Galileo Galilei

    Galileo Galilei was born in Pisa in 1954, the son of well-known musician on Vincenzo Galilei and Giulia Ammannati.  He studied in Pisa and was later promoted to the chair in mathematics, which he held from 1589-1592.  He then was appointed to the chair of mathematics at the University of Padua, which he held until 1610.  During his time at Padua conducted many studies in mechanics and built the thermoscope:

  

    Galileo's thermoscope was built in 1597 and was confirmed by Benedetto Castilli in a letter dated September 20, 1638.  The thermoscope, designed to measure hot and cold, was a long glass bottle (about the size of an egg), with a long glass neck.  The bottle was heated with hands and then placed in a vessel and partially immersed in a liquid.  After the hands were removed, the liquid rose to a certain level in the neck that was above the level of the remaining liquid.

    Galileo then made a geometrical and military compass and in 1594 made a machine that would raise water levels.  He then invented the microscope and made a telescope with which he used to observe the satellites of Jupiter.  In 1610 he was nominated foremost Mathematician of the University of Pisa and appointed mathematician to the Grand Duke of Tuscany, during which time he observed the phases of Venus and studied Saturn.  In 1611 he went to Rome and joined the Accademia dei Lincei and observed sunspots.  In 1612 he began to encounter serious opposition to his ideas about the motion of the Earth, mainly from the church. In 1614 Father Tommaso Caccini denounced Galileo's opinions from the pulpit of the Santa Maria Nevella.  To defend his ideas, Galileo went to Rome but was then admonished because his ideas went against the ideas of Copernicus. In 1622 he wrote the Saggiatore  and in 1632 Dialogue on the two chief World Systems was published.  In October 1632 he was summoned to Rome and was sent into exile and compelled to abjure his theory.  He was exiled in Siena but in December of 1633 he was allowed to retire to his villa in Arcetri, the Gioiello. ( Information found at http://galileo.imss.firenze.it/museo/b/egalilg.html)

    In 1581 Galileo was supposedly watching a chandelier swing back and forth.  After watching it for several minutes, it occurred to him that the period of each swing was about the same. To measure this he used his pulsebeat and then went home and tried it for himself.  Using two pendulums of equal length and swung one in larger sweeps and one in smaller sweeps.  Once released he observed that one pendulum stayed in sync with the other at all times.  After his death, Cristiaan Huygens, a Dutch philosopher, used the principle of the pendulum as a means by which to regulate a clock.  (Information found at http://www.curriculumunits.com/galileo/science/pendulum.htm)

    

    We repeated Galileo's pendulum experiment using a metal ball and a washer tied on a length of string.  By varying the length of the pendulum we were able to collect enough data to determine that the pendulum was more accurate than the stopwatch.  This was determined by using the sound of the ball hitting the track to start the pendulum.  Since the stopwatch requires reaction time to press the button and another fraction of the second to start the timer, it has a slightly larger amount of error.  The pendulum has very little if any reaction time as when the sound is heard the only thing that needs to be done is to release the pendulum and count the number of cycles it makes.  Then the equation t = .2sqrt(l) can be used to find the time per cycle of the pendulum by substituting the length for (l) and then multiplying t times the number of cycles.  This will give you the exact time it took for the ball to travel down the track.  

    We also used a quarter-cycle pendulum compared to a stopwatch to time the ball.  The pendulum used in this experiment is more accurate than the makeshift pendulums used in the previous experiment as it has a stationary base and a fixed length.  By counting the number of hits then multiplying by 2 and then subtracting one, after which we divided the result by 4, we were able to determine the number of complete cycles.  The equation t = 0.2sqrt(l) was then used to find the rate of cycles per second again.  The result was then multiplied by the number of cycles to get the total time it took for the ball to travel down the track.
Example:

length: 41 cm

8 hits.

8*2=16

16-1=15

15/4=3.75 (number of cycles)

t =.2sqrt(41 cm) = 1.28 cycles per second

1.28 cycles/sec * 3.75 (number of cycles) = 4.802 seconds

This length and number of hits gave us a total time of 4.802 seconds between the release point and the point at which the ball stopped.