Find the force-couple system check my answer please

[doubled]

Homework Statement

The problem is actually for a car but I'm going to simplify it so it''s easier to type on here. Basically there's a point (let's call it point A) located at (-1,-.5)m. An upward force A acts at point A with 7000N and a horizon force F acts on point A but points left so it's negative. The resultant force due to A&F makes an angle 15 deg w/ respect to the vertical. Determine the equivalent force couple system at the origin. Basically I find the moment.

Homework Equations

i choose to do the cross product M=rxR, where R=resultant force

The Attempt at a Solution

1. I found force F by doing tan(15)=F/7000 which gave me F=1875.6N <<<magnitude or -1875.6N
2. so R=7000i-1875.6j N
3. Then I found r by doing point A-origin which would be <-.5,-1>-<0,0> which got me -1i-.5j m
Then I took the cross product rxR and got -7938 N.

The answer in the book was 7938 N. I don't understand why they had a positive answer, it's obvious that the answer should be negative because the moment is acting in a clockwise direction.

 

[tiny-tim]

welcome to pf!

hi doubled! welcome to pf!

… there's a point (let's call it point A) located at (-1,-.5)m. An upward force A acts at point A with 7000N and a horizon force F acts on point A but points left so it's negative.
…
… it's obvious that the answer should be negative because the moment is acting in a clockwise direction.

yes, you're right …

(but it should be Nm, not N, of course)

A is left and down from the origin, the force is left and up, it clearly goes to the left of the origin, so the moment is clockwise, which is negative

The problem is actually for a car …

you haven't over-simplified this, have you? clockwise from one side of the car is anti-clockwise from the other

 

[doubled]

Umm i don't think so, but thanks. The way they drew the forces was in a xy plot which the 7000N going up and F going left at the same point