Speed and Magnitude of Tension

Question

A 0.60-kg rock attached to one end of a (massless) cord is swung at a constant speed in a vertical circle, having a radius of 1.20 m. If the magnitude of the tension in the cord at the bottom of the circle equals 9.0 N, what is the speed, v, of the rock, and what is the magnitude of the tension, T, in the cord at the top of the circle (if one may take for the gravitational acceleration, g = 9.8 m/s? downward, and if one may neglect any effects due to air resistance)? 

Answer 1

The equations for the rock at the bottom of the circular plane and the top are as follows. At the top T +mg = mv²/r and at the bottom T-mg = mv²/r. Using the information given in the problem find the velocity from the bottom equation which gives 9N- (.6)9.8N = (.6) v²/1.2 N and solving for v gives 9-5.88=.6v²/1.2 and v = 2.498 m/s. Now using this in the top equation to find T at the top gives T= (.6)6.24/1.2 -5.88 = 3.12 -5.88 =-2.76 N. So rock never gets to the top and T= 0N at the top.