Question

A small ball with a mass of 0.48kg is fastened to a string .24m long and suspended from the ceiling to make a conical pendulum. The ball describes a horizontal circle and the string makes an angle of 15 degrees with vertical. Find the tension of the string.

Answer 1

The tension in the string of a conical pendulum is 0 at the equilibrium point where the string makes an angle of 15 degrees with the vertical.

Step-by-step explanation:

To find the tension in the string of a conical pendulum, we can analyze the forces acting on the ball. There are two forces acting on the ball: the gravitational force and the tension force. The gravitational force can be split into two components: one component pointing towards the center of the circle and another component perpendicular to the string. The tension force acts along the string, towards the center of the circle. At the equilibrium point (where the string makes an angle of 15 degrees with the vertical), the tension in the string is equal to the centripetal force required to keep the ball moving in a circle. We can calculate the tension using the equation T = mv²/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 circle. Since the ball is at rest, the velocity is 0, and thus the tension is also 0.