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Don’t heavier objects actually fall faster because they exert their own gravity?

When true: The force pulling the "heavy" object down is greater BUT it also takes more force to accelerate a heavy object. These two effects cancel out.

As I heard, the bigger mass/size an object the bigger attraction force between each other, then, why the big mass object did not accelerate faster due to the attraction force is greater than light object.

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Possible duplicate: physics.stackexchange.com/q/3534/2451 –  Qmechanic Jan 15 '13 at 14:30
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marked as duplicate by Qmechanic Jan 15 '13 at 14:31

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An object that is 2 times more massive as another experiences 2 times the force of attraction but takes 2 times the force to achieve the same acceleration. As said, these effects cancel, so that bowling balls and feathers would accelerate the same way under the influence of gravity, in absence of other forces.

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