula F = m * g, where F is the force, m is the mass of the water, and g is the acceleration due to gravity. In the initial state with an empty bucket, the mass of the water is minimal, resulting in a negligible force on the scale.
The measured force is a consequence of the gravitational pull acting on the mass of the water. As the water accumulates in the bucket, the scale reading will increase proportionally to the added mass. It's crucial to recognize that the acceleration due to gravity remains constant, so any change in the scale reading directly corresponds to the accumulating mass of water.
This process aligns with Newton's law of gravitation, emphasizing the fundamental relationship between mass and gravitational force.