How do I get the magnitude and direction of a force experienced by, in this case, the ball at the top?

Question

Three glass ornaments become electrically charged when Noel removed them from the packaging material in their box. If each ornament has acquired a charge of 2.0 E -10, what is the magnitude and direction of the force experienced by the ball at the top?

> The image I have is an equilateral triangle with 60° and the sides of the triangle measure .2 meters

Answer 1

We need to find the sum of the forces from the two bottom ornaments on the ornament at the top. Since all of the ornaments are assumed to be identical, the two bottom ornaments will both repel the top ornament. We can use the coulomb force equation and find the contribution from both ornaments to get the net force on the top ornament. F = kqq/r^2 = (9E9)(2E-10)^2/(0.2)^2 = 9E-9N. The angle 60 deg can be used to find the x and y components of the force. F_x = 9E-9cos(60) = 4.5E-9N, F_y = 9E-9sin(60) = 7.79E-9N. if one draws a free body diagram for the forces acting on the top ornament, it can be seen that the F_y components add together, but the force components in the x-direction F_x will subtract and therefore cancel out. This means that the net force is simply the sum of the y-components of the force Fnet = 2Fsin(60) = 1.56E-8N