A mad scientist is designing a trap for intruders that will lift them up into the air and hold them helpless. The device consists of an equilateral triangle, 10.0 meters to a side, embedded in his floor. When he flips a switch, the corners of the triangle will be charged equally by a generator and any negatively charged object above the center of the triangle will be lifted upwards by the electric force. A computer-controlled system of giant fans keeps the intruder from straying horizontally from the center of the triangle. While he is testing the system, his cat walks into the trap. She has a net charge of −1.00 nanocoulombs due to electrons that rubbed off from the carpet. The cat, which has a mass of 5.00 kg, begins to hover 3.00 meters up in the air. Find the charge on each corner of the triangle.
The relevant equations are k|q||q|/(r^2) and 1/(4piE) |q||q|/(r^2) and summation of electrostatic forces using superposition principle.
The Attempt at a Solution
Using superposition principle, it's essential to add all the forces in the x direction and y direction. However, the problem also takes into account a geometric property in that I need to know about bisector and so forth. I'm not so sure how to tackle this problem.