An object that falls through a vacuum is subjected to only
one external
force,
the gravitational
force, expressed as the
weight
of the object.
The weight
equation defines the weight W
to be
equal to the mass of the object m
times the gravitational acceleration
g:
W = m * g
the value of g is 9.8 meters per square second on the surface
of the
earth. The gravitational acceleration g decreases with the
square of
the distance from the center of the earth. But for many practical
problems, we can assume this factor to be a constant.
An object that moves because of the action of gravity alone is
said to be
free falling.
If the object
falls through the
atmosphere, there
is an additional
drag force
acting on
the object and the
physics involved with
the motion of the object
is more complex.
The motion of any moving object is described by Newton's
second law of motion,
force F
equals mass m times acceleration a:
F = m * a
We can do a little
algebra and solve for the
acceleration of the object in terms of the
net external force and
the mass of the object:
a = F / m
For a free falling object, the net external force
is just the
weight of the object:
F = W
Substituting into
the second law equation gives:
a = W / m = (m * g) / m = g
The acceleration of the object
equals the gravitational
acceleration. The mass, size, and shape of
the object are not a factor
in describing the motion of the object.
So all objects, regardless of size
or shape or weight,
free fall with the same acceleration.
In a vacuum, a beach ball falls at
the same rate as an airliner.
Knowing the acceleration, we can
determine the
velocity and location
of any free
falling object at any time.
The remarkable observation that all free falling objects fall
with the
same acceleration was first proposed by
Galileo Galilei 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 experiment was successful because he was using a ball for the falling object
and the friction between the ball and the plane was much smaller than the gravitational
force. He also used a very shallow incline, so the velocity was small and the
drag on the ball was very small compared to the gravitational force.
(The story that Galileo demonstrated his findings by
dropping two cannon
balls off the Leaning Tower of Pisa is just a
legend.).
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