Net gravitational force problem in a straight line?

[erik-the-red]

Question

In the figure attached, what is the magnitude of the net gravitational force exerted on the 0.100-kg uniform sphere by the other two uniform spheres? The centers of all three spheres are on the same line.

So, I'm thinking $$F_1=(Gm_1m_2/r_1^2)$$ and $$F_2=Gm_1m_3/r_2^2$$.

$$F_1=(6.673*10^-10)(.100)(10.0)/(.600^2)$$
$$F_2=(6.673*10^-10)(.100)(5.00)/(.400^2)$$

$$F_1=1.854*10^-10$$
$$F_2=-2.085*10^-10$$

$$F_x=F_1+F_2=-2.31*10^-11$$ N

I don't think there is a force in the y-direction, so $$F=\sqrt(F_x^2)=2.31*10^-11$$ N.

Is this correct?

 

[Doc Al]

Looks good to me. (You did have a few typos in some of your steps.)