# Find net force on a mass centered between four other masses

I'm not going to post the full question, I just want a general idea of how I should go about solving this type of problem.

There is a square with 4 charged masses on each of the corners, in the center of the square, there is a fifth charged mass. I am supposed to find the net force acting on the center mass ($m_{5}$).

Now I could find the gravitational forces between the center mass and each of the corner masses, split that into x and y components, and then repeat the same process for the electrostatic forces. I'm pretty sure there is an easier, less cumbersome way to do this. Any ideas?

m2--------m1
|          |
|    m5    |
|          |
m3--------m4


None of the charges/masses directly cancel each other out, however the electrostatic ones seem to be small enough to be trivial in the final result.

• So, find the $F_{g}$ of m1 + m3 on m5, and then do the same for m2 and m4? Sep 9 '14 at 2:34
• no. G-force by m1 on m5 and m3 on m5 would be in opposite directions (attractive in both cases) so find the force on m5 by $|m_1-m_3|$. It's direction is towards the larger mass. Similarly, for all other forces. Sep 9 '14 at 2:37