Galileo's Experiment on Falling Bodies

- 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...

- The force of gravity acting on an object (i.e. its weight) is
proportional to its mass.
- Our intuitive perception that lighter objects fall more slowly than heavier ones is a manifestation of air resistance.
- In a vacuum all objects fall at the same rate.