Resolving 3D Forces: A Guide for Determining xyz Components

[LukaD]

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:

F_y= (200)cos55 = 114.72 N
F_x=(200)cos35 = 163.83 N
F_z=(200)cos12= 195.63 N

However, F should equal sqrt{(F_x²+F_y²+F_z²)} but it does not, so I know I'm going wrong somewhere. Any hints?

 

[Bandersnatch]

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?

 

[LukaD]

F is the full magnitude yes. F is the same force in both diagrams viewed from different angles.

 

[Bandersnatch]

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?

 

[LukaD]

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!