Question

A 5.0 Kg mass is subject to three forces: an 8.0N force pulling due north, a 5.0N force pulling due South, and a 4.0N force pulling due West. What is the magnitude and direction of the resulting acceleration?

Answer 1

Fx = 8.0n*cos(90)+5.0n*cos(270)+4.0n*cos(180) = -4
Fy = 8.0n*sin(90)+5.0n*sin(270)+4.0n*sin(180) = 3

sqrt((-4)^2 + (3)^2) = 5

arctan(3/-4) = 138.59 degrees

direction = 5/5 = 1

Can you tell me if I am on the right path for this question.

Answer 2

I'm not sure what you've been learning in your physics class, but I wouldn't even bother with the trigonometry. This is a fairly simple vector addition problem! You looked like you were on the right track but I can't say i looked too much at your numbers...

Anyways heres how you could do it with vector addition!


As I tried to illustrate, your north and south forces directly oppose each other and partially cancel, leaving you with a net force of 3 N northward. The westward force has nothing opposing it (no counteracting easterly force) so it remains the same. Hence, your resultant vector would be <-4,3> where east west is your x axis (east is positive) and north south is your y axis (north being positive, so that it aligns with standard Cartesian coordinates)

You can calculate the resultant magnitude by finding the length of this vector.
Its probably easiest to think of it as a triangle and use pythagorean theorem, or you can think of it as the distance formula from the origin:



Alternately, if you realized that this is a 3,4,5 right triangle, you can just tell that the hypotenuse has a length of 5. Therefore the magnitude of the force is 5 N (looking back you had that right!)

I'm not sure where your direction of 5/5 = 1 came from though. I'd stick with an angle as a direction, and just be sure to specify where the angle is starting from.

Your arctan calculation was fine and You should put that as your direction, noting that its 138.59 degrees counterclockwise from east. (alternately you could subtract 90 and say its from North. really up to you as long as youre clear!)

Overall your work was good. Hope this cleared things up and let me know if you have any questions!