Acceleration Question

[FutureMd08]

Hey guys! I am wondering if anyone understands why the following statement is false?

1. If an elephant and a feather are dropped from the same height, then the elephant has a greater acceleration of gravity than the feather and therefore falls faster. (do not ignore effects of air resistance).

Is it that the elephant experiences a smaller acceleration because F/m = a ? Or do they experience the same acceleration? Please explain!

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[t5Nitro]

They experience the same gravitational pull from the same height. Look at the gravitational force equation: F_g = GMm/r^2. When you set this equal to 'ma' by Newton's second law, then you can see the mass of the object cancels out and is not factored in. So altogether you have this: F_g = GMm/r^2 = ma. Mass of the object (m) cancels and you are left with GM/r^2 = a. In this case, 'a' is acceleration due to gravity.

I would say the surface area:volume ratio of the feather is much higher than that of the elephant and so it takes more time to fall, considering air resistance.

Hope this helps.

Edit: With the equation you listed (F/m = a), I think you may be able to see how the mass of the object cancels out with the information I typed above. If the elephant was 10x as massive, then the force it experiences is 10x as great (F_g equation comparing both objects). An 'F' and 'm' term both increasing 10x has a neutral impact on the 'a' term. I think this works. Let me know.

 

[DrknoSDN]

Acceleration (from gravity) at a given distance from a gravity source is a constant and the same for any object at that distance.
Conceptually all objects at earths surface experience the same gravitational acceleration. Also at any orbit distance the acceleration of two objects at a given radius would also equal each other.

The "do not ignore air resistance" is a distractor because air resistance is just a force in the opposite direction of the acceleration from gravity and would only change the net acceleration, not the acceleration from gravity (always ~10 m/s^2 near earths surface).