# Uniform Circular Motion and Water Falling From A Bucket

1. A 2kg bucket of water is attached to a 1.5m long string and swung in a vertical circle with a constant speed of 12 m/s. What is the minimum speed the bucket can be swung at while still retaining the water.

2. The bucket has a maximum tension force on the string at the bottom, with 212 N (198 N + the force of gravity). At the top, it has a minimum tension force, with 172 N (198 - gravity). The centripetal force can be found using (mv2)/(r), where v is the velocity, m the mass of the rotating object, and r the radius.

3. I'm honestly lost here. I know there has to be some sort of minimum speed, because conceptually I can see that with a huge radius and a low speed the water will fall out regardless of centripetal force. That's about it. -___-

ehild
Homework Helper
Think in the way that the water in the bucket travels along a circle of given radius. What forces act on it? The resultant of these forces must be equal to the centripetal force. From this condition, you get the normal force. Note that the bucket can only push the water, it can not pull it.

ehild

Just think that what will cause the water to spill out of the bucket. Then try to minimize it.