Find Force Vector (30N) as Cartesian Vector

In summary, a force vector is a quantity that represents the magnitude and direction of a force, typically represented by an arrow. A Cartesian vector uses x, y, and z coordinates in a three-dimensional space to represent a vector, different from other representations like polar coordinates. To find the force vector (30N) as a Cartesian vector, the formula Fx = Fcosθ and Fy = Fsinθ can be used. Converting a Cartesian vector to other representations involves using trigonometric functions. A force vector can have negative components in a Cartesian coordinate system, indicating the force is acting in the opposite direction of the positive axis.
  • #1
kahless2005
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0
I need to find the Forve Vector (30N) as a Cartesian vector.

Given the information given, I believe that the angles of the Triangle are: 90, 32.37, and 57.63. This gives the projected vector in the x, y plane as 16.1 N.

The answer should be : - 13.2i - 17.7j + 20.3k.

Help?

http://img2.freeimagehosting.net/image.php?fc19261c34.jpg
 
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  • #2
The picture is not serving up correctly. Can you post a link to it?
 
  • #3


Based on the given information, it appears that you are trying to find the Cartesian vector components of the force vector (30N). This can be done by using trigonometry and the given angles of the triangle.

First, we can label the sides of the triangle as follows: the side opposite the 90 degree angle is the hypotenuse (30N), the side opposite the 32.37 degree angle is the adjacent side (16.1N), and the side opposite the 57.63 degree angle is the opposite side (20.3N).

Next, we can use the trigonometric ratios (sin, cos, tan) to find the Cartesian vector components. Recall that the x-component is given by the adjacent side (16.1N) multiplied by the cosine of the angle (32.37 degrees) and the y-component is given by the opposite side (20.3N) multiplied by the sine of the angle (57.63 degrees). The z-component will be 0 since there is no angle in the z-direction.

Therefore, the Cartesian vector components of the force vector (30N) can be written as:

Fx = 16.1N * cos(32.37 degrees) = 13.2N
Fy = 20.3N * sin(57.63 degrees) = 17.7N
Fz = 0

Hence, the Cartesian vector for the force vector (30N) would be -13.2i - 17.7j + 0k.

I hope this helps!
 

What is a force vector and how is it represented?

A force vector is a quantity that represents the magnitude and direction of a force. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the force.

What is a Cartesian vector and how does it differ from other vector representations?

A Cartesian vector is a vector that is represented using Cartesian coordinates, which are x, y, and z coordinates in a three-dimensional space. This is different from other vector representations, such as polar coordinates, which use magnitude and angle to represent a vector.

How do you find the force vector (30N) as a Cartesian vector?

To find the force vector (30N) as a Cartesian vector, you can use the formula Fx = Fcosθ and Fy = Fsinθ, where F is the magnitude of the force (30N) and θ is the angle at which the force is applied. This will give you the x and y components of the force vector, which can then be represented as a Cartesian vector (30N, 0N, 0N).

What is the process for converting a Cartesian vector to other vector representations?

The process for converting a Cartesian vector to other vector representations, such as polar coordinates, involves using trigonometric functions to find the magnitude and angle of the vector. For example, to convert a Cartesian vector (30N, 0N, 0N) to polar coordinates, you would use the formula r = √(x^2 + y^2 + z^2) to find the magnitude and θ = tan^-1(y/x) to find the angle.

Can a force vector have negative components in a Cartesian coordinate system?

Yes, a force vector can have negative components in a Cartesian coordinate system. This simply means that the force is acting in the opposite direction of the positive axis. For example, a force vector with components (-30N, 0N, 0N) would be acting in the negative x direction.

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