Problem 15.

Two identical spheres are each attached to a rope of length 1 m and hung from a common point. Each sphere has mass 1 kg. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. The spheres have positive charges. The spheres are in equilibrium and each rope makes an angle 30 degrees with the vertical. Find the tension of the ropes.

Solution

The system is in equilibrium. It means that the net force is 0. It means that the sum of the tension force and the gravitational force should have horizontal direction. Then we can write:

From this equation we can find the tension: