Electrostatic Force in a Mad Scientist's Trap

[Abelard]

Homework Statement

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.

Homework Equations

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.

Homework Statement

 

[ehild]

Make a sketch to find out the distance of the cat from a corner of the triangle by using the length of one side and the height of the cat.

ehild

 

[gneill]

Start with what you know about equilateral triangles. What is the angle at each vertex? Draw bisectors of the angles. Where do they meet?

 

[Abelard]

OK, so the centroid divides each median length. But do these medians be cut in half length? So in this case, the centroid is located 5sqrt(3) from the base? and the same distance from each side? Then to find the charges, do I need to divide into x and y components by using cosine and sine. Then add all the electrostatic forces and equate it with 150N?

When adding all the electrostatic forces, how do they add up? In other words, do they add up regardless of directions? I mean they do, but do I necessarily have to divide into x and y components?

 

[gneill]

Find the distance of the centroid from an apex. That's the planar distance from a charge to the cat's position when viewed from above. Say the centroid is labeled point B, and an apex is point A. The cat is at point C. The hypotenuse of triangle ABC is the distance from the charge to the cat.

So, what's the distance from an apex to the centroid?

If you consider all the symmetries involved, you should be able to get away without dealing with too many force vector components.

 

[Abelard]

So, the cat is not at the centroid? Now the picture becomes very blurred.

 

[gneill]

So, the cat is not at the centroid? Now the picture becomes very blurred.

The cat is hovering above the centroid. 3.00 meters above it, to be precise.