As a 3.0-kg bucket is being lowered into a 10-m deep well,starting from the top,the tension in the rope is 19.6 N.The acceleration of the bucket will be: A) 6.5 m/s² downward. B) 9.8 m/s² upward. C) zero. D) 3.3 m/s² downward.

Question

Quizplus · Accepted Answer

The tension in the rope while lowering the bucket is given as 19.6N. The weight of the bucket can be calculated as the product of mass and acceleration due to gravity (g = 9.8 m/s^2) as:
W = mg = 3.0 kg × 9.8 m/s^2 = 29.4 N
Since the bucket is being lowered downwards, the direction of acceleration is also downwards. Using Newton's second law of motion, we can equate the net force on the bucket with the product of its mass and acceleration as:
Net force = Tension - Weight = ma
where Tension is the force applied by the rope, and Weight is the force due to gravity. Solving for acceleration, we get:
a = (Tension - Weight)/m = (19.6 N - 29.4 N)/3.0 kg = -3.3 m/s^2
The acceleration is negative because it is in the downward direction (opposite to the positive direction). Therefore, the bucket will be moving downwards with a speed of 3.3 m/s^2. Hence, the best choice is D.

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