Calculate the angle between the total acceleration

[Momentum09]

Homework Statement

A ball tied to the end of a string swings in a vertical arc under the influence of gravity. When the ball is at an angle of 23.5 degrees to the vertical, it has a tangential acceleration of magnitude gsin(theta). Calculate the angle between the total acceleration a and the string at theta 23.5.

Homework Equations

I first solved for the total acceleration using a = square root of [A(radial)^2 + A (tangential)^2]

The Attempt at a Solution

But then I don't know what to do next. Can someone please give me some hints? Thanks!

 

[chaoseverlasting]

If you use vectors to find the total acceleration and take the dot product with a vector representing the string, then you should get your angle.

 

[Momentum09]

Sorry I don't quite understand. I did total acceleration x cos 90, but it wasn't correct.

 

[jackiefrost]

[Don't pay any attention to this non-sense! I posted further down what I'm overlooking here. - jackiefrost -]

Does the ball ever move radially? Does it ever move closer or further away from the pivot point? What does that then say about the radial acceleration? How about the total acceleration?

 

[pardesi]

the total accelaration is vector sum of the radial and atngential accelaration so when u have their dot product(as chaoseverlasting said) with the radial accelaration divide the entire thing with the magnitude of radial and total accelartion u get ur ans

 

[jackiefrost]

the total accelaration is vector sum of the radial and atngential accelaration so when u have their dot product(as chaoseverlasting said) with the radial accelaration divide the entire thing with the magnitude of radial and total accelartion u get ur ans

I don't understand something here? The radial acceleration must be the sum of all radial forces. The only radial forces are the tension in the string, T, and the gravitational component in the radial direction, mg*cos(theta). But, assuming the string is inelastic, wouldn't the tension T be exactly canceled by mg*cos(theta) and the sum of radial forces be zero? If so, how can there be any radial acceleration?

But, as I've sat here thinking about this, I guess what I stated above is only true when the velocity of the ball is zero (at extremes of swing or when initially released). Hmmm... I think I forgot about the v^2/L aspect when it's swinging .