# Forces and Vectors adding to zero

• sdoi
In summary, the problem involves finding the third force needed to balance two given forces, F1 and F2. Using vector addition and trigonometric functions, the resultant force is calculated to be 70.6N at an angle north of west. The components of the resultant force can then be used to determine the necessary third force to create a net force of zero.
sdoi

## Homework Statement

Given F1= 36N[25degrees N of E] and F2= 42N [15 degrees E of S], determine the force F3 that must be added to the sum of F1+F2 to produce a net force of zero.

## Homework Equations

Sine law, a/sina= b/sinb
Cosine law: c^2= a^2 + b^2- 2(a)(b) Cos(theta)

## The Attempt at a Solution

I first went about the question by drawing a vector diagram of all the two know forces, and then I broke down each force into horizontal and vertical components.

For F1:
F1y= 36N sin25
F1y= 15.2N

F1x= 36NCos25
F1x= 32.6N

For F2:
F2y= 42NCos15
F2y= 40.5N

F2x= 42NSin15
F2x= 10.8N

Then I added all of the x and y values:
ƩFx= 32.6N +10.8N
ƩFx= 43.4N

ƩFy= 40.5N +15.2N
ƩFy=55.7N

I then went on to find the resultant vector:
F=√43.4N^2 + 55.7N^2
F=70.6N

From this point on I have no idea where to go.

Pay attention to the reference axes for the angle specifications. The angles for the two forces have been specified with respect to different axes, so you'll need to be careful about extracting their components.

Once you've calculated the magnitude of the resultant be sure to also locate it on the Cartesian plane -- you want its angle with respect to some reference axis.

Suppose you were to take the components of that resultant force. What values would you add to each of them in order to leave them at zero? Make those values the components of your "new" vector.

Within my calculations I have used the appropriate angles, right? I've kept each axes in mind.

Did I calculate the resultant correctly? I'm not entirely sure how to find the angle. I do however know from my diagram that it will be some degree N of W.

Without the appropriate angle I cannot begin to draw a proper diagram to find the x and y components

sdoi,

I'm working on it, I can't seem to find it in my PF.

Last edited by a moderator:
sdoi said:
Within my calculations I have used the appropriate angles, right? I've kept each axes in mind.

Did I calculate the resultant correctly? I'm not entirely sure how to find the angle. I do however know from my diagram that it will be some degree N of W.

Without the appropriate angle I cannot begin to draw a proper diagram to find the x and y components

Well, F2 is specified as lying "15 degrees E of S". That would place it in the 4th quadrant with a negative y component...

As for your resultant vector, you can sketch the vector using the components and determine the trig to find an appropriate angle from some axis.

And that simple mistake complicated everything. That pretty much fixes all of the problems I was having. Thank you very much!

## What is the concept of "forces and vectors adding to zero"?

The concept of "forces and vectors adding to zero" refers to the principle of equilibrium, where the sum of all forces acting on an object is equal to zero. This means that the object is either at rest or moving at a constant velocity.

## How can forces and vectors add to zero?

Forces and vectors can add to zero when they are balanced and cancel each other out. This means that the magnitudes and directions of the forces are equal and opposite, resulting in a net force of zero.

## What is the significance of forces and vectors adding to zero?

When forces and vectors add to zero, it means that the object is in a state of equilibrium. This is important in understanding the motion and stability of objects, as well as in engineering and design.

## What are some real-life examples of forces and vectors adding to zero?

Some examples of forces and vectors adding to zero include a book resting on a table, a person standing still on the ground, and a balanced see-saw. In each of these cases, the forces acting on the object are balanced and add to zero.

## How can we use vector addition to analyze forces?

We can use vector addition to analyze forces by breaking down each force into its components (magnitude and direction) and then adding them together using vector addition rules. This allows us to determine the net force and whether it is equal to zero, which indicates equilibrium.

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