Centripetal Force of swung keys Problem

[MiniOreo1998]

Homework Statement

Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

A) What is the slowest speed the keys can swing and still maintain a circular path?

B) What is the tension in the string at the bottom of the circle?

I'm confident with A, however am still a bit shaky with B... Any tips would be greatly appreciated!

Homework Equations

A)
F_c = F_g
m v² / r = m g

B)
F_net = F_T - F_g
F_T = F_net + F_g

The Attempt at a Solution

A)
[/B]
F_c = F_g
m v² / r = m g
v = (rg)²
v = √(0.25) (9.8)²
v = 1.57 m/s


B)

F_net = F_T - F_g
F_T = F_net + F_g
F_T = m v² / r + m g
F_T = (0.1) (1.57)² / 0.25 + (0.1) (9.8)
F_T = 2.0 N

 

[haruspex]

Is the speed constant?

 

[MiniOreo1998]

Is the speed constant?

The problem is word for word what I've given here. (I wish more info were made available, it seems as if this can be interpreted in more than one way)

 

[haruspex]

The problem is word for word what I've given here. (I wish more info were made available, it seems as if this can be interpreted in more than one way)

My question was intended as rhetorical. I would say it is not constant. According to what law would you expect it to vary?

 

[MiniOreo1998]

My question was intended as rhetorical. I would say it is not constant. According to what law would you expect it to vary?

Conservation of energy.

 

[haruspex]

Conservation of energy.

Right.