Pendulum Physics Problem: Finding Stretch Force at Equilibrium

[Petrulis]

Homework Statement

Mass m ball hangs on the L length thread. This system is turned up by angle alfa from the vertical. What is the stretch force when the ball passes the state of balance (where ball's kinetic energy is the biggest)?

The Attempt at a Solution

At the alpha position, potential energy = mgL(1 - cos(alpha)).
This gets converted into KE at the bottom.

So, m*v^2/2 = mgL(1 - cos alpha). This gives the velocity at the balance point.

Now the stretch force will not only be balancing the weight but also the centrifugal force which is m*v*v/L.

So T = mg + m*v*v/L = mg(3 - 2*cos alpha).

Is anything Ok in my solution? Isn't here any mistakes?

Thanks in advance.

 

[Doc Al]

Everything is fine

Now the stretch force will not only be balancing the weight but also the centrifugal force which is m*v*v/L.

I would phrase things a bit differently. Viewed from the usual inertial reference frame, you mean centripetal not centrifugal force. (I assume you did not consciously choose a non-inertial frame, which is fine too.) And centripetal force is not a separate force, but just the name we give to whatever net force is providing the centripetal acceleration. So I would write it as:
F(net) = T - mg = mv^2/L

(Of course, if you meant to use a noninertial frame, no problem; just make that clear.)