# Did i rearrange this equation correctly? (circular motion)

1. Dec 7, 2013

### SmallPub

d1. The problem statement, all variables and given/known data 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?

2. Relevant equations v=√gr , FT = -mv2/r + mg ,

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

3. The attempt at a solution a) v=√rg = √1.10m x 9.81m/2^s = 3.28m/s

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

2. Dec 7, 2013

### hjelmgart

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

3. Dec 7, 2013

### SmallPub

can you show the correct equation to find v?

4. Dec 7, 2013

### 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)

5. Dec 7, 2013

### 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.