How Do You Determine the Third Force in a 3-Force Equilibrium Problem?

[kriegera]

Homework Statement

A body is in equilibrium under the influence of three forces. Two of these forces act in directions inclined at 60° to one-another, and their magnitudes are 40 Newtons and 30 Newtons respectively. Find the magnitude and direction of the third force.

Homework Equations

The Attempt at a Solution

I did a similar problem where the first two forces were at a right angle but that one gave direction - so the third force had to equal the first two and be in the opposite directon. However, would the same principle apply here?

First two forces add up to sq rt (40)2 + (30) ) 2 = 50

The third force would be 50 N but in what direction/angle? I can't figure this part out.

 

[radou]

It's always a good start to make a sketch of the forces and apply the rules of vector addition.

 

[kriegera]

I did sketch it out but still couldn't get my head around it. can you explain what you mean about vector addition?

 

[radou]

Write down the equilibrium equations for the components (x and y) of the given forces. The components must add up to zero, right?

 

[adk]

how do we know the forces will add up to 0?

would the equilibrium equations be:
40sin(60)=34.64
30cos(60)=15