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, 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.).
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