How Is the Net Gravitational Force Calculated in a Triangular Particle System?

AI Thread Summary
The net gravitational force on one particle in a triangular system of three identical spherical particles is calculated using the formula Fg = sqrt(3) Gm^2/r^2. Each particle experiences gravitational attraction from the other two, and the forces must be summed as vectors. The challenge lies in determining the gravitational force between each pair and using geometric principles to find the resultant magnitude. Understanding the vector addition of forces is crucial for solving the problem. This approach highlights the importance of geometry in calculating gravitational interactions in a triangular configuration.
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Homework Statement



Three identical spherical particles of mass m are each located at the corners of an equilateral triangle with edge length r (each sphere is centered at each corner). Show the magnitude of the net gravitational force on anyone of the particles due to the other two particles is given by:

Homework Equations



Fg = sqrt(3) Gm^2/r^2

The Attempt at a Solution



Again... had no idea where to start.
 
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what's the gravitational force between each pair? and then sum the 2 vectors (i.e, 2 forces acting on 1 particle) using geometry to find the magnetude of the force.
 

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