A sling-thrower puts a stone (0.260 kg) in the sling's pouch (0.0400 kg) and then begins to make the stone and pouch move in a vertical circle of radius 0.650 m. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is 35.0 N or more. Suppose the sling-thrower could gradually increase the speed of the stone.

Will the breaking occur at the lowest point of the circle or at the highest point?

T=mg+m(v^2/r)

Explanation:

Givens:

A stone (0.260 kg) puts into a sling's pouch (0.0400 kg) and move in a vertical circular path. The circular path has radius 0.65 m. The tension on the cord is 35 N and here the cord will break.  

Part a:  

At the top there are two forces act on the mass are the normal which can be considered as the tension and the gravitational all of these are downward in addition to the centripetal acceleration in the same direction.  

-T-mg=-m(v^2/r)

but the body will fall away the path and we need it in the contact with the way so we can consider the normal (tension) force is Zero.then,  

g=v^2/r

At the bottom the tension is upward ,also the centripetal acceleration:

T-mg=m(v^2/r)

T=mg+m(v^2/r)

T=mg+m(v^2/r)

here the normal force is max.  

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.