Resolving 3D Forces for Determining xyz Components

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In summary, the conversation is about resolving a force into xyz components. The force is 200 N and when viewed at 35 degrees from the horizontal, the y-component is 114.72 N and the x-component is 163.83 N. However, when viewed at 12 degrees from the horizontal, there seems to be a mistake as the resulting force does not equal the magnitude of 200 N. Upon further examination, it is discovered that the line representing the force in the second diagram should actually be the xy plane at 102 degrees, leading to correct calculations.
  • #1
LukaD
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Hi, I am trying to resolve a force into xyz components and I think I'm getting a bit confused.

When viewed face on the force is 35 degrees from the horizontal.

When viewed from above the force is at 12 degrees from the horizontal (not sure if one would refer to it as the horizontal but see the attached figure for clarity).

The magnitude of the force is 200 N.

The attempt at a solution:

Fy= (200)cos55 = 114.72 N
Fx=(200)cos35 = 163.83 N
Fz=(200)cos12= 195.63 N

However, F should equal sqrt{(Fx2+Fy2+Fz2)} but it does not, so I know I'm going wrong somewhere. Any hints?
 

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  • #2
Hi, LukaD.

The two projections both have the force labeled as F. But is F in any of them the actual, full magnitude of 200N?
 
  • #3
F is the full magnitude yes. F is the same force in both diagrams viewed from different angles.
 
  • #4
Heh, I wasn't actually asking a question. I was pointing out the mistake. Can you take it from here, or do you need another clue?
 
  • #5
Oh I see, I drew the diagram wrong, the line representing F in the second diagram should actually be the xy plane, so it's 102 degrees not 12. Is that right? It seems to work out!
 

FAQ: Resolving 3D Forces for Determining xyz Components

1. What is the purpose of resolving 3D forces?

The purpose of resolving 3D forces is to determine the individual components (x, y, and z) of a force vector that acts in three-dimensional space. This is necessary in order to accurately calculate the overall effect of the force on an object.

2. How do you determine the x, y, and z components of a 3D force?

To determine the x, y, and z components of a 3D force, you can use trigonometric functions and vector analysis. First, determine the angle between the force vector and each coordinate axis. Then, use the cosine and sine functions to calculate the x and y components, respectively. For the z component, use the dot product of the force vector and the unit vector in the z direction.

3. What are some examples of real-world applications of resolving 3D forces?

Resolving 3D forces is important in many fields, such as engineering, physics, and architecture. Some examples of applications include designing structures that can withstand forces from different directions, calculating the motion of objects in three-dimensional space, and understanding the effects of wind and water currents on structures such as bridges and buildings.

4. Can you resolve 3D forces without using trigonometric functions?

No, in order to accurately determine the components of a 3D force, trigonometric functions are necessary. These functions allow us to calculate angles and side lengths in right triangles, which are essential for resolving forces in three dimensions.

5. Are there any common mistakes to watch out for when resolving 3D forces?

Yes, some common mistakes when resolving 3D forces include using the wrong angle or forgetting to include the sign of the force component. It is also important to remember that forces acting in opposite directions have opposite signs for their components. Double-checking calculations and using clear diagrams can help avoid these mistakes.

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