Answer :
A 10.0-kg bucket is lowered vertically by a rope in which there is 165 n of tension at a given instant. the acceleration of the bucket is approximately 9.8 m/s^2 when rounded to two significant figures.
The tension in the rope can be equated to the weight of the bucket. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth. In this case, the tension is given as 165 N.
Since the tension in the rope is equal to the weight of the bucket, we can write the equation as:
165 N = (mass of the bucket) * (acceleration due to gravity)
Rearranging the equation to solve for the mass of the bucket, we get:
mass of the bucket = 165 N / (acceleration due to gravity)
Substituting the given values, we have:
mass of the bucket = 165 N / 9.8 m/s^2 = 16.84 kg
Now we can calculate the acceleration of the bucket. The weight of the bucket is equal to the mass of the bucket multiplied by the acceleration due to gravity. Rearranging the equation, we have:
weight of the bucket = (mass of the bucket) * (acceleration of the bucket)
Substituting the known values, we get:
165 N = (16.84 kg) * (acceleration of the bucket)
Solving for the acceleration of the bucket, we find:
acceleration of the bucket = 165 N / 16.84 kg = 9.79 m/s^2
Therefore, the acceleration of the bucket is approximately 9.8 m/s^2 when rounded to two significant figures.
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