# Three forces simultaneously acting on an object

1. Oct 26, 2009

### kathyt.25

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

F=ma

3. 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 cant mathematically do that.

Thanks for the help!

2. Oct 26, 2009

### 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.

3. Oct 26, 2009

### 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?

4. Oct 26, 2009

### jdwood983

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.