# Vectors & Force Physics

1. May 24, 2013

### rico22

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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

θx= cos-1(510/779) ≈49°

θy= cos-1(306/779) ≈67°

θz= 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 im doing wrong. Any type of help would greatly be appreciated.

#### Attached Files:

• ###### phpRKwJ2v.png
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2. May 24, 2013

### barryj

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

Last edited: May 24, 2013
3. May 24, 2013

### rico22

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