YOU CAN NEVER
BLAME GRAVITY
FOR PEOPLE
FALLING IN-LOVE!
Objectives:
1. Explain the conditions how Free Fall is achieved
and the factor(s) affecting it;
2. Express the importance of equality by showing
respect to individual differences; and
3. Solve problems involving free-falling objects.
Which will hit the floor
first?
1-Peso coin
a piece of paper
Suppose that an elephant and a feather
are dropped off a very tall building
from the same height at the same
time. Suppose also that air resistance
could somehow be eliminated such
that neither the elephant nor the
feather would experience any air
drag during the course of their fall.
Which object - the elephant or the
feather - will hit the ground first?
The animation at the right accurately
depicts this situation. The motion of
the elephant and the feather in the
absence of air resistance is shown.
Further, the acceleration of each
object is represented by a vector
arrow.
Test your understanding by making an effort to identify the
following statements as being either TRUE or FALSE.
a. The elephant and the feather each have the same force of
gravity.
b. The elephant has more mass, yet both elephant and feather
experience the same force of gravity.
c. The elephant experiences a greater force of gravity, yet both
the elephant and the feather have the same mass.
d. On earth, all objects (whether an elephant or a feather) have
the same force of gravity.
e. The elephant weighs more than the feather, yet they each have
the same mass.
f. The elephant clearly has more mass than the feather, yet they
each weigh the same.
g. The elephant clearly has more mass than the feather, yet the
amount of gravity (force) is the same for each.
h. The elephant has the greatest acceleration, yet the amount of
gravity is the same for each.
Free Fall: A Brief Description
Three (3) Cases of Free
Fall
Case 1: Dropping
(vi = 0)
Case 2: Throwing Down
(vi , downward)
Case 3: Throwing Up
(vi , upward)
a. The elephant and the feather each have the same force of
gravity. False
b. The elephant has more mass, yet both elephant and feather
experience the same force of gravity. False
c. The elephant experiences a greater force of gravity, yet both
the elephant and the feather have the same mass. False
d. On earth, all objects (whether an elephant or a feather) have the
same force of gravity. False
e. The elephant weighs more than the feather, yet they each have
the same mass. False
f. The elephant clearly has more mass than the feather, yet they
each weigh the same. False
g. The elephant clearly has more mass than the feather, yet the
amount of gravity (force) is the same for each. False
h. The elephant has the greatest acceleration, yet the amount of
gravity is the same for each. False
None of the statements is True. In the
absence of air resistance, both the
elephant and the feather are in a state of
free-fall. That is to say, the only force
acting upon the two objects is the force
of gravity. This force of gravity is what
causes both the elephant and the feather
to accelerate downwards.
A simple rule to bear in mind is that all
objects (regardless of their mass)
experience the same acceleration when
in a state of free fall. When the only
force is gravity, the acceleration is the
same value for all objects.
On Earth, this acceleration value is 9.8 m/s2
or the acceleration due to gravity (g).
If something falls freely under the
effect of earth’s gravity without any
effect of air then the phenomenon is
called free fall.
While the free fall, no matter how big,
small or weighty the object is, every
object feel the same constant
acceleration, the constant acceleration
during free fall is called free fall
acceleration.
This definition of free fall leads
to two important characteristics
about a free-falling object:
– Free-falling objects do not
encounter air resistance.
– All free-falling objects (on
Earth) accelerate downwards
at a rate of 9.8 m/s2 or 32 ft/s2.
Galileo Galilei
1564 –1642
vf = vi + gt
(Eqn. 1)
y = vi t + ½ gt2
(Eqn. 2)
vf2 = vi2 + 2gy
(Eqn. 3)
where a = g = 9.8 m/s2, downward in earth
Sample Problem:
If the ball is dropped from a
height (y) of 50 m, find
(a) time of flight, and
(b) velocity before
the impact
Given:
y = 50 m
g = 9.8 m/s2
vi = 0 (Case 1: Dropping)
Find:
a) t
b) vf
Solution:
(a)
From y=vi t + ½gt2 and vi = 0,
(Eqn. 4)
Thus,
=
= 3.19 s
(b)
vf2 = vi2 + 2gy
(Eqn. 5)
vf =
31.3m/s
Using Equation 1:
since t = 3.2 s,
vf = vi + gt
= 0 + 9.8 m/s2 (3.2 s)
= 31.3 m/s
Table of Values
Time
(s)
Velocity
(m/s, down)
Displacement
(m, down)
0
0
0
3.2
31.30 m/s
50 m
*Use Equations 1 and 2
Table of Values
Time
(s)
Velocity
(m/s, down)
Displacement
(m, down)
0
0
0
0.8
7.84 m/s
3.14 m
1.6
15.68 m/s
12.5 m
2.4
23.52 m/s
28.2 m
3.2
31.30 m/s
50 m
The Schematic Diagram of the Fall
Essential Questions:
1. How do you describe the motion of the ball
as it travels toward the ground?
2. What do you think will happen if the object
having this vf falls from a building and hits
the ground?
3. After knowing the concept of Free Fall, what
did you realize in your life now?
Problem:
1. A stone is dropped from the
top of a building. If it takes 5 s
for the stone to hit the
ground, (a) how high is the
building? (b) What is the
velocity just before it hits the
ground?
2. A stone is dropped from a cliff
490 m above its base. How
long does it take for the stone
to fall?
Homework:
3. A ball is dropped from the top of a
building 44.1 m high. How many seconds
later will it hit the ground?
4. A stone dropped from the top of a tower
hits the ground 6 seconds later. How high
is the tower?
5. A bomb is dropped from a plane which is
flying with a constant horizontal velocity.
Locate the bomb after 1 second in
relation to the plane.
Hammer vs Feather - Apollo 15 on the Moon
Feather and Ball Bearing Dropped in Vacuum
Agreement/Assignment
1. Cite some situations where Free
Fall is
(a) an advantage, and (b) a
disadvantage.
2. Give a strategy people use
nowadays to minimize Free Fall.
FREE FALL
Case 2: Throwing Down
Three (3) Cases of Free
Fall
Case 1: Dropping
(vi = 0)
Case 2: Throwing Down
(vi , downward)
Case 3: Throwing Up
(vi , upward)
Sample Problem
From the top of a 122.5-m building, a stone is
thrown downward with a velocity of 10 m/s.
(a)What is the velocity just before it hits the
ground?
(b)How long does it take the stone to reach the
ground?
Given
vi = 10 m/s, downward
y = 122.5 m
g = 9.8 m/s2
Find
(a) vf
(b) t
Solution
(a)
vf = √vi2 + 2gy
vf = √(10 m/s)2 + 2 (9.8 m/s2) (122.5 m)
vf = √(100 m2/s2 + 2 (9.8 m/s2) (122.5 m)
vf = √(100 m2/s2 + 2 401 m2/s2
vf = √ 2 501 m2/s2
vf = 50 m/s
(b)
vf = vi + gt
vf - v i
t=
g
50 m/s – 10 m/s
t=
9.8 m/s2
40 m/s
t=
= 4.08 s
9.8 m/s2
1. A ball is thrown vertically
downward at 10 m/s. What is its
velocity (a) 1 s after? (b) 2 s later?
2. At what velocity should a stone be
thrown downward from a cliff of
120 m high to reach the ground in
4 s?
FREE FALL
Case 3: Throwing Up
What would happen if the ball were thrown upward?
In this case, we would have two types of motion: upward and
then downward. We would be treating each case differently.
When the ball is thrown upward, its displacement and
velocity is upward, but acceleration, g acts downward,
causing the ball to slow down until it stops. Once the ball
stops, its behavior is similar to Case 1, but the height is
higher because of the initial upward motion.
The best way to show this type of motion is through this
example. Take note, ALL TIMES during the flight, the
acceleration is ALWAYS equal to 9.8 m/s2 downward, even
if the ball stops at the highest point.
Sample Problem
From the top of a 122.5-m building, a stone is
thrown upward with a velocity of 10 m/s.
(a)What is the velocity just before it hits the
ground?
(b)How long does it take the stone to reach
the ground?
Thank
You!
