Coulomb's Law involving triangle

[Benny851]

Homework Statement

There are three point masses. 1 is fixed in space with the 2nd point mass directly below it on the ground. The 3rd point mass is an unknown distance to the right of mass number 2. These 3 point masses for a rt triangle with point 2 at the 90 degree angle. The vertical distance between point mass 1 and 2 is 1.5 m. The mass of each point mass is 5.5kg. Also there is kinetic friction between point mass 2 and the ground. All three point masses have a charge of +15 Coulombs. If mass 3 starts moving toward mass 2, how far away from 2 will 3 be when 2 starts to move?

Homework Equations

F=MA
F=Eq
F=Qq/r^2
F=KQ/R^2

This problem seems to combine coulomb's law with with 2-d motion. However, I am stumped as to how to combine the 2 concepts. also, not knowing the original starting distance between 3 and 2 is complicating matters.

The Attempt at a Solution

I am able to calculate the force that 1 exerts on 2 no problem but have no idea how to figure out the force that 3 exerts on 2. i also have no idea how to incorporate friction

 

[Simon Bridge]

It is the same as normal only now you know the origins of the forces.
Draw a free body diagram for mass 2.

 

[Benny851]

I see what you mean. So the force acting on 2 is equal to the frictional coefficient*(mg + force of 1 acting on 2), right.

I'm thinking I use the conservation of energy equation to determine how far 3 is from 2 when 2 starts to move, is that right?

 

[Simon Bridge]

How does conservation of energy help here?
Why not just add up all the forces - you know what they have to sum to?
Keep the variables (it helps that all the masses and charges are the same) and solve for the distance to charge 3.

 

[Benny851]

I am a little confused still. I have calculated the original distance between 2 and 3 before 3 starts to move from the right. Does 2 start to move at same time 3 starts to move, if so then the original starting distance is the distance from 2 that I am solving for.

 

[Simon Bridge]

Does 2 start to move at same time 3 starts to move

Of course not :)
3 starts out so far away that the friction is enough to hold 2 where it is.
As 3 approaches 2, the coulomb force increases - at some point the force will be so large that the friction no longer holds 2 in place.

All the problem wants to know is how close 3 can get to 2 without 2 moving.