Gravity and Free Fall
Gravity
• Sir Isaac Newton (1642-1727) developed a law
of gravitation which said all objects in the
universe attract each other through
gravitational force
• Universal Gravitation Equation
•
F = G m1m2
d2
• Equation shows grav. Force ↑ as both
masses ↑
• Equation shows grav. Force ↓ as the distance
b/w masses ↑
Free Fall
Free fall- when gravity is the
only force acting on an object
(free fall acceleration is directed
toward center of earth)
The acceleration of gravity (g)
for objects in free fall at the
earth's surface is 9.8 m/s2.
Galileo found that all things
fall at the same rate in the
absence of air resistance,
regardless of their mass
Free Fall
The rate of falling
increases by 9.8 m/s
every second.
Height = ½ gt2
For example:
½ (9.8 )12 = 4.9 m
½(9.8)22 = 19.6 m
½ (9.8)32 = 44.1 m
½ (9.8)42 = 78.4 m
Air Resistance
• In air…
– A stone falls
faster than a
feather
• Air resistance
affects stone
less
• In a vacuum
– A stone and a
feather will fall at
the same speed.
Mass and Weight
 different!
► Mass is an intrinsic property of an object. It is
completely determined by the number and type of
atoms that make up the object. It does not depend
on the environment in which the object is located.
► But weight is different. Weight depends on both
the object itself, and on some other object that exerts
the gravitational force.
So, for example, the mass of an object
would be the same on the moon or the
Earth; but the weight would be different.
What does weight depend on?
• The weight of an object depends on the
object’s mass.
– In fact, an object’s weight is directly
proportional to the object’s mass.
• The weight of an object also depends on
the object’s location.
– In fact, an object’s weight is directly
proportional to its free fall acceleration, g at
its current location.
Weight = the force of gravity
The weight of an object is, by definition,
the strength of the force of gravity pulling
the object downward.
W=mg
force of gravity
newtons
kg
Weight of a 1 kg object
• Since W = mg, the weight of a 1 kg
object is:
– W = (9.8 m/s2)(1 kg) = 9.8 N on Earth
– W = (1.6 m/s2)(1 kg) = 1.6 N on the Moon
Mass vs. Weight
• Mass is not Weight
• Weight is a force - an interaction between
2 objects involving a push or a pull. One
of these objects is typically VERY big - the
Earth or the Moon, for instance.
• Weight is NOT a property of an object
Weight
• In symbols:
W = mg
W
m g
Gravity
What is the force acting on the
mass m due to the Earth’s gravity?
F
Solution
g = 9.81 m/s2
If released, the acceleration
of m would be …
a  g downward
By Newton’s second law
the force on m must be …
F  mg
downward
That is, the magnitude, or strength, is mg
and the direction is downward.
By the way, what is the reaction force?
2-5. Free Fall
A ball thrown
horizontally
will fall at the
same rate as a
ball dropped
directly.
2-5. Free Fall
A ball thrown into the
air will slow down, stop,
and then begin to fall
with the acceleration
due to gravity. When it
passes the thrower, it
will be traveling at the
same rate at which it
was thrown.
Example. Playing catch with a softball
The trajectory has 3 parts.
free fall
What is the force acting on the ball, during each
part of the trajectory?
Projectile Motion
•An object thrown upward at an angle to the
ground follows a curved path called a
parabola.
• combines vertical and horizontal motion
•Orbiting objects- forward motion combines
with free fall and object follows a curved path
2-6. Air Resistance
• Free Fall
– A person in free fall reaches a
terminal velocity of around 54
m/s which means the person
stops accelerating b/c:
– Force of air resistance =
gravitational force
– Called terminal velocity
(balanced forces)
– With a parachute, terminal
velocity is only 6.3 m/s
• Allows a safe landing
Free Fall Review
• Dropping something from a resting
position (gains speed as it falls so it
accelerates)
• Gravity pulls objects down (air resistance
can affect how fast) (no air resistance- in a
vacuum)
• When gravity is the only thing that affects
falling object → FREE FALL
• Acceleration due to gravity is 9.8 m/s2
Free Fall equations
• V=gxt
• D = 1 gt2
2