Can someone show me how to do this?

Question

Four 9.0 kg spheres are located at the corners of a square of side 0.70 m. Calculate the magnitude and direction of the gravitational force on one sphere due to the other three.
Magnitude
N

Answer 1

gravitational force between two baddies masses say m1, m2
is
F(1<-->2) = G(m1 * m2)/r^2
where G is a universal constant

where r is the separation between the two baddies

Note :
the force have magnitude as given by equation and also a direction when summing the forces you should deal with both direction and magnitude.

Answer 2

It's actually very easy to see if you draw a picture, but let's try w/o one. For each pair of spheres the direction of the gravitational force vector is from the sphere to which the force is applied toward the sphere that applies the force. If you draw all 3 force vectors and sum them using simple vector geometry rules you will see that the resulting force vector is directed along the diagonal of the square and from the sphere in question toward the most distant sphere (in the opposite corner). The resulting absolute force is computed (for example) as follows:

(m^2*g/(d^2))*(sqrt(2)/2)+
(m^2*g/(d^2))*(sqrt(2)/2)+
(m^2*g)/((d*sqrt(2))^2)=
=m^2*g*(sqrt(2)+0.5)

here m is the mass of one sphere, g is the gravitational constant, and d is the side of the square.

The sqrt(2)/2 multipliers in the first two terms result from taking the projections of the forces (exerted by the two closest spheres) on the diagonal of the square.