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Problem concernng Newton's Law of Gravitation

  1. Aug 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Four particles, each of mass m , are situated at the vertices of a regular tetrahedron of the side a. Find the gravitational force exerted on any one of the particles by the other three.

    2. Relevant equations

    3. The attempt at a solution

    Since the mass of the four particles are equivalent, F=m^2*G/a^2. Each of the particles lie at each of the four vertices of the base of the tetrahedron. I assumed the base of the tetrahedron is a square since the polyhedron is a regular tetrahedron. particle one exerts a force on each of the remaining three particles that lie on the vertices. So I will write out 3 forces



    F(1,4)= m^2*G/a^2

    F(total)=F(1,2)+F(1,3)+F(1,4)= 5/2*(m^2/a^2).

    The book says that the total Force is sqrt(6)*m^2*G/a^2. What did I do wrong? I think the calculation for my net Force was slightly closed to the books answer, I happened to be off by .05 decimal places.
  2. jcsd
  3. Aug 31, 2008 #2
    Is my problem understandable to anyone?
  4. Aug 31, 2008 #3

    A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex.
  5. Aug 31, 2008 #4
    What is wrong with my Force equations?
  6. Aug 31, 2008 #5


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    The total force is the sum of three vectors. These three vectors are the same length but don't point in the same direction.
  7. Aug 31, 2008 #6
    I assumed the base of the tetrahedron is a square

    the base is a triangle
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