Expert: Scott A Wilson - 7/28/2010

Question
Three forces of magnitudes of 250 lbs 60 degrees N of W, and 200 lbs S act on an object.Find the direction and magnitude of the the resultant force. (This is out of my league so be gentle)
Thank you for your time.

Answer
For the force that is 60° N of W, take 1/2 of the force to the west and 0.866 of the force to the north.  For the force going to the south, subtract this from the force to the north to give the result of how much force to the north.

It sounds like there are 3 forces going 60° N of W at 250lbs, which means a total of 750 lbs. in this direction.  This gives a force of 375 lbs of force to the west and (750 lbs)*0.866, which is almost 650 lbs, of force to the north.  Since there is an additional 200 lbs of force to the south, that gives a net force of 650-200=450 lbs to the N.

Thus, the total force is 450 lbs to the north and 375 lbs to the west.
This means tan(Θ) = 450/375, where Θ is the angle north of west.
Since the force is the squareroot of the the sum of the squares to the north and west,
it is around 585 pounds when rounded to the nearest 5.