FREE FALLING BODIES GALILEO GALILEI 1564 1642 Italian

FREE FALLING BODIES GALILEO GALILEI (1564 – 1642) Italian astronomer & physicist “Father of Experimental Science” Source: http: //www-groups. dcs. st-and. ac. uk/~history/Pict. Display/Galileo. html Supported the Heliocentric Theory of Nicolaus Copernicus Invented the first telescope, thus the first person to look at the Moon through a telescope Discovered the four moon circling Jupiter & LAWS OF PENDULUM http: //scienceworld. wolfram. com/biography/Galileo. html http: //inventors. about. com/library/inventors/blgalileo. htm

GALILEO VERSUS ARISTOTLE’S LAWS OF NATURE ARISTOTLE Born: 384 BC Died: 322 BC Greek philosopher, mathematician & scientist ”Father of Science” Systematized deductive logic/reasoning determined the orientation and the content of Western intellectual history. Western culture was Aristotelian. Proponent of the “laws of nature”

ARISTOTLE’S ASSUMPTIONS “There is a natural place for everything to seek, as: Heavy things go downward, Fire upward, And rivers to the sea - Aristotle It was in the nature of falling, said Aristotle, that heavy objects seek their natural place faster than light ones -- that heavy objects fall faster. Aristotle's word had been accepted as gospel truth, and there had been few attempts to actually test Aristotle's conclusions by actually conducting an experiment!

GALILEO’S EXPERIMENT IN THE LEANING TOWER OF PISA Aristotle’s Assumption: “Heavy Objects fall faster then light ones” Galileo’s Experiment: Drop two balls from the tower (canon & wooden ball)

GALILEO’S FINDING “HEAVY AND LIGHT OBJECTS FALL AT THE SAME TIME IN THE ABSENCE OF AIR RESISTANCE OR AIR FRICTION” Suppose that an elephant and a feather are dropped off a very tall building from the same height at the same time. Suppose that air resistance could be eliminated such that neither the elephant nor the feather would experience any air drag during the course of their fall.

In the absence of air resistance, the elephant and the feather strike the ground at the same time. Why is this so?

MOTION OF FREE FALLING BODIES A free-falling object is an object which is falling under the sole influence of gravity. Any object which is moving and being acted upon only by the force of gravity is said to be "in a state of free fall”. All objects (regardless of their mass) experience the same acceleration when in a state of free fall.

FREE FALLING BODY Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of approximately 10 m/s 2 or to be exact, 9. 8 m/s 2. Thus, g = 9. 8 m/s 2 is also known as “acceleration due to gravity”.

EQUATIONS OF MOTION APPLIED TO FREE FALLING BODIES Vf = Vi + gt Since Vi = 0 then the formula can be written as: Vf = gt Problem 1: Mitch forgot his key to her locker in school. She asked her sister to drop it on their window so she does not need to go upstairs again. How fast will the key fall from the window if it reached the ground in 10 seconds?

SOLUTION: Vf = Vi + gt or Vf = gt g = 9. 8 m/s 2 The key is a free falling body” Thus, Vf = (9. 8 m/s 2)(10 s) Vf = 98 m/s final velocity of key

Problem 2: A patient accidentally dropped off from the rooftop of a hospital. The body hit the ground in 6 sec. How high is the building of the hospital? d = Vit + ½ gt 2 or d = ½ gt 2

SOLUTION: d = Vit + ½ gt 2 or d = ½ gt 2 d = ½(9. 8 m/s 2)(6 s)2 d = 176. 4 meters Thus, the hospital is 176. 4 meters tall

Problem 3: An object falls from an airplane at an altitude of 12000 meters at a final velocity of 20 m/s. How long will the object hit the ground? HOW WILL YOU SOLVE THE NEXT PROBLEM?

Exercise 11: Free Falling bodies Solve the following problems completely! 1. An object dropped from a cliff 100 meters above the ground. How long will it take the object to reach the ground? What is the final velocity of the object? 2. A hospital building is 200 meters high. If a dextrose bottle is dropped from its top, what will be the velocity as it reaches the ground? How many seconds will it reach the ground? 3. The time it took for a ball to reach the ground is 40 seconds. If the ball has a final velocity of 1. 5 m/s then how much distance was covered by the ball? 4. Find the final velocity of a shooting star that fell on the surface of the earth in 25 minutes. 5. Find the time it will take a shooting star to reach the surface of planet earth if the distance above the ground it will travel is 5000 kilometers.