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## Homework Statement

A bucket of water (10kg) is swung vertically. Radius is 1 m. It takes 1 second to spin the bucket in a full circle.

a. How much force has to be exerted at the top of its motion?

b. How much force must be exerted at the bottom?

## Homework Equations

v

_{top}=sqrt(gr)

top: F

_{tension}= mv

^{2}/r - mg

bottom: F

_{tension}= mv

^{2}/r + mg

a

_{c}=v

^{2}/r

## The Attempt at a Solution

This is a fairly straightforward question, but I'm getting different answers. I'm not sure if this exerted force means the same thing as force of tension. If so, then I have force at the top = 0 N, force at the bottom is 588 N.

If v=sqrt (9.8) as the minimum velocity at the top, then conservation of energy gives 1/2mv

^{2}

_{top}+mg2r=1/2mv

^{2}

_{bottom}.

Thus, velocity at the bottom of the bucket's motion is 7 m/s. Using the equation F=mv

^{2}/r+mg, I get the 588 N answer.

However, when I initially completed this in class, I was told that 490 N was the correct answer for part b. Does this somehow have to do with the 1 second time provided in the original problem, such as assuming constant velocity? I've been thinking over this for quite a while and I just keep getting more confused.

Thanks for any help in advance!