ie-Physics

Experiment I-2

Aristotle (384-322 B.C.) suggested that heavier objects fall faster than lighter ones towards the center of the cosmos, the earth.  Nearly 20 centuries, later Galileo (1564-1642) believed that Aristotle badly misunderstood the behavior of the cosmos.  Galileo believed that the earth moved around the sun as suggested by Copernicus.  But this idea was criticized for lack of evidence and because it was inconsistent with Aristotle's causes of motions.  Late in life Galileo suggested that Aristotle's description of falling objects was also flawed, and furthermore, those flaws could be experimentally confirmed.

Galileo suggested that free from significant resistance, all objects fall the same.  They start from rest and accelerate constantly as they fall.  Galileo proposed that objects very different in weight would keep pace, even when dropped from great height such as from the bell tower at the cathedral of Pisa.

While Galileo might be right, he had no technology to actually measure the acceleration of a rapidly falling object.  So he reasoned that an inclined plane would dilute the fall of a ball, but not change the nature of the steady acceleration.

Galileo was able to show that if the acceleration is steady, the the distance fallen will be proportional to the square of the time of fall:  d = 1/2 at², where a is the acceleration constant.

Galileo used a water clock to measure time.  If a large container of water is maintained at the same fill level, the amount of water allowed to flow out will be proportional to the time of flow.  The amount of water draining out is a direct measure of the time.  (i.e., twice as much water means twice the time elapsed.)

By using experimental evidence to overthrow ideas believed true for 2000 years, Galileo did much to start a new science that developed the most successful procedures known to human beings for learning about the universe.  For that reason (and many more), this is an experiment important to repeat and to understand.

Experiment

1. Measure distances down from the starting position on the ramp that are in relationships to perfect squares:  one arbitrary distance, 4 times that distance, 9 times the distance, 16 times, etc.  The ramp needs to be as straight and uniform as possible.  If the angle of the ramp is too shallow, imperfections in the ramp are more likely to cause errors in your measurements.  If the angle of the ramp is too steep, errors in timing will become more significant.
2. Repeatedly time the ball rolling down each distance using a water clock like Galileo used (or a stop watch).  Galileo said the times should be in the ratios of 1 : 2 : 3 : 4 : etc.  The distances transversed should be proportional to the squares of the water released (the elapsed times).
3. If Galileo is correct, a graph of the squares of the amounts of water verse distances should be a straight line from the origin.

Record your observations recorded in your journal.  If you need course credit, use the information in your journal to construct a formal report.

Reference

• George Sarton, A History of Science: Ancient Science Through the Golden Age of Greece, Wiley, 1952.
• Michael Fowler, Galileo and Einstein, see Selection from Galileo's Dialog Concerning Two New Sciences, University of Virginia