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## Homework Statement

Assuming the keys are moving in uniform circular motion!!!!![/B]

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 that the keys can swing and still maintain a circular path?

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

## Homework Equations

Given: V =10m/s, R=25m, Fc = mv^2/r, Ff = UFn

[/B]

a) Centripetal Force is Fg, so Fg = MV^2/r

So, mg = mV^2/r

0.1(9.8) = (0.1)(V^2/0.25)

Mass cancels out..

9.8 = V^2/0.25

So, (0.25)(9.8) = V^2

Therefore, V^2 = 2.45, so V = 1.56m/s

The slowest speed the keys can travel and still maintain circular motion is 1.56m/s.

b) b) Fnet = Ft - Fg or Ft = Fnet + Fg (assuming this is uniform circular motion!!)

Ft = mV^2/r + mg

Ft = [ (0.1)(1.56)^2 / 0.25 ] + (0.1)(9.8)

Ft = 0.97N

Therefore, assuming that the keys are moving in uniform circular motion, the Ft at the bottom of the circle is 0.97N.

**Ok.. Really having a tough time with this one.**

Been looking over it for too long and eyes are gone blurry.. any help is appreciated!!!

Been looking over it for too long and eyes are gone blurry.. any help is appreciated!!!