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 Galilei (b1564, d1642 A.D. ←portrait left) 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 mathematically 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.
in factcorrect (or wrong).
Record your observations recorded in your journal. If you need course credit, use the information in your journal to construct a formal report.
Several principles of relativity were assumed by Galileo: The laws of nature must be the same regardless of the person measuring them. And any law of nature should be the same at all times. In addition, motion observed by one person should be equivalent to what is observed by another. Galileo first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship traveling at constant speed, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary.
xto the right of in front of the first observer would be measured at a distance of
x + 2 mto the right of the second observer.
Galileo's principles of relativity describe a kind of symmetry in nature where any event must look equivalent to two observers. This concept has been greatly expanded by later physicists who have used such symmetry as a guide for further discoveries. (Amalie) Emmy Noether (German pronounced 'nø:té, ←photograph at left, b1882, d1935) proved in 1915 two deep theorems, and their converses, on the connection between symmetries and conservation laws which were subsequently published in 1918. The first states that any symmetry of an action of a physical system (which has a mathematical description which can be differentiated) has a corresponding conservation law. Noether's theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra. Instead her help was requested to solve what Albert Einstein and several of their colleagues felt might be a failure of local energy conservation in the general theory of relativity which they had been developing. Her theorems eliminated that concern and became a fundamental tool of modern theoretical physics.
There are now many such conservation laws. For examples, time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum (which will be described in subsequent experiments). Such laws are powerful devices for both understanding what can and cannot occur in the universe and for making useful predictions. Noether's theorems also were instrumental in the great discoveries of gauge field symmetries of the 20th century which led to our Standard Model of matter.