Circular Motion and Centripetal Force of a Swinging Bucket

[ama]

Homework Statement

You swing a 6.5 kg bucket of water in a vertical circle of radius 3.6 m.
What speed must the bucket have if it is to complete the circle without spilling any water?
mass=6.5 kg
r= 3.6

Homework Equations

ay=(v^(2)/(r))
may= A-N-Mg

The Attempt at a Solution

I know that the force of gravity on the water and the normal force of the bucket on the water both point down. I assume you need to get the centripetal acceleration first. But I do not know what the applied force is and have no way of knowing. What do I do?

 

[mateomy]

What would need to happen for the water to stay in the bucket? (something needs to equal something else)

 

[ama]

the normal force and gravity must equal the applied force. But if that is the case, then ay is 0 and the problem is unsolvable.

 

[mateomy]

You need to use centripetal acceleration (or a reaction against it), and acceleration of gravity for this one.

 

[ama]

at the top of the path, the normal force the bucket exerts on the water is 0. therefore, applied force, which is equal to normal force, is 0. Thus mg=(m)(v2/r) solving for v gets 5.94 m/s.