You tie a cord to a pail of water, and you swing the pail in a vertical circle of radius 0.700 m
What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it?
The Attempt at a Solution
I got the correct answer. 2.62 m/s, but I'm not entirely sure WHY I got the correct answer. So, what I did was I drew a force diagram and labeled all my forces. I got that my my forces in the centripetal direction are Tension (FT) and Gravity (mg). I found no forces in tangential direction.
Setting up my Newtons 2nd Law equation I got:
FT + m g = m a
FT + m g = m (v2/r)
When I looked at this I basically used some intuition. I figured since m,g, and r are considered to be constants, the only thing I could do is eliminate my tension force by setting it to 0. This made sense to me to a degree because if I set tension to 0 then only gravity is acting on my water, which meant the right side (ma) would be equal to gravity (mg) to keep the water in place.
However, I'm not really sure why this means I would set tension to 0. I basically tried to imagine if I had complete slack in the chord what would happen, and intuitively my answer made sense. I'm just not sure of the math behind WHY it makes sense. It was more or less a lucky guess with a bit of intuitive inclination on my part. Why did this work out?