# Gravitational pull, superposition

## Homework Statement

Two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is M in terms of m? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere?

## Homework Equations

Fnet = F1,4 + F2,4 + F3,4
F = GMm/r2

## The Attempt at a Solution

F1,4 = GMm/r2
F2,4 =Gm2/r2
F3,4 =Gm2/r2

Fnet = 0 = F1,4 + F2,4 + F3,4
0 = GMm/r2 + Gm2/r2 +Gm2/r2
0 = Mm + 2m2
Mm = -2m2
M = -2m

D H
Staff Emeritus
Hint: You are not using m4 in any of your force calculations.

oh, for some reason i thought it said m = m4.

Fnet = 0 = F1,4 + F2,4 + F3,4
0 = GMm4/r2 + Gmm4/r2 + Gmm4/r2
0 = M + 2m (canceling out G, m4, and r2)
M = -2m

um...

D H
Staff Emeritus
Gravitational force, like all forces, is a vector. You are treating it as a scalar.

i understand that it's a vector, but where do i set the origin? if i set it at m4, i still don't get the answer that i want. i get M = 2m, which is still not correct.

D H
Staff Emeritus