# Homework Help: Problem concernng Newton's Law of Gravitation

1. Aug 30, 2008

### Benzoate

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.

2. Aug 31, 2008

### Benzoate

Is my problem understandable to anyone?

3. Aug 31, 2008

### granpa

http://en.wikipedia.org/wiki/Tetrahedron

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex.

4. Aug 31, 2008

### Benzoate

What is wrong with my Force equations?

5. Aug 31, 2008

### Dick

The total force is the sum of three vectors. These three vectors are the same length but don't point in the same direction.

6. Aug 31, 2008

### granpa

I assumed the base of the tetrahedron is a square

the base is a triangle