X- and Y-Components of a Force Vector

Example: The magnitude of a vector F > is 10 units and the direction of the vector is 60 ° with the horizontal. Find the components of the vector. F x = F cos 60 ° = 10 ? 1 2 = 5. F y = F sin 60 ° = 10 ? 3 2 = 5 3. So, the vector F > is 5, 5 3. The x component is a scalar (a number, not a vector), and you write it like this: vx. The y component of the ball’s velocity vector is vy. Therefore, you can say that. v = (vx, vy) That’s how you express breaking a vector up into its components.

This article discusses the x- and y-components of a force vector. Understand that the diagrams and mathematics here could be applied to any type of vector such as a displacement, velocity, or acceleration vector. For an understanding of vectors see the Vectors section of the Physics Department. For an understanding of right triangle trigonometry see the Trigonometry and Right Triangles section of the Trigonometry Realms. When you are finished with the material here, be sure to visit the Force Component Machine.

It will show you how the positive and negative signs for the force components work for any direction that the two dimensional force vector may be pointing. A force vector can be expressed in two dimensions on the x, how to play the harmonica key of c plane.

For example, imagine the surface of a table top to be an x, y plane. Objects can be pushed across this table surface in several different directions, not just parallel to the length or width of the table. Objects can be pushed across a table top at a slanted direction relative to the edges of the table top.

In the animation below we see several different directions in which you could push an object across a table top, or the several directions one can apply a force to an object on an x, y plane. The object being pushed is the green disk, and the force vector is the black arrow:. Force vectors like the one shown above are said to be two dimensional force vectors. You can think of them as forces that have a part that pushes right or left ffind, and that have another part that pushes up or down.

These parts of the force are called the components of compoment force. The component that pushes right or left is called the x-componentand the part that pushes up or down is called the y-component. Mathematicallythe components act like shadows of the force vector on the coordinate axes. In the picture directly below we see **how to find the x component of a vector** vind vector on the x, y plane.

The force vector is white, the x-axis is red, the y-axis is green, the origin is white. It is common to position force vectors like this with their tails at the origin. The light in this picture is comoonent directly into the x, y plane, and we see no shadows from this view. For our purposes here the axes and vector how much formula is a newborn supposed to eat drawn unusually wide; they are normally drawn as thin lines in diagrams.

Vctor below is the same scene yow another viewpoint. The light is now shining vectot from above. That is, the light is shining straight down parallel to the y-axis. Note the shadow of the vector on the componenr. This shadow represents the x-component of the force vector. Next, below, we have the same situation except the direction of the light has changed.

The light now is shining from the how to get from lisbon to lagos, parallel to the x-axis.

A shadow of the force vector can be seen on the y-axis. This shadow, mathematically, is the y-component of the force vector.

The black vectir is the two dimensional force vectorlabeled F. The red vector is the x-component of the force vector, labeled Fx. It would be pronounced 'F sub x'. Vectkr 'x' is actually a subscript, this notation usually looks vrctor this:.

However, in Zona Land Education the subscript's position is often implied, as here, hopefully without any loss of meaning. The green vector is the y-component of the force vector, labeled Fy, pronounced 'F sub y'. The components of the force vector can also be arranged this way, forming a right triangle :. If what is the meaning of echogenic kidney know the size of the two dimensional force vector, the black one in the above diagram, and the angle it makes with the x-axis, then tue can use right triangle trigonometry to find the values for the components.

In the following diagram 'A' is the angle that the two dimensional force vector makes with the x-axis. Using right triangle trigonometry, Fx is adjacent to angle A, Fy is opposite to angle Componetn, and F is the hypotenuse, as:. The above diagram shows how to keep old newspapers the trigonometry is usually presented - the cosine function is associated with the x-component and the sine function is associated with the y-component.

However, it is not the only way to think about it. The following is a legitimate vector diagram for this force vector, but the x-component is calculated with the sine function, the y-component with the cosine. Note we are using angle B now; it's a different angle:. Remember, the diagram and formula derivation above, although correct within its own context, is unusual as far common textbook examples are concerned. They are usually set up to solve for the x-component using the cosine function and the y-component using the sine, as was presented originally with angle 'A'.

There is good reason for this. If the direction of the force vector is given in standard position, as angle A could be interpreted, then the original derivations give correct results. When right triangle trigonometry is used, you componebt to consult your vector diagram to decide which way the components are pointing and then ocmponent the correct sign to your calculated values as a last step in your solution.

The right triangle trigonometry as presented here will always yield positive results. It is really only solving for vecto lengths of the legs of a right triangle, as one might do in Geometry studies. F, the value for the size of the two dimensional hoq vector, is always stated as a positive number. Cpmponent object is pushed across a table top with a ifnd of What are the x- and y-components of this force?

Right triangle trigonometry: The cosine of an acute interior angle of a right triangle is equal to the length of the adjacent side to the angle divided by the length of the hypotenuse. Use the go of the force vectors as the lengths of vectlr adjacent side and hypotenuse. Fx is the adjacent side, F is the hypotenuse. Final result stated with units. Note compoennt positive value of the final result. It is positive because this is an vvector, and in the diagram it is aimed to the right.

As usual with numbers, the plus sign is optional. Right triangle trigonometry: The sine of an acute interior angle of a right triangle is equal to the length of the opposite side to the angle divided by the length of the hypotenuse. Use the length of the force vectors as the lengths of the opposite side and hypotenuse. Fy is the opposite side, F is the hypotenuse. Note the negative value of the final result. It is negative because this is an y-component, and in the diagram it is aimed down.

Always remember to check back to the diagram to make sure you have the sign of the components correct.

Questions and Answers

Aug 21, · Finding x component of $vec{v}$ $v_x=-|\vec{v}|\cos\theta = \ cos (70^{\circ}) \approx $ Here negative sign appears because our vector is in the second quadrant where all values of x are negative as can be seen clearly from the figure and values of y are all positive. Finding y component of $\vec{v}$. The components of a vector in two dimension coordinate system are usually considered to be x-component and y-component. It can be represented as, V = (v x, v y), where V is the vector. These are the parts of vectors generated along the axes. In this article, we will be finding the components of any given vector using formula both for two-dimension and three-dimension coordinate system. . So to find the x-component, form the vector c = (1,0) and form the product as above (with your input vector), then divide by the length (magnitude!) and take the arc-cosine of the result. For the y-component, repeat the above with c = (0,1).

We already know what are vectors in physics and How to represent vectors graphically. In this article, we will look at the way to find vector components from magnitude and angle. Let us proceed further with a problem which is how to find the components of a vector given magnitude and angle. So our problem is to.

In terms of components vector v is written as. From trigonometry we know that for any right angled triangle with hypotenuse H , base B and perpendicular P. You can verify this answer by finding the magnitude of the vector using the components of the vector we have calculated.

Let us look at our another solved example where we would find vector components from magnitude and direction. Here negative sign appears because our vector is in the second quadrant where all values of x are negative as can be seen clearly from the figure and values of y are all positive. Similarly you can find the vector components from magnitude and angle even if vector lie in third or fourth quadrant.

Finding vector components from magnitude and angle Let us proceed further with a problem which is how to find the components of a vector given magnitude and angle. Let us now represent our vector graphically from the information given in the problem. Notify of. Inline Feedbacks. Would love your thoughts, please comment.

Thanks Anson. Great generosity of spirit.