- #1

Dougggggg

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## Homework Statement

Word for word from textbook. . .

"You tie a cord to a pail of water, and you swing the pail in a vertical circle of a radius of 0.600 m. What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it?"

R=0.600 m

g=9.80 m/s

^{2}

## Homework Equations

I tried to use this though I am unsure if it can be used since I believe this is a case of nonuniform circular motion.

a

_{rad}= [tex]\frac{v^2}{R}[/tex] = [tex]\frac{4\pi^2 R}{T^2}[/tex]

I have also tried using [tex]\Sigma[/tex]F equations but those lead me into a mess.

## The Attempt at a Solution

I first tried to figure out what forces were involved at the top and bottom of the circle. I kept getting things that I couldn't really do anything with since I only knew one acceleration. I then went on to look at what I could do with a

_{rad}and kept making a mess of algebra that wasn't really helping anything at all. I know how this problem works conceptually to some degree, the inertia makes the water resistant to change directions and so on, but I am not getting how I am supposed to do the math here. If someone could give me some idea of which direction I should start going I would be greatly appreciative.Edit: Found right answer, if I ignored tension as a force acting on the bucket then I came up with a

_{rad}= g

then

[tex]\sqrt{gR}[/tex] = v

Solved for v. I am not sure how that gives me the minimum speed required to complete the circle but it said it was the right answer in the back of the book. If anyone could please explain why that math worked the way it did I would be really really really thankful.

Answer was v = 2.43 m/s

Edit 2: Does it work because for that whole equation to work v has to be big enough to complete a whole circle?

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