Statics: Forces in Cartesian Vector form

In summary, the conversation is discussing the calculation of forces in Cartesian vector form for cable AD, with a known magnitude of 14 kips, an x-component value of -6.216, and a z-direction angle of 83.63°. The goal is to find the coordinates of point D on the x-z plane, given that point A is at (0, 20, 0). There is some confusion about the meaning of the x-component and its relation to the overall magnitude of the tension in cable AD.
  • #1
rico22
51
0

Homework Statement


For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216, the direction angle in the z-direction is 83.63°, and Fy is less than zero. Find forces in Cartesian vector form, coordinates of point D if it lies on the x-z plane and point A is (0, 20, 0).


Homework Equations





The Attempt at a Solution


I know that the z component of TAD is 14000(cos83.63°)= +1553.28[itex]\hat{}k[/itex] but I don't know how to solve for the x and y components. Any help would be greatly appreciated.
 
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  • #2
But it tells you the x-component, no? And you know the z component and the overall magnitude, so the magnitude of the y-component should be easy. Is it the sign that has you stumped?
 
  • #3
im just not sure if this means that its -6.216i for the position vector of AD or -6.216i for the actual x component for the tensile force...I just don't see how it could be -6.216 for the tensile force when the magnitude is 14000 lbs.

Having the x component of the position vector of AD doesn't really help me because I can't solve for the magnitude of the position vector. Maybe I am just making it more complicated than what it really is.
 
  • #4
rico22 said:
im just not sure if this means that its -6.216i for the position vector of AD or -6.216i for the actual x component for the tensile force...
In that case you will need to state the question exactly as given. I have the impression you have reworded it somewhat.
 
  • #5
I wrote it exactly as it was given.
 
  • #6
rico22 said:
I wrote it exactly as it was given.
Then it is poorly worded.
For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216
This seems to be leaping into the middle of a question. There has been no mention of any tension in the cable, so what is this supposed to be the magnitude of? It could be windshear! If we assume it refers to tension in AD, then it is logical to suppose the 'x-component' is a component of that tension. I agree the mismatch in precision is a worry, but I see no other basis on which to proceed.
 
  • #7
ok thank you very much...
 

1. What is statics?

Statics is a branch of mechanics that deals with the study of objects at rest or in equilibrium. It focuses on the analysis of forces acting on an object without any consideration of its motion.

2. What is meant by forces in Cartesian vector form?

Forces in Cartesian vector form refer to the representation of forces using Cartesian coordinates. In this form, forces are described by their magnitude and direction in terms of x, y, and z components.

3. How are forces resolved in Cartesian vector form?

Forces can be resolved in Cartesian vector form by using trigonometry and vector addition. The x, y, and z components of a force can be determined by breaking it down into its horizontal and vertical components.

4. What is the importance of using Cartesian vector form in statics?

Using Cartesian vector form in statics allows for easier and more accurate analysis of forces. It allows us to break down forces into their individual components, making it easier to determine the overall effect of multiple forces acting on an object.

5. Can forces in Cartesian vector form be used to analyze any type of object?

Yes, forces in Cartesian vector form can be used to analyze any type of object as long as it is in a state of static equilibrium. This means that the object is not moving or rotating, and all the forces acting on it are balanced.

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