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:Select one:a.9.8 m/s2 upward.b.6.5 m/s2 downward.c.3.3 m/s2 downward.d.zero.
Question
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:Select one:a.9.8 m/s2 upward.b.6.5 m/s2 downward.c.3.3 m/s2 downward.d.zero.
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is F = ma, where F is the net force, m is the mass, and a is the acceleration.
Step 1: Identify the forces acting on the bucket. There are two forces: the force of gravity pulling it down and the tension in the rope pulling it up.
Step 2: Calculate the force of gravity. This is given by the formula F = mg, where m is the mass and g is the acceleration due to gravity. Plugging in the given values, we get F = (3.0 kg)(9.8 m/s^2) = 29.4 N.
Step 3: Calculate the net force acting on the bucket. This is the force of gravity minus the tension in the rope, or 29.4 N - 19.6 N = 9.8 N.
Step 4: Use Newton's second law to find the acceleration. Rearranging the formula to solve for a, we get a = F/m = 9.8 N / 3.0 kg = 3.3 m/s^2.
So, the acceleration of the bucket is 3.3 m/s^2 downward, which corresponds to option c.
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