A bucket of mass 1.40 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
Find the speed of the bucket.
How fast must the bucket move at the top of the circle so that the rope does not go slack?

Hint: the tension in the rope has two components - one due to the weight of the bucket (mg) and one due to the centripedal acceleration of the bucket (mv^2/R). Gravity always pulls downward ans the force to create the centripedal acceleration is always towards the center of the circle. Think about how these two forces add or subtract as the bucket swings through its arc.