The force of gravity of two objects on a third?

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Homework Help Overview

The discussion revolves around the gravitational interaction between three masses, m1, m2, and m3, where m2 is greater than m1, and m3 is smaller than both. The original poster is curious about the behavior of m3 when placed at the midpoint between m1 and m2, questioning the implications of gravitational forces acting on m3.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reason that since m2 is greater than m1, m3 would be drawn towards m2. However, they express confusion about the implications of this force, particularly regarding the potential for m3 to collide with m2. Other participants question the reasoning behind the increasing net force and explore the concept of equilibrium and perturbations affecting m3's position.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of gravitational forces and equilibrium. Some guidance has been offered regarding the concept of unstable equilibrium, but no consensus has been reached on the implications of nudging m3 towards either m1 or m2.

Contextual Notes

Participants are considering the effects of gravitational forces in a theoretical setup, with an emphasis on the balance of forces and the concept of equilibrium. The original poster's concerns about the behavior of m3 suggest a need for clarification on gravitational interactions and stability in this context.

Mr Davis 97
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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?
 
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Mr Davis 97 said:
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..)?
 
gneill said:
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?
 
Mr Davis 97 said:
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.
 
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