Question

A rope is tied to a pail of water and the pail is swung in a vertical circle of radius 1.3m. What must be the minimum velocity of the pail at the highest point of the circle if no water is to spill?

Answer 1

First, find the Force in the y-direction.

Fy=T+Fg=ma

..or in this case

T+Fg=(mv^2)/R

Tension equals to 0 because when the pail of water is at its highest peak, there, tension does not exist.

so now we have

mg=(mv^2)/R

Cancel out mass to get...

g=(v^2)/R
(gR)^(1/2)=v
Plug in values.