Finding tension of the string while ball is at top of its path

[chenying]

Homework Statement

A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 85.0 cm. If the speed of the ball is 3.25 m/s and its mass is 0.335 kg, calculate the tension in the string when the ball is at the

a) top of its path

Homework Equations

$$\Sigma$$F_{net force} = ma

F_centripetal = v²/R

The Attempt at a Solution

OK, I have not made an attempt at this problem because my concept of this situation is a little unsure. I don't want any numbers or any calculations, I just want someone to explain to me this problem in just formulas. No numbers at all pleaseeeee

 

[Anden]

I think you should try it yourself, it's not so hard, at least try. Think of what forces that is exerted upon the ball at the top of the path and in what direction they work.

 

[chenying]

So let me share what I believe it is:

Because the ball is at the top of its path, the forces acting on it include gravity and centripetal acceleration.

If I want to find the tension in the string, then it would be sum of gravity and centripetal acceleration?

 

[Anden]

You're correct about the forces, except with how they interact. When you use a rotating frame of reference for analysis, the centripetal force is replaced by a sort of fictious centrifugal force directed away from the centre.
You can also see it like this: For example: When you travel through a curve in a car, you feel like you are "pushed" outwards toward the edge of the curve. This force which "pushes" you out is fictious and doesn't exist in the real sense, but it still feels like so.

So instead of a centripetal force directed toward the centre at the top, replace it with an equally large opposite facing force