The force of gravity of two objects on a third?

[Mr Davis 97]

Homework Statement

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Imagine we have three masses, m1, m2 and m3. m2 is greater than m1. m3 is smaller than both. If we hold m1 and m2 in place without movement, and place m3 in the midpoint of the line adjoining m1 and m2, what will happen to m3?

Homework Equations

Newton's law of gravitation

The Attempt at a Solution

Since m2 > m1, I would think that the net force would be towards m2. However, this doesn't seem to make sense because the net force would just get greater and greater and eventually collide with m2. But this doesn't seem to be right. What would happen?

 

[gneill]

Since m2 > m1, I would think that the net force would be towards m2. However, this doesn't seem to make sense because the net force would just get greater and greater and eventually collide with m2. But this doesn't seem to be right. What would happen?

I'm not sure why this result bothers you. Sounds quite reasonable to me that m3 will be drawn towards the larger mass.

Can you give a bit more detail to your statement " the net force would just get greater and greater and eventually collide with m2"? What happens to make the net force increase? What is colliding (it sounds like you have the force colliding..)?

 

[Mr Davis 97]

I'm not sure why this result bothers you. Sounds quite reasonable to me that m3 will be drawn towards the larger mass.

Can you give a bit more detail to your statement " the net force would just get greater and greater and eventually collide with m2"? What happens to make the net force increase? What is colliding (it sounds like you have the force colliding..)?

I guess it is reasonable, but what if I placed m3 right at the point on the line where the force m1 exerts on it is equal to the force m3 exerts on it. If I nudged m3 a little in tehe direction of m1, would it then collide with m1? And if I nudged it a little in the direction of m2, would it then collide with m2?

 

[gneill]

I guess it is reasonable, but what if I placed m3 right at the point on the line where the force m1 exerts on it is equal to the force m3 exerts on it. If I nudged m3 a little in tehe direction of m1, would it then collide with m1? And if I nudged it a little in the direction of m2, would it then collide with m2?

Sure. The balance point represents what is known as an unstable equilibrium: Any small perturbation will cause the mass to "fall" one way or the other.