What is the correct way to find the speed of the bucket in circular motion?

[RedBurns]

bucket of mass 1.80 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
Find the speed of the bucket.

f(t)-mg=mA

25-17.64=1.8 A
7.36 = 1. 8 A
A= 4.08

I'm told the answer above is incorrect, and someone point out my mistake?

 

[nrqed]

bucket of mass 1.80 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
Find the speed of the bucket.

f(t)-mg=mA

25-17.64=1.8 A
7.36 = 1. 8 A
A= 4.08

I'm told the answer above is incorrect, and someone point out my mistake?

They are asking for the speed . You found the centripetal *acceleration*. You know how the two are related in circular motion?

 

[RedBurns]

acceleration is velocity squared over time

Speed would be 2 pi radius over time

4.08= v^2/1.10
4.08/1.1 = 3.71
Square root of 3.71 = 1.93

Would 1.93 then be the speed?

 

[nrqed]

acceleration is velocity squared over time

no! (over the radius! Not the time!)

Speed would be 2 pi radius over time

I don't see how this help syou since you don't have the time...But it's true, if by "time" you mean the time for one rotation, the period.

4.08= v^2/1.10
4.08/1.1 = 3.71
Square root of 3.71 = 1.93

Would 1.93 then be the speed?

Check you algebra!