Finding the magnitude necessary to balance two forces

[Shadow236]

Homework Statement

Two forces are acting on an object. The magnitudes of them are F1=10.0N, F2=4.0N. If a third force F3 is applied on the object, what is the smallest magnitude of F3 needed to balance the first two forces?

Homework Equations

N/A

The Attempt at a Solution

I've done a lot of internet searching for this question and had no luck. With that being said, I am really starting from ground zero here (hence no equation). I'm guessing that this problem has to do with F_NET and is probably easier than it looks? If someone could give me an equation to use I would probably be in good shape. Thank you!

 

[paisiello2]

Yes, it's very easy and you guessed the right equation. The word "balanced" can only mean the object is in equilibrium.

 

[CWatters]

Try a graphical approach. For example choose arbitrary values, say F1 = 3 and F2 = 4 and draw a few vector sum diagrams to scale with F1 and F2 pointing in different directions such as...

a) F2 and F1 pointing in the same direction
b) F2 at 90 degrees to F1
c) F2 at 45 degrees to F1
d) F2 at 135 degrees to F1
c) F2 in the opposite direction to F1

In which direction must they point to give the smallest Fnet that F3 must oppose?