How Do You Calculate the Third Force in a Three-Force System?

[Callen9]

Homework Statement

A 20-kg object is subjected to three forces which produce an acceleration a = -8 m.s-2 i + 6.0 m.s-2 j on the object. Two of the forces are:
F1 = 3.0 N i + 16.0 N j
F2 = -12.0 N i+ 8.0 N j
Find the third force.

Homework Equations

The Attempt at a Solution

To be honest, I've been doing physics for the past 8 hours so I'm brain dead right now. This is my last problem on my homework. I know that F=ma, so I'm thinking maybe I have to set up an equation like (F1+F2+F3)=20a. But something about that doesn't seem right. Any help and I would be very grateful.

Thanks,

 

[wbandersonjr]

You're exactly right. Use F=ma and set up two equations for the two components. Set up one equation for the i direction and one equation for the j direction. F1+F2+F3=ma, then you just need to solve for F3

 

[gneill]

Write separate equations for the vector components of the equation F = m*A. Here F is the net force acting on mass m, so F = F1 + F2 + F3. each of these F's have two vector components (x,y directions).

So suppose you start by looking at just the x-components. Can you write the F = m*A equation for that?