A bucket of mass 2.40 kg is whirled in a vertical circle of radius 1.55 m . At the lowest point of its motion the tension in the rope supporting the bucket is 28.0 N .

Question

How fast must the bucket move at the top of the circle so that the rope does not go slack?

I did this where the sum of the centripetal forces is equal to the gravitational force and tension are added together and got the wrong answer. I got the right answer by setting tension equal to 0 but why?

Answer 1

Because the minimum tension that can exist in the rope is zero. That is the least tension you can have in the rope. The question is asking for a minimum speed. It could go faster with a tension greater than zero.