Determine the tension in the pendulum string

[Ry122]

Homework Statement

The ball in this conical pendulum is moving at constant velocity.
The length of the string is 1m and the ball is 0.5kg.
Determine the tension in the string.

[PLAIN]http://img685.imageshack.us/img685/7868/pedns.png

Homework Equations

The Attempt at a Solution

The force that the ball exerts on the string is the tension inside the string
and the ball experiences two different forces.
One is the force the ball experiences due to gravity and the other is the force it experiences
due to the circular motion that it's undergoing.
The resultant of these two forces will give the tension inside the string.
The force due to gravity can be calculated with F=m x a
But I'm unsure as to how the force on the ball due to the circular motion of the ball can be calculated.
Does anyone know how this can be done?

 

[graphene]

What is the expression for centrifugal force in terms of velocity & radius ?

 

[Ry122]

F = m x (v^2)/R
But R can't be determined because theta is unknown.

 

[graphene]

You do not need the exact value of $$\theta$$.
Just write down the equations for a generic $$\theta$$ and you could figure out how to proceed.

 

[rwisz]

I can provide the following response:

To determine the tension in the pendulum string, we can use the equation T = m x v^2 / r, where T is the tension, m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circular motion. In this case, the radius is equal to the length of the string, 1m. Since the ball is moving at a constant velocity, we can assume that the acceleration is zero, and therefore the force due to gravity is also zero. Thus, the only force acting on the ball is the force due to the circular motion, which is equal to the tension in the string. Plugging in the values of m = 0.5kg, v = constant, and r = 1m, we can calculate the tension in the string to be T = 0.5 x v^2 / 1 = 0.5 x v^2. Therefore, the tension in the string is directly proportional to the square of the velocity of the ball.