# Question about making vectors equilibrium

#### preluderacer

1. The problem statement, all variables and given/known data

The figure shows two forces of equal magnitude acting on an object. If the common magnitude of the forces is 4.6 N and the angle between them is 40°, what third force will cause the object to be in equilibrium?

3. The attempt at a solution

What I did was split them down the middle, then used 4.6cos(40) degrees and then got 4.3N I just pointed it in the opposite direction to make it equilibrium. Does this sound like the correct method to use?

#### fzero

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What is the definition of equilibrium? What does equilibrium mean for the sum of forces on the object?

#### preluderacer

It means they are balanced right? I thought by pointing the vector in the opposite direction balances it.

#### fzero

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Gold Member
"Pointing the vector in the opposite direction" is the right idea, but we need to be more mathematically precise than that to solve the problem.

Equilibrium means that the object doesn't move. What does that say about the acceleration of the object? What does that imply about the sum of forces on the object?

#### preluderacer

The original opened up leftward. I messed up when stating it. When I split them i also split the degrees so I used 4.6Ncos(20) degrees. I wound up with 4.3 N pointed toward the left My logic is that it has to be pointed to the right to balance out the forces to make them zero. Is 4.3N the right magnitude of the 2 velocities?

#### fzero

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From what you describe, you have the direction of the 3rd vector correct. If you'd answer my questions from post #4, you'd have a strong hint about how to compute the magnitude of the force.

#### preluderacer

It means the acceleration is zero. Im so confused are u implying that my magnitude is wrong?

#### fzero

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It means the acceleration is zero. Im so confused are u implying that my magnitude is wrong?
I'm just trying to explain to you how to verify whether your magnitude is correct. If the original 2 vectors were more complicated, your method would not have worked.

If the acceleration is zero, what does that imply about the sum of all of the forces? Rearranging the sum will give you a relationship between the 3rd force and the other two. This will let you compute the magnitude of the 3rd force.

#### preluderacer

The sum of forces are zero

#### fzero

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Gold Member
Can you write an expression for the 3rd force in terms of the first two? How about computing the magnitude of the 3rd force from that?

#### preluderacer

You're losing me =( sorry. Iam so confused now.

#### fzero

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Gold Member
$$\vec{F}_1+\vec{F}_2+\vec{F}_3=0,$$

can you solve this for $$\vec{F}_3$$? Then compute $$|\vec{F}_3|$$.

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