Three forces simultaneously acting on an object

[kathyt.25]

Homework Statement

Forces of 10.5 N north, 19.3 N east, and 15.4 N south are simultaneously applied to a 3.81 kg mass as it rests on an air table. What is the magnitude of its acceleration?

Homework Equations

F=ma

The Attempt at a Solution

Well I got the resultant force for the y direction to be 4.9N South. And from here I have no idea what to do, I started drawing triangles of the forces and just placing diagonal lines just so i can connect them, while knowing I can't mathematically do that.

Thanks for the help!

 

[rl.bhat]

Using the relevant equation, find ay along North-south direction.
Similarly find ax.
ax and ay are perpendicular to each other. So find the resultant a.

 

[kathyt.25]

would I use the force of gravity as a part of the ay force? So it would be 15.4 + (force gravity) - 10.5?

 

[jdwood983]

would I use the force of gravity as a part of the ay force? So it would be 15.4 + (force gravity) - 10.5?

I wouldn't think you would use gravity. This problem is looking acceleration in the plane (N/S & E/W).

You should just use the forces and mass the give you:

$$\left(\frac{ \sum F_{N,S}}{m}\right)^2+\left(\frac{\sum F_{E,W}}{m}\right)^2=a^2$$

and make sure you keep you signs correct.