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Answer :
Final answer:
The 10.0-kg bucket is moving b) downward because the tension is less than the gravitational force on the bucket. For the block-and-tackle system, the load will move the same distance as the rope is pulled, assuming the system is ideal. The tension in the rope will be different when accelerating up or down in an elevator, with 22.6 N when accelerating up and 19.6 N when accelerating down for a 2.0 kg mass.
Explanation:
The question is discussing the forces acting on objects in different scenarios, particularly focusing on the concept of tension in ropes and the movement of objects under various conditions. For instance, when a 10.0-kg bucket is lowered with a rope exerting 145 N of tension, the bucket is moving downward. This is because the tension in the rope is less than the gravitational force on the bucket (which would be 98 N if we assume g = 9.8 m/s²), suggesting that the net force is acting downwards, hence the bucket moves down.
In the case of the rope pulling up the load, if the rope in Figure 10B is pulled up by 50 cm, the load will also move up by the same distance, assuming there is no slack and the system is ideal (no stretch or compression in the rope). Similarly, for a block-and-tackle system, as depicted in Figure 10A, pulling the rope down by 50 cm will raise the load by 50 cm if the system is ideal.
The tension in a rope suspending a 2.0 kg mass from the ceiling of an accelerating elevator can be calculated. When the elevator accelerates upward at 1.5 m/s², the tension would be greater than when the elevator accelerates downward at the same rate. The correct tensions for these scenarios are (i) 22.6 N and (ii) 19.6 N, respectively, due to the additional force required to accelerate the mass upward and the reduced tension due to the downward acceleration.
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