Where will the forces of Earth and Moon cancel out?

[tascja]

Homework Statement

The mass of the moon is 7.35x10^22 kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is canceled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (centre to centre) is 3.84x10^5, calculate where this will occur, relative to Earth

Homework Equations

Fg = (G x m1 x m2) / r^2

The Attempt at a Solution

I know you have to make the Earth's gravitational attraction equal the Moon's gravitational attraction (by putting the preceding equation equal to each other). But i don't know where to plug in the 3.84x10^5. Am i looking for the Moon's r? or Earth's r? I am just not too sure about how to go about solving this?

 

[rohanprabhu]

Am i looking for the Moon's r? or Earth's r? I am just not too sure about how to go about solving this?

Neither of them. The 'r' is the distance from the center of either moon or Earth [for your question, you need the answer as the distance from the center of the earth] along the axis joining the moon and the earth. At this distance, the gravitational forces due to the moon and the Earth cancel. Plug in the equation and solve for 'r'.

 

[tascja]

I don't get it?? so I am still using: Fg = (G x m1 x m2) / r^2 right? and I am looking for r... but what are my masses then? Earth and... it doesn't give the mass of the object so is it the mass of the moon?

 

[rohanprabhu]

At any point along the axis.. there will be two forces acting on the particle. One due to the Earth and one due to the moon. The direction of both the forces will be opposite. You need to equate those two forces and the 'r' you find from the equation will be the 'r' you are looking for. This happens because, at the point 'r' where you make the two forces equal, there are 2 forces acting on the particle in opposite directions. As such, they both will cancel each other out and hence there will be no net resultant force.