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A 14 kg bucket is lowered vertically by a rope with a tension of 163 N at a given instant. What is the acceleration of the bucket?

Answer :

Final answer:

The tension in the rope is equal to the weight of the bucket. The weight of the bucket is 137.2 N. The acceleration of the bucket is 1.843 m/s².

Explanation:

The tension in the rope is equal to the weight of the bucket. The weight of the bucket is given by the formula W = mg, where m is the mass of the bucket and g is the acceleration due to gravity. In this case, the mass of the bucket is 14 kg and the acceleration due to gravity is approximately 9.8 m/s². So the weight of the bucket is W = 14 kg × 9.8 m/s² = 137.2 N.

Since the tension in the rope is 163 N, and the weight of the bucket is 137.2 N, there is an unbalanced force of 163 N - 137.2 N = 25.8 N. This unbalanced force causes the bucket to accelerate.

To find the acceleration of the bucket, we can use Newton's second law, which states that F = ma, where F is the net force applied to an object, m is the mass of the object, and a is the acceleration of the object. Rearranging the formula, we get a = F/m. Plugging in the values, we get a = 25.8 N / 14 kg = 1.843 m/s².

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