Masses in a Triangle - Gravitational Force

[Student3.41]

Homework Statement

Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 1.23 m. Two of the spheres have a mass of 2.84 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere

Homework Equations

F=Gm1m2/f^2

The Attempt at a Solution

Not sure what to do here.

 

[Mindscrape]

Try out superposition.

 

[tiny-tim]

Bump

erm … we're waiting for you to start

 

[Student3.41]

Ok well, mass 1 is on the top corner, mass 2 and 3 are on the bottom corners of the triangle.

F_12 = (6.67x10^-11)(2.84)(2.84)/(1.23)^2 = 3.56x10^-11N

I assumed the acceleration is going to be the same for each mass.

a = 3.56x10^-11/2.84 = 1.25x10^-11

 

[tiny-tim]

(try using the X² icon just above the Reply box )

But the question is asking for the (initial) acceleration of the third sphere.

(and btw, what was the point of multiplying by 2.84 and then dividing by it again? )

 

[Student3.41]

I have no idea.

There is no information given for [m][3], I am assuming I would have to find the mass of sphere 3 to the inital acceleration. I know F=ma so, m=F/a I am not sure if I would let x = [m][3] and solve for x, then once I have the mass I can easily get acceleration? or am I completely off

 

[tiny-tim]

There is no information given for [m][3], I am assuming I would have to find the mass of sphere 3 to the inital acceleration. I know F=ma so, m=F/a I am not sure if I would let x = [m][3] and solve for x, then once I have the mass I can easily get acceleration? or am I completely off

Call the mass m, find the force, then divide by m …

what do you get? ​

 

[Student3.41]

Call the mass m, find the force, then divide by m …

what do you get? ​

You will get the inital acceleration of the mass, but I am unsure how to get the mass and the Force on M₃

 

[tiny-tim]

You will get the inital acceleration of the mass, but I am unsure how to get the mass and the Force on M₃

Call the mass m, and find the force.