# Why do all objects fall with the same acceleration regardless of mass?

## Main Question or Discussion Point

I am well aware that objects of varying masses, shapes, and surface areas will fall at different speeds and accelerations in an environment with a gas in the way such as air due to air resistance. Why is it though, that gravity causes all objects to fall with the same acceleration in a vacuum? Objects that fall further and have more energy and less time to decelerate have much more impact force, so why is it that this happens?

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Dale
Mentor
This happens due to the equivalence of inertial mass and gravitational mass. For inertial mass we have ##\Sigma F = m_i a##. For gravitational mass we have ##F_g=G M m_g/r^2##. If the object is in free fall then ##\Sigma F = F_g## so we have ##m_i a = G M m_g/r^2##. Then, because inertial mass and gravitational mass are the same we can set ##m=m_i = m_g## and get ##a = G M/r^2##, which is independent of ##m##.

Nugatory
Mentor
This is an FAQ over in the General Physics section: https://www.physicsforums.com/showthread.php?t=511172 [Broken]

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ZapperZ
Staff Emeritus
I am well aware that objects of varying masses, shapes, and surface areas will fall at different speeds and accelerations in an environment with a gas in the way such as air due to air resistance. Why is it though, that gravity causes all objects to fall with the same acceleration in a vacuum? Objects that fall further and have more energy and less time to decelerate have much more impact force, so why is it that this happens?