Benzoate
Aug30-08, 09:39 PM
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
F=m*M*G/R^2
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(1,2)=m^2*G/a^2
F(1,3)=m^2*G/2a^2
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.
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
F=m*M*G/R^2
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(1,2)=m^2*G/a^2
F(1,3)=m^2*G/2a^2
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.