Question

as the heavier bucket moves downward to the ground, what will have been the change in mechanical energy of a system consisting of the lighter bucket and the earth, and what will have been the tension in the rope? give your answer as an ordered pair, with the change in mechanical energy first, followed by a comma, followed by the tension in the rope.

Answer 1

The change in mechanical energy of the system is the decrease in gravitational potential energy. The tension in the rope decreases as the heavier bucket moves downward.

Step-by-step explanation:

The mechanical energy of a system consisting of the lighter bucket and the earth is conserved. As the heavier bucket moves downward to the ground, the change in mechanical energy of the system will be the decrease in gravitational potential energy of the system.

The tension in the rope can be calculated using the equation Tension = Weight of the heavier bucket - Weight of the lighter bucket. The tension in the rope decreases as the heavier bucket moves downward.

Answer 2

The change in mechanical energy of the system will be negative, and the tension in the rope will decrease from the weight of the lighter bucket to zero.

Step-by-step explanation:

In this system consisting of the lighter bucket and the Earth, the mechanical energy will decrease as the heavier bucket moves downward to the ground. This is because the potential energy of the system is converted into kinetic energy of the descending bucket. The tension in the rope can be calculated using Newton's second law:

1. At the start of the motion, when the heavier bucket is at its highest point, the tension in the rope is equal to the weight of the lighter bucket.
2. As the heavier bucket moves downward, the tension in the rope will decrease due to the decrease in the weight of the lighter bucket.
3. At the end of the motion, when the heavier bucket reaches the ground, the tension in the rope will be zero.

Therefore, the change in mechanical energy of the system will be negative, and the tension in the rope will decrease from the weight of the lighter bucket to zero.