1. The problem statement, all variables and given/known data Assuming the keys are moving in uniform circular motion!!!!! 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? 2. Relevant equations Given: V =10m/s, R=25m, Fc = mv^2/r, Ff = UFn 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!!!