Free-Falling
What goes up must come down!
Presentation 2003 R. McDermott
Free Fall
 An object is “free-falling” whenever it is
moving, unsupported, through the air
 It may be moving straight up or down
 It may be moving sideways as well as up or
down
 It may have been dropped
 It may have been thrown downward
 It may have been thrown upward
Free Fall
Free-falling objects obey acceleration equations, and the
acceleration is a constant 9.81 m/s2 downward no matter
how the object was initially moving.
Free Fall
All free-falling objects fall at the same rate:
If it’s Rising, How can
it be Falling?
 An object “falls” 4.9 meters in the first second
 If it is dropped from rest, it will be 4.9 meters
down after one second
 If it is thrown upward at 10 m/s, it will be 5.1
meters above its starting point after one second
(10 – 4.9)
 However it may be moving, it will be lower than
it would have been without gravity acting, by an
amount equal to what it lost by falling.
Gravity-Free Path
Free Fall (cont)
 If an object is “free-falling”, its vertical motion
may be treated as linear motion
 All linear motion equations apply
 The object starts at rest if you drop it (Vi = 0)
 The object is at rest (Vf = 0) at its highest point if
it is initially thrown upward
 When an object falls, it speeds up. As it rises, it
slows down
Falling (cont)
 The acceleration for a free-falling object is 9.8
m/s2 downward regardless of the object’s motion
 A falling object gains 9.8 m/s of speed each
second it falls
 A rising object loses 9.8 m/s of speed each
second it rises
 The acceleration of gravity (9.8 m/s2 ) is given
the symbol “g” in equations. For example: Vf =
Vi + gt
Example #1:
An object is dropped and falls for 3.0
seconds. How far does it fall?
Identify symbols:
Vi = 0 m/s, a = g,
t = 3.0 s, x = ?
Identify Equation:
x = Vit + ½ at2
Example #1 (cont):
An object is dropped and falls for 3.0
seconds. How far does it fall?
Determine the
sign of “g”:
Since the object is falling and
speeding up, acceleration has the
same sign as the velocity
(negative).
Substitute: x = (0 m/s)(3.0s) + ½(-9.8 m/s2 )(3.0s)2
#1 (cont):
An object is dropped and falls for 3.0
seconds. How far does it fall?
Solve the equation:
x = 0 - 4.9(9.0)
Write the solution:
x = -44.1 m
Example #2:
An object is thrown upward at a speed of
49 m/s. How long does it rise?
Identify symbols:
Vi = 49 m/s, a = g,
Vf = 0 m/s, t = ?
Identify Equation:
Vf = Vi + at
Example #2 (cont):
An object is thrown upward at a speed of 49 m/s.
How long does it rise?
Determine the sign
of “g”:
Since the object is rising and
slowing down, acceleration is
opposite velocity (negative).
Rearrange the
equation:
t = Vf - Vi
g
Substitute:
t = 0 m/s – 49 m/s
-9.8 m/s2
#2 (cont):
An object is thrown upward at a
speed of 49 m/s. For how long does
it rise?
Solve the equation:
t = -49
-9.8
Write the solution:
t = 5.0 seconds
How Does Gravity Work?
Force between two masses
The force is proportional to the product of
the masses, and inversely proportional to
the square of their separation
F = GM1M2
R2
R
G – Gravitational Constant
Same value everywhere in the universe
6.67x10-11 N-m2/kg2
Don’t confuse G and g!
Big G is constant
Small g is the gravitational field strength,
which changes value depending on the
planet and your altitude.
Proportions:
g - Gravitational Field Strength
The field strength of object 1 is generally
expressed as the force acting on object 2
divided by object 2’s field characteristic
For gravity, the field characteristic is mass
so: g = F/m2
g = GM1
R2
Distance and g
Orbiting Conditions
Gravitational force supplies the centripetal
force needed
GM1M2 = M2v2
R2
R
Io orbiting Jupiter – Courtesy NASA Jet Propulsion Lab