Minimum speed at the circular track

[inky]

Homework Statement

What is the minimum speed of the car must have at the top of the loop? There are three methods. I would like to know which method or answer is correct.

Please see attached file.

Homework Equations

Please see attached file.

The Attempt at a Solution

Please see attached file.

 

[rock.freak667]

I would choose the third one,provided that H> 2r.

 

[inky]

I would choose the third one,provided that H> 2r.

Thanks a lot. Why didn't consider the force at the top?

 

[rock.freak667]

I think if H> 2r, then the speed will be enough to provide the centripetal force.