# Circular motion

1. May 7, 2014

### scrubber

1. The problem statement, all variables and given/known data

A small ball of mass 0.50 kg is attached to a cord and perform uniform-speed circular motion of radius 2.0 m in a vertical plane.

i) If the speed of the circular motion is 10m/s, determine the tension in the cord at the lowest point of the circular motion.
ii) Determine the minimum possible speed of this circular motion.
2. Relevant equations

radical acceleration = v^2/r
Fnet=ma

3. The attempt at a solution

i) T-mg=mAc, where Ac is the radical acceleration.
T=mAc+mg=m(Ac+g)=0.5*(10^2/2+9.81)=30N

ii) At the top position,
mg-T=mAc
T=0 for minimum speed,
mg=mAc=m(v^2/r)
v=√(gr)=√(9.81*2)=4.4m/s

2. May 7, 2014

### quawa99

Your attempt at the first bit of the question is correct. In the second bit of the question you considered the top most point of the vertical circle to be the point where tension is zero but as the mass is attached to a flexible chord the tension becomes zero before the ball reaches to the top and hence the ball leaves the circle and goes into a projectile motion. Try framing your equation as a function of the angle made by the string with the verticle then locate the point where tension becomes zero.