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Confused about the role of mass

I know that two different masses fall at the same rate in the same gravitational field because the greater gravitational force of the heavier one is exactly offset by its greater inertial resistance. What I don't understand is why the larger mass wouldn't fall more slowly at first and then once the inertial resistance is overcome, it would then accelerate faster than the less massive one. It seems that the rate of acceleration (not velocity, which obviously does) would vary according to the distance of the fall

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What is inertial resistance? Can you please show inertial resistance in the equation that is being used? Thank you –  Arjang Aug 10 '11 at 8:27
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marked as duplicate by David Z Aug 10 '11 at 19:08

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[note this is an extremely common question already answered: Confused about the role of mass]

The inertia of an object is constant as long as its mass is constant. so the inertia is never overcome, it just stays the same for all times for our puroposes and while the inertia of the heavier object is greater than the inertia of the lighter object, as you said, the gravitational force is proportionally greater such that both objects have the same acceleration (and thus same position with respect to time if they both are at initially at rest) as provided by Newton's law of gravitation. This requires vacuum and that the objects are aligned at the same radial distance from the body that is attracting them. It also requires that we neglect the gravitational forces between the two objects compared to the gravitational force between each object and the earth. (as well as neglecting any other forces etc.

note, this is really quite elementary:

newtons law of gravitation says:

$ \vec {F} = \frac{GMm}{r^2}{\hat{r}}$ where $\hat{r}$ is a line radially connecting the 2 bodies

note that if M is the mass of the earth the force vector will be greater if little m is also greater as in the example above

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sorry Arjang, you are wrong, remember we are considering the force between the objects and the earth, not the force between the two objects. in that case you would be correct –  Timtam Aug 10 '11 at 8:45
    
of course all this is a consequence of GR but I don't think it's necessary to get in to all that –  Timtam Aug 10 '11 at 8:51
    
then upvote me! –  Timtam Aug 10 '11 at 8:58
    
Timtam , can you please rephrase it, I have read it few times and I still don't get it, I also deleted all my previous comments. –  Arjang Aug 10 '11 at 9:17
    
ok I will add a little bit at the end for you –  Timtam Aug 10 '11 at 9:26
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