# Question about making vectors equilibrium

• preluderacer
In summary, the figure shows two forces of equal magnitude acting on an object, with a common magnitude of 4.6 N and an angle of 40° between them. To find the third force that will cause the object to be in equilibrium, the magnitude of the force should be 4.3 N and pointed in the opposite direction. This means that the acceleration of the object is zero and the sum of all forces is also zero. To compute the magnitude of the third force, an expression can be written in terms of the first two forces and solved for the third force.
preluderacer

## Homework Statement

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?

## 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?

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

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

"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?

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?

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.

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

preluderacer said:
It means the acceleration is zero. I am 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.

The sum of forces are zero

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?

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

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

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

## 1. How do you define a vector equilibrium?

A vector equilibrium is a state in which the sum of all the forces acting on an object is equal to zero. In other words, the object remains stationary or at a constant velocity.

## 2. What is the significance of vectors in determining equilibrium?

Vectors are important in determining equilibrium because they represent the magnitude and direction of forces acting on an object. In order for an object to be in equilibrium, the sum of all the forces acting on it must be equal to zero, which can be determined through vector addition.

## 3. How do you calculate the resultant vector for multiple forces acting on an object?

To calculate the resultant vector, you need to first determine the individual vectors for each force acting on the object. Then, using vector addition, you can add all the individual vectors together to find the resultant vector, which represents the overall force acting on the object.

## 4. Can an object be in equilibrium if there are multiple forces acting on it?

Yes, an object can be in equilibrium even if there are multiple forces acting on it. This occurs when the vector sum of all the forces acting on the object is equal to zero, meaning the forces are balanced and the object remains stationary or at a constant velocity.

## 5. What are some real-life examples of objects in vector equilibrium?

Some examples of objects in vector equilibrium include a book sitting on a table, a person standing still on a flat surface, or a ball hanging from a string. In all of these cases, the forces acting on the object are balanced, resulting in a state of equilibrium.

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