# Vector Addition Using Components

• Turquoise
In summary, the problem involves two forces, 40.0 N and 30.0 N, acting on a mass at different angles. Using the Pythagorean Theorem and trigonometric functions, the magnitude of the resultant force is found to be 15.6 N. The key is to subtract, not add, the x and y components when finding the magnitude.
Turquoise

## Homework Statement

Two forces are acting on a mass. One of the forces is a 40.0 N force and the other force is 30.0 N at the angles shown below:

The magnitude of the force is:
a) 15.3 N
b) 15.6 N <-- correct answer
c) 46.6 N
d) 69.0 N

## Homework Equations

Pythagorean Therom
Cosine, Sine

## The Attempt at a Solution

Vector

X component

A ax = (30.0N) Cos 20.0 = 28.2 N
B bx = (40.0 N)Cos 40.0 N = 30.6 N

Y component
ay = (30.0N)Sin 20.0 = 10.3 N
by = (40.0 N) Sin 40.0N = 25.7 N

C = ax+bx = 58.8 N Cy = 36 N

C = cx^2 + cy^2
C = 58.8N^2 + 36 N^2
C = 69 N

I keep getting 69 N and its not the correct answer. The correct answer is 15.6. I'm following the directions from my notes, but it gives me 69 every time. Help! What am I doing wrong?

Vectors have magnitude and direction.

Your ax and by are pulling in opposite directions, so are ay and by.

So subtraction, not addition, is the order of the day.

Then the magnitude of the resultant vector C will be the square root of the sum of the squares of the x and y components

Thanks! I got the correct answer now ;)

## 1. What is vector addition using components?

Vector addition using components is a mathematical process used to find the resultant vector of two or more individual vectors. It involves breaking down each vector into its horizontal and vertical components and then adding the corresponding components together to get the resultant vector.

## 2. How do you find the components of a vector?

The components of a vector can be found using trigonometric functions such as sine and cosine. The horizontal component (x) is found by multiplying the magnitude of the vector by the cosine of its angle, and the vertical component (y) is found by multiplying the magnitude by the sine of its angle.

## 3. What is the difference between scalar and vector quantities?

Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include temperature and speed, whereas examples of vector quantities include displacement and velocity.

## 4. Can you add vectors with different directions?

Yes, vectors with different directions can be added using vector addition using components. The resultant vector will have both magnitude and direction, which can be found using the Pythagorean theorem and trigonometric functions.

## 5. What is the importance of vector addition using components in science?

Vector addition using components is essential in science as it allows us to accurately calculate the resultant vector of multiple forces acting on an object. This is crucial in understanding the motion and equilibrium of objects, and it is used in various fields such as physics, engineering, and navigation.

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