Accelaration in a vertical circle

[mazz1801]

A ball is attached to an inextensible string of negligable mass and hangs vertically under gravity. At time t=0, it is given a horizontal velocity u and begins to move in a vertical circle of radius r. At any time t>0, the ball is at an angle θ to the vertical and has a velocity v tangential to its circle of motion. There is no friction acting so that the mechanical energy of the ball is conserved/

If ^u=4rg, find the angle θ at which the string goes slack. For how long will the string remain slack before becoming taut again?

I'm having trouble even starting with this part of the question. (The first part was to prove that the difference in tension at the bottom and tension at the top was 6 times the weight of the ball- I got that bit)

I have tried using the equations for motion in a circle. Basically all of them and they are all leading me down the same street!

I'm pretty desperate here... could someone just tell me what equation I should be using!
Also will the answer be numerical or contain m and g...

 

[tms]

A ball is attached to an inextensible string of negligable mass and hangs vertically under gravity. At time t=0, it is given a horizontal velocity u and begins to move in a vertical circle of radius r. At any time t>0, the ball is at an angle θ to the vertical and has a velocity v tangential to its circle of motion. There is no friction acting so that the mechanical energy of the ball is conserved/

If ^u=4rg, find the angle θ at which the string goes slack. For how long will the string remain slack before becoming taut again?

I'm having trouble even starting with this part of the question. (The first part was to prove that the difference in tension at the bottom and tension at the top was 6 times the weight of the ball- I got that bit)

I have tried using the equations for motion in a circle. Basically all of them and they are all leading me down the same street!

I'm pretty desperate here... could someone just tell me what equation I should be using!

You are looking for the point at which the tension goes to zero. Since you must already know how to calculate the tension from the first part, that should be a hint.

However, are you sure you have the initial velocity correct? The units don't seem right to me.

Also will the answer be numerical or contain m and g...

How can you get a numerical answer if there are no numbers? Seriously. When I was a TA I would give quizzes with no numbers in them and get back numerical answers. How does that work?

 

[mazz1801]

I made a mistake! Inital velocity is u²=4rg
I used the function wrong.

Also the unit thing must have been a blonde moment! Thanks for your help!