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**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 (mv**

^{2})/(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. -___-**