Our intuition, combined with supporting evidence from
everyday experience/observations, suggests that heavier objects
should (and do appear to) fall more rapidly than lighter ones.
Indeed, based on everyday observation,
Aristotle proposed that the rate of fall of an object
was proportional to its weight. Many people believe intuitively that heavier objects fall faster.
Galileo tested this hypothesis by droping objects of different weight
and observing their fall (some say from the Leaning Tower of Pisa, although this
story may be apocryphal)
Nevertheless, he determined that bodies of different weight fall at the same rate.
Indeed, Newton's Second Law (combined with the Law of Gravitation) shows that the rate of fall (that is, the object's acceleration) should be independent of its mass/weight.
The force of gravity acting on an object (i.e. its weight) is
proportional to its mass.
The larger the mass the greater the force.
An object accelerates, however, at a rate inversely proportional
to its mass. So the increased force of gravity for a larger mass
is exactly cancelled by the larger mass' resistance to being accelerated.
All objects accelerate uniformly regardless of mass. Combining the two equations above
the mass of the object has cancelled out...
Our intuitive perception that lighter objects fall more slowly
than heavier ones is a manifestation of