An object that falls through a vacuum is subjected to only
one external force, the gravitational
force, expressed as the
weight
of the object. An object that is
moving only because of the action of gravity is said to be free
falling and its motion is described by Newton's
second law of motion.
With algebra we can solve
for the acceleration of a free falling object.
The acceleration is constant
and equal to the gravitational acceleration g which
is 9.8 meters per square second at sea level on the Earth.
The weight, size, and shape of the object
are not a factor in describing a free fall.
In a vacuum, a beach ball falls with the same acceleration as an airliner.
Knowing the acceleration, we can
determine
the
velocity and location
of any free falling object at
any time using the following equations.
V = a * t
X = .5 * a * t^2
where a is the acceleration, V is the velocity, and
X is the displacement from an initial location.
If the object falls
through the atmosphere,
there is an additional drag force
acting on the object and the physics
involved with
describing
the motion of the object is more complex.
Here is a table of calculated
acceleration (meters per second squared),
velocity (meters per second), and displacement (meters) at 1 second intervals.
Time = 0, Accel = 9.8, Velocity = 0.0, Distance = 0.0
Time = 1, Accel = 9.8, Velocity = 9.8, Distance = 4.9
Time = 2, Accel = 9.8, Velocity = 19.6, Distance = 19.6
Time = 3, Accel = 9.8, Velocity = 29.4, Distance = 44.1
Time = 4, Accel = 9.8, Velocity = 39.2, Distance = 78.4
Time = 5, Accel = 9.8, Velocity = 49.0, Distance = 122.5
Time = 6, Accel = 9.8, Velocity = 58.8, Distance = 176.4
Time = 7, Accel = 9.8, Velocity = 68.6, Distance = 240.1
Time = 8, Accel = 9.8, Velocity = 78.4, Distance = 313.6
Notice that the acceleration
is a constant, the velocity increases linearly, and the location
increases quadratically.
The remarkable observation that all free falling objects fall at
the same rate was first proposed by Galileo, nearly 400 years
ago. Galileo conducted experiments using a ball on an inclined plane
to determine the relationship between the time and distance traveled.
He found that the distance depended on the square of the time and
that the velocity increased as the ball moved down the incline. The
relationship was the same regardless of the mass of the ball used in
the experiment. The story that Galileo demonstrated his findings by
dropping two cannon balls off the Leaning Tower of Pisa is just a
legend. However, if the experiment had been attempted, he would
have observed that one ball hit before the other!
Falling cannon balls are not actually free falling  they are subject to
air resistance and would fall at different
terminal velocities.
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