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FREE FALLING BODIES
GALILEO GALILEI (1564 – 1642)
 Italian astronomer & physicist
 “Father of Experimental Science”
Source:
http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/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/s2 or
to be exact, 9.8 m/s2.
Thus, g = 9.8 m/s2 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 = 9.8m/s2 The key is a free falling body”
Thus, Vf = (9.8m/s2)(10 s)
Vf = 98m/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 gt2 or d = ½ gt2
SOLUTION:
d = Vit + ½ gt2 or d = ½ gt2
d = ½(9.8m/s2)(6s)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 12000meters at a final velocity
of 20m/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.