What Is the Initial Acceleration of the Third Sphere in a Gravitational System?

[kai89]

Homework Statement

3 uniform spheres are located at the corners of an equilateral triangle. each side of the triangle has a length of 1.2 m. two of the spheres have a mass of 2.8 kg. the 3rd sphere (mass unknown) is released from rest. Considering only the gravitation forces the spheres have on each other, what is the magnitude of the initial acceleration of the 3rd sphere?

Homework Equations

F= G m1m2/r2

possibly 1 of the kinemetic equations

The Attempt at a Solution

I know that the force of the first 2 masses is 2.59x10-10 N. I am not sure how to finish the 2nd part of the problem. I know that the 3rd mass' initial velocity=0, but that's all. Can someone help me? I got a 51 on a open note open book quiz in this quiz last week, extremely pathetic. Thanks a lot!

 

[lanedance]

what does the force of the first two masses mean? a force acts on something...

consider the force form each mass (i=1,2) on the test mass say M

\textbf{F}_i = \frac{G m_i M}{r^2} \hat{\textbf{r}}
the bold r hat it is a vector pointing towards m_i

now the acceleration of Mass m is proportional to the net force
\textbf{a} = \frac{\sum_i \textbf{F}_i }{M}
note that this is vector addition of the forces

see anything that cancels...