How Do You Calculate the Net Gravitational Force on a Mass in a 3D Force System?

[harrysawizard]

Homework Statement

A cube has an edge length of 2.0m. At each corner there is a different spherical mass. The masses are 1kg, 2kg, 3kg, 4kg, etc. u to 8kg. They Coordinate system: 1kg is at the origin and the 4kg, 2kg, and 8kg masses lie on the positive x, y, and z axis respectively. What is the net gravitational force acting on the 1kg mass? (magnitude and direction)

(I know I don't have an image, but it won't let me insert one and at the point I'm at, I think I'm past needing the image)

Homework Equations

To find the force each mass is putting on the 1kg mass, I used equation:
F = G m₁m₂/r²
where G is 6.67 * 10^-11 and r is the distance between 2 objects.

I substituted 1 for m₁ and 2 for r, coming up with simplified equation:
F = (6.67*10^-11) (m₂) / 4

The Attempt at a Solution

I used that equation to find the x, y, and z components of every force.
I then added to find $$\Sigma$$x, $$\Sigma$$y, and $$\Sigma$$z.
I got:
$$\Sigma$$x = 3.0015 * 10^-10
$$\Sigma$$y = 2.668 * 10^-10
$$\Sigma$$z = 4.3355 * 10^-10

My question is, what do I do now to find the total magnitude of the force?
Once I get that, how do I find the angle / direction of the force?

If I were to use the 3-d distance equation, how would I find the angle?
I'm completely stuck, so any help is greatly appreciated!

Thanks so much guys, this is my first day on the site so I don't quite know what I'm doing! (:

 

[harrysawizard]

is no one answering because my wording is way off or is it something else? just wondering!

 

[tiny-tim]

welcome to pf!

hi harrysawizard! welcome to pf!

(have a sigma: ∑ )

My question is, what do I do now to find the total magnitude of the force?
Once I get that, how do I find the angle / direction of the force?

you've found F_x F_y and F_z …

so the force is the vector (F_x,F_y,F_z) …

its magnitude is √(F_x² + F_y² + F_z²), and for the unit vector of the direction, just divide by the magnitude!

(btw, you can't generally expect quick answers here … people are asleep, or doing something … you should give it 24 hours before worrying)

 

[harrysawizard]

thanks so much for all your help!
i used the distance formula for 3 dimensions and get 5.9096 * 10^-10 to be the final magnitude.

We've only covered a bit of unit vectors in math, and we haven't touched them at all in physics, so how would I use them to find the direction?

When it's just 2 dimensions that I'm finding the net force of, I'll break the vector down into x and y and use the inverse tangent to find $$\Theta$$, but I just don't understand how to approach it in 3 dimensions.

 

[tiny-tim]

hi harrysawizard!

(have a theta: θ )

… When it's just 2 dimensions that I'm finding the net force of, I'll break the vector down into x and y and use the inverse tangent to find $$\Theta$$, but I just don't understand how to approach it in 3 dimensions.

You could use Euler angles (see http://en.wikipedia.org/wiki/Euler_angles" ), but i don't think anybody does for something like this …

you either specify the unit vector, or you just leave it as (F_x,F_y,F_z)