Part (a) of the drawing shows a bucket of water suspended from the pulley of a well; the tension in the rope is 69.0 N. Part (b) shows the same bucket of water being pulled up from the well at a constant velocity. What is the tension in the rope in part (b)?
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To determine the tension in the rope in part (b), we need to consider the forces acting on the bucket of water and apply Newton's second law of motion.
In part (a) when the bucket is suspended from the pulley, the weight of the bucket (mg) acts downwards due to gravity. The tension in the rope (T) acts upwards, balancing the weight of the bucket. Therefore, we have the equation:
T - mg = 0
Where:
T = tension in the rope
m = mass of the bucket
g = acceleration due to gravity (approximately 9.8 m/s^2)
We are given that the tension in part (a) is 69.0 N. Therefore, we can determine the mass of the bucket using the equation:
T = mg
Rearranging the equation, we have:
m = T / g
Substituting the given values:
m = 69.0 N / 9.8 m/s^2 ≈ 7.04 kg
Now, in part (b), when the bucket is pulled up from the well at a constant velocity, the acceleration of the bucket is zero. This means the net force acting on the bucket is zero. The forces acting on the bucket are the tension in the rope (T') acting upwards and the weight of the bucket (mg) acting downwards. Therefore, we have:
T' - mg = 0
Rearranging the equation, we get:
T' = mg
Substituting the values we found earlier:
T' = (7.04 kg) × (9.8 m/s^2) ≈ 68.9 N
Therefore, the tension in the rope in part (b) is approximately 68.9 N.