What Happens to Acceleration When Two Equal Masses Attract Each Other?

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Discussion Overview

The discussion revolves around the implications of Newton's law of gravity, particularly focusing on the acceleration experienced by two equal masses attracting each other. Participants explore the concepts of gravitational force, acceleration, and the nature of attraction between masses, with references to both theoretical and conceptual aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether two equal masses, each attracting the other with an acceleration of 9.8 m/s², would result in a total acceleration of 19.6 m/s².
  • Another participant points out that acceleration should not be measured in Newtons (N), but in meters per second squared (m/s²), indicating a misunderstanding in units.
  • A different participant clarifies that there is no concept of "total acceleration" in this context, emphasizing that each mass experiences an acceleration of 9.8 m/s² towards each other.
  • One participant notes that while both masses attract each other with equal force, the acceleration of the Earth towards a person is negligible due to the Earth's much larger mass.
  • It is mentioned that this analysis applies only to objects in free fall, where gravitational attraction is considered without other forces acting on the system.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of acceleration in the context of gravitational attraction, with some clarifying misunderstandings about units and concepts. There is no consensus on the implications of "total acceleration," and the discussion remains unresolved regarding the initial question posed.

Contextual Notes

Participants highlight limitations in understanding the correct units of measurement and the conceptual framework surrounding gravitational attraction. The discussion reflects a need for clarity on the definitions and implications of acceleration in gravitational contexts.

Nissan
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I was thinking about Newton's law of gravity:
F = Gm1m2/r^2.
with this law we can see that the acceleration of on object in Earth is (G*mass of the earth) which is 9.8N.
what happens if we cosider in our equation abody which his mass is equvalnce to the mass of the earth?
each object will give the other an acceleration of 9.8N, does it mean's that the total acceleration would be 19.6N? does that mean's that we attract the Earth as well in a fixed acceleration?
 
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Nissan said:
does that mean's that we attract the Earth as well in a fixed acceleration?

Look at the equation again. (m2...)
 
Nissan said:
I was thinking about Newton's law of gravity:
F = Gm1m2/r^2.
with this law we can see that the acceleration of on object in Earth is (G*mass of the earth) which is 9.8N.
what happens if we cosider in our equation abody which his mass is equvalnce to the mass of the earth?
each object will give the other an acceleration of 9.8N, does it mean's that the total acceleration would be 19.6N? does that mean's that we attract the Earth as well in a fixed acceleration?

Your post is simply incomprehensible. The acceleration is not measured in N (Newtons), but in [itex]\mbox{m s}^{-2}[/itex].

Daniel.
 
Good catch, Dexter. I've never used Newtons for anything, so I didn't know what that N meant. :redface:
(Seriously... I never heard of a Newton until I got onto PF. I still don't know what it is. Everything that I've ever done was in Watts, Foot-pounds, psi, etc..)
 
In addition, there is no such thing as "total acceleration". If two objects were the same mass and at a distance such that the acceleration was 9.8 meters per second squared, the each would be attracted toward the other at 9.8 meters per second squared. You could then calculate that the distance between them was decreasing at a rate that was increasing at 19.6 meters per second squared but that would not be an "acceleration" of any object.

To answer your last question: yes, we attract the Earth at a fixed acceleration. Since "we" attract the Earth with the same force as that the Earth applies to the object, but the Earth is much more massive than "we" are, that fixed acceleration is unmeasurably small.

This applies, of course, only to objects in free fall. If I am standing on the earth, the Earth and I attract each other with the same force, but there is no acceleration.
 

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