A child is swinging a .325 kg ball at the end of a .74 m long string in a vertical circle. string can withstand a tension of 12 N before breaking. What is the tension in the string when the ball is at the top of the circle if its speed at that point is 3.4 m/s?
The Attempt at a Solution
So I made a free body diagram for the ball...
since it is at the top of the circle, it has no forces acting on it at that time in the x direction. It's velocity is in the positive x direction, but no forces are acting on it in that direction.. right?
Since its acceleration is going towards the center of the circle, I use a = v^2 / r which is = 15.6216 m/s^2, then multiply by mass to get centipetal force, = 5.0772 N
mg gives me force of gravity = 3.18825 N,
Since both of the forces point towards the center of the circle, I would add them up right, and say tension is = to the opposite direction but same magnitude, right?
That would be around a little more then 8 Newtons, but my books answer is 1.89 N, which is the result you get from subtracting Fg from Fcentripetal.
Can anyone explain to me where my logic is going wrong??