How Do You Calculate Magnitude of Acceleration from Multiple Forces in Physics?

[ganondorf29]

Homework Statement

Three forces in the x-y plane act on a 3.40 kg mass: 9.10 N directed at 25o, 12.40 N directed at 156o, and 4.70 N directed at 259o. All angles are measured from the positive x-axis, with positive angles in the Counter-Clockwise direction. Calculate the magnitude of the acceleration.

Homework Equations

F=ma
Rx = F₁cos(theta) - Quadrant 1
Ry = F₁sin(theta) - Quadrant 1
R = (Rx^2 + Ry^2)^1/2

The Attempt at a Solution

I tried to find the x and y components of each force. Then I added the square of the x-components and took the square root of that answer and I did the same with the y-components. Finally I took the answers from the last step and took the square of them and then the square root of them added. Finally I plugged in that force into F=ma and tried to solve for a, but it doesn't work. I think I am doing something wrong, in that I am not sure what to do about the x,y components that are negative.

 

[tiny-tim]

Hi ganondorf29!

Then I added the square of the x-components and took the square root of that answer …

ah … that's where you're going wrong …

these are vectors, so you use ordinary vector addition …

just add the x-components without squaring first.