# Homework Help: How to Express the force as a Cartesian vector?

1. Aug 28, 2011

### JON123

I am having trouble solving this problem, I also have it attached:

http://i160.photobucket.com/albums/t193/John123321_bucket/Capture.png

Here is a short version of how I got my answers, but it says it’s wrong:

X=500cos(30)=433N

i= 433sin(45)=306.2
j=-433cos(45)=-306.0
k=-500sin(60)=-250

If you can, please explain what I’m doing wrong, thanks.

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2. Aug 29, 2011

### Hootenanny

Staff Emeritus
Welcome to Physics Forums.
You can tell that the answer is wrong immediately as the highlighted line would suggest that F has a component in the negative z-direction. However, if you refer to the picture, it is clear that F acts "upwards" rather than "downwards". I would also check the angle (it shouldn't be sin(60).

3. Aug 29, 2011

### JON123

Thanks for the reply. The force is acting in the negative direction because it's 60 degrees from the negative z-axis, meaning that it's 30 degrees bellow the x&y-axis. And I just had a typo on the third line, it was supposed to be k=-500cos(60)=-250 giving me the z-component. I did figure out the answer and it was 250i-354j-250k. I got it using 500sin(30)i-500cos(45)j-500cos(60)k. I was just wondering if this is the right way to setup the problem.

4. Aug 29, 2011

### Hootenanny

Staff Emeritus

5. Aug 29, 2011

### vela

Staff Emeritus
Explain how you came up with 500 sin 30 for the x-component.

6. Aug 30, 2011

### JON123

I figured out how to solve the problem, and i see what i was doing wrong. I came up with the 500cos(30) by going at the problem backwards because I had found out the answer from someone, but i see that's not the right way to get the answer. I solved it by using the formulas:
Fx=Fcos(alpha)
Fy=Fcos(beta)
Fx=Fcos(gamma)

Because i didn't have alpha for Fx, i found Fy & Fz and used the magnitude to solve for Fx. F=sqr(Fx^2+Fy^2+Fz^2) -> Fx=sqrt(500^2-Fy^2+Fz^2)