Gravitation Problem Homework: Calculate Magnitude & Direction

[Gauss177]

Homework Statement

Four 8.0-kg spheres are located at the corners of a square of side 0.50 m. Calculate the magnitude and direction of the gravitational force on one sphere due to the other three.

Homework Equations

F = (G*m1*m2)/r^2

The Attempt at a Solution

I labeled each sphere as A, B, C, and D, like this:
B C

A D

I chose A as my "focus," and found the force B, C, and D pulls on A.

B pulls on A with: (6.67*10^-11)(8)(8) / .5^2 = 1.71*10^-8 N
C pulls on A with: (6.67*10^-11)(8)(8) / .707^2 = 8.54*10^-9 N
D pulls on A with: 1.71*10^-8 N

Is there anything wrong with the numbers above? I don't know what to do from here on to find the magnitude of the total gravitational force and the direction (an angle measured counterclockwise from the positive x-axis) it acts in.

Thanks for any help.

 

[Saketh]

It will probably help you to draw out a diagram of each force acting on A. Then you can see which components to add to find the net force.

You've found the magnitudes correctly, it seems (I haven't plugged your numbers into a calculator).

If you want a never-fail way to solve this kind of problem, find each force as a vector in unit vector form. Then add them up to find the net force on A. Granted, this could be a waste of time in your opinion, but at least it's consistent. If you don't understand what this means, you should learn it, as it helps you visualize what is going on.

 

[Gauss177]

**Edit**
I figured out the angle, and I end up with the right answer now. Thanks for your help.