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A 15.0 kg bucket is lowered vertically by a rope with 182 N of tension at a given instant. What is the acceleration of the bucket?

Answer :

Final answer:

The acceleration of the 15.0 kg bucket, which is being lowered by a rope with a tension of 182 N, is 2.33 m/s².

Explanation:

The subject of this question is Physics, specifically the study of forces and acceleration. The student is looking to find the acceleration of a 15.0 kg bucket, which is being lowered by a rope with a tension of 182 N. To find the acceleration, we would need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

In this case, the forces acting on the bucket are its weight (which acts downward) and the tension in the rope (which acts upward). The weight of the bucket can be found with the formula W = mg, where m is the mass and g is the acceleration due to gravity. Substituting the given values, we find W = (15.0 kg)(9.8 m/s²) = 147 N.

Since the bucket is descending, the net force (Fnet) is the tension minus the weight, or Fnet = T - W = 182 N - 147 N = 35 N. We can now find the acceleration by rearranging Newton's second law to isolate a: a = Fnet / m = 35 N / 15.0 kg = 2.33 m/s². Therefore, the acceleration of the bucket is 2.33 m/s².

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