# Vector Addition - Find Angle of Resultant Force

• razored
In summary, the discussion was about finding the angle between two vector forces of equal magnitude, where the resultant is one-third of either original force. The Pythagorean Theorem was mentioned as a possible equation to use, and the solution involved drawing a diagram and forming a parallelogram to find the answer of 160.8 degrees.
razored

## Homework Statement

Find the angle between two vector forces of equal magnitude, such that the resultant is one-third as much as either of the original forces.

## Homework Equations

Pythagorean Theorom, I assume

## The Attempt at a Solution

This is from Schaum's 3000 Problems in physics, page 7, # 1.35... I don't understand their explanantion thus I don't understand where to begin. Can someone give me a lead?

The answer is 160.8 degrees by the way...

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First off, let's state the Pythagorean Theorem as a^2 + b^2 = c^2. Cool.

Next since we are using that equation we know that the answer involved has a right angle it it somewhere.

Draw a picture of a right triangle then make it into a rectangle. Draw a line from corner to corner and going threw the other side(the size where the first right angle was)
http://img182.imageshack.us/img182/3530/pythaghelpvw8.png

Then play around with the numbers and angles and see if you can come up with the same answer. I hope this helps you out a little bit! Although I am not exactly sure on how to solve it myself.

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I don't have a program that can do any of that stuff?(like the diagram you just did)

Dont you have pen and paper? I did that on my paper before I made it with photoshop

I've figured it out :D Thanks. I simply formed a parallelogram and was able to get the answer.

No prob, Glad you got it!

## 1. How do you find the angle of the resultant force in vector addition?

In order to find the angle of the resultant force, you will need to use trigonometric functions such as sine, cosine, and tangent. First, find the x and y components of each vector and add them together. Then, use the inverse tangent function to find the angle of the resultant force.

## 2. Why is it important to find the angle of the resultant force in vector addition?

The angle of the resultant force is important because it determines the direction in which the resultant force is acting. This is crucial in understanding the overall motion and forces involved in a system.

## 3. Can the angle of the resultant force be negative?

Yes, the angle of the resultant force can be negative. This would indicate that the resultant force is acting in the opposite direction of the positive x-axis.

## 4. Are there any special cases when finding the angle of the resultant force?

Yes, if the resultant force is zero, the angle cannot be determined as the vectors are in equilibrium and have no net direction. Additionally, if the vectors are perpendicular, the angle would be 90 degrees or pi/2 radians.

## 5. How can I visualize the angle of the resultant force in vector addition?

You can use a graphical method such as the head-to-tail method or the parallelogram method to construct a visual representation of the vectors and the resultant force. The angle of the resultant force can then be measured using a protractor or calculated using trigonometric functions.

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