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

1. Mar 18, 2014

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?

2. Mar 18, 2014

### Staff: 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 $m$.

3. Mar 18, 2014

### Staff: Mentor

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

Last edited by a moderator: May 6, 2017
4. Mar 18, 2014

### ZapperZ

Staff Emeritus
Please start by reading this FAQ entry: