Finding where a third mass experiences zero net gravitational force

[NAkid]

[SOLVED] Newton's law of gravitational attraction help?

Homework Statement

M1 is a spherical mass (38.6 kg) at the origin. M2 is also a spherical mass (10.3 kg) and is located on the x-axis at x = 61.2 m. At what value of x would a third mass with a 15.0 kg mass experience no net gravitational force due to M1 and M2?

Homework Equations

F=(Gm1m2)/R^2

The Attempt at a Solution

The force of m1 on m3 and m2 on m3 should be equal, so
Gm1m3/r1^2 := Gm2m3/r2^2

G and m3 are constant, so rearrange and get

sqrt (m1/m2) = r1/r2

not sure what to do here, should i just multiply this ratio by the distance 61.2m?

 

[Snazzy]

But what are $$r_1$$ and $$r_2$$ in terms of x?

 

[NAkid]

r1 + r2 = x

 

[Snazzy]

If r1 is the distance from mass 1 to mass 3, and r2 is the distance from mass 3 to mass 2, and the distance between mass 1 and mass 2 is 61.2, then what is r2 (the distance between mass 3 and mass 2)?

 

[NAkid]

r2 = 61.2 - r1

ok, so substitute this into the ratio r1/r2 --> r1/(61.2-r1) = sqrt (m1/m2)

?

 

[Snazzy]

Yes, and then solve for r_1.