Did i rearrange this equation correctly? (circular motion)

[SmallPub]

d

Homework Statement

A bucket 2.00kg is whirled in a vertical circle of a radius 1.10m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N a) find the speed of the bucket b) how fast must the bucket move at the top of the circle so that the rope does not go slack?

Homework Equations

v=√gr , FT = -mv2/r + mg ,

g=9.81m/s^2
m=2.00kg
r=1.10m
FT= 25.0 N

The Attempt at a Solution

a) v=√rg = √1.10m x 9.81m/2^s = 3.28m/s

b) v=√FTr-mg/-m <----- I am not sure if i rearranged that correctly

 

[hjelmgart]

Maybe you should show the steps in how you rearranged it. Go through every step, and you will see, that it is wrong.

 

[SmallPub]

Maybe you should show the steps in how you rearranged it. Go through every step, and you will see, that it is wrong.

can you show the correct equation to find v?

 

[hjelmgart]

FT = -mv^2/r + mg
FT - mg = -mv^2
(FT - mg)*r/m = -v^2
-(FT - mg)*r/m = v^2

v = sqrt(-(FT - mg)*r/m)
v = sqrt((mg*r - FT*r)/m)

 

[hjelmgart]

Although I don't think that is the correct method for this problem, anyway. I didn't look too much into it, though, but I am guessing, you will get some complex number from this.