A ball of mass moves in a horizontal circular path of radius a with speed v as shown in the illustration below. Find the tension in the cord.
To find the tension in the cord, we need to consider the forces acting on the ball.
First, let's identify the forces at play:
1. Tension force (T): This is the force exerted by the cord pulling the ball towards the center of the circular path.
2. Centripetal force (Fc): This is the force required to keep the ball moving in a circular path. It acts towards the center and is provided by the tension force.
3. Weight (mg): This force acts vertically downwards and is equal to the mass of the object (m) multiplied by the acceleration due to gravity (g).
Since the ball is moving in a horizontal circular path and the weight acts vertically, it does not contribute to the centripetal force. Therefore, the tension in the cord (T) is responsible for providing the required centripetal force (Fc).
Using the following equation for centripetal force:
Fc = (mv^2) / r,
where m is the mass of the ball, v is the speed, and r is the radius, we can solve for T.
Therefore, the tension in the cord (T) is given by:
T = (mv^2) / r.