To determine the correct point on the U-shaped curve based on the energy conservation principle in the given model, we can analyze the relationship between kinetic energy (KE) and potential energy (PE) at different positions of the ball.
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When the ball reaches the lowest point on the curve: At this position, the potential energy is at its minimum (usually set to zero), and the kinetic energy is at its maximum because the ball's speed is greatest here. Therefore, KE is high and PE is low.
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When the ball is halfway up its ascent of the curve: At this point, the ball has some height, meaning it has potential energy that is not at its maximum, and it is moving, so it also has kinetic energy. The PE would be higher than at the lowest point, and KE would be lower than at the lowest point.
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When the ball reaches the highest point on the curve: At this position, the ball has the maximum potential energy and the minimum kinetic energy (momentarily zero if the ball is at rest before rolling back down). Thus, PE is high and KE is low.
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When the ball is halfway down its descent of the curve: At this point, the ball is lower than it was at the top, so it has lost some potential energy and gained kinetic energy. The total energy remains constant, but KE is greater than it was at the highest point, and PE is lower than at the highest point.
Given these analyses, the point in the U-shaped curve that would correspond to the highest kinetic energy and the lowest potential energy is when the ball reaches the lowest point on the curve.
Thus, the correct answer is:
When the ball reaches the lowest point on the curve.
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