How Do You Calculate Acceleration and Angle from Multiple Forces in Physics?

[alexandra91]

Homework Statement

Hey, I'm not sure how to continue...
Forces of 10N north, 20N eat and 5N south act on an object of mass 4kg. How big is its acceleration and what angle does it make with the force in the eat direction.

Homework Equations

F=ma

The Attempt at a Solution

I drew and free body diagram. Now I'm not sure if its correct to add up all three forces to get the accerlation. Or do i have to figure out the angle through using cos sin ect.
Thanks for your help
Alex

 

[berkeman]

Yes, add up the vector components to get the net vector force, and use F=ma to get the resulting acceleration.

Welcome to the PF, BTW.

 

[alexandra91]

thank you very much. Now i found the acceleration but how do i now fund the force towards the east direction.

 

[berkeman]

thank you very much. Now i found the acceleration but how do i now fund the force towards the east direction.

You must first find the components of the net force vector. Since the coordinate system is (e,n) instead of (x,y), you just find the total Fe and the total Fn, and plug those into the vector equation F=ma to find ae and an.