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 [tex]F_1=(Gm_1m_2/r_1^2)[/tex] and [tex]F_2=Gm_1m_3/r_2^2[/tex].

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

[tex]F_1=1.854*10^-10[/tex]
[tex]F_2=-2.085*10^-10[/tex]

[tex]F_x=F_1+F_2=-2.31*10^-11[/tex] N

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

Is this correct?

 

[Doc Al]

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

 

[quicknote]

Yes, your calculations are correct. The net gravitational force in this problem is in the x-direction, as there is no component of force in the y-direction due to the arrangement of the spheres. The magnitude of the net gravitational force is 2.31*10^-11 Newtons.