How Do You Calculate Resultant Force Vectors and Their Angles?

[rico22]

Homework Statement

a) Express each force as a Cartesian vector.

b) Determine the magnitude and coordinate direction angles of the resultant force acting on the hook.

See figured attached.

Homework Equations

The Attempt at a Solution

First I expressed F1 and F2 into its x, y, and z components.
F1: 300(cos 30°)$\hat{}i$ +0$\hat{}j$ -300(sin30°)$\hat{}k$... this gives 260$\hat{}i$ +0$\hat{}j$ -150$\hat{}k$

F2: 500(cos 45)(sin 45) + 500(cos 45)(cos 30) - 500(sin 45)
250$\hat{}i$ + 306$\hat{}j$ - 354$\hat{}k$

Resultant (FR) = F1 + F2: 510$\hat{}i$ +306$\hat{}j$ - 504$\hat{}k$

magnitude of resultant = √(510²+306²+(-504)²) ≈779 N

θ_x= cos^-1(510/779) ≈49°

θ_y= cos^-1(306/779) ≈67°

θ_z= cos^-1(504/779) ≈130°

But this is wrong its supposed to be magnitude of resultant = 733N with angles of 53.5, 65.3, 133 respectively. I don't really know what I am doing wrong. Any type of help would greatly be appreciated.

 

[barryj]

Double check this: F2: 500(cos 45)(sin 45) + 500(cos 45)(cos 30) - 500(sin 45)
Particulary 500(cos 45)(sin 45)

 

[rico22]

oh wow, ... thanks!... even when I was typing it I didn't catch it...

 

[Ahmed Said]

F2x=500cos(45)sin(30)
that is the right one

 

[PeroK]

F2x=500cos(45)sin(30)
that is the right one

You might be six years too late with that answer!