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Falling Balloon
Name: dan
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Question:
WE ARE STUDYING NEWTONS LAWS (8TH GRADE) INCLUDING THE LAW
OF FALLING BODIES. DO YOU KNOW WHAT THE PRINCIPLE IS THAT
ALLOWS A BALLOON TO FALL AT THE SAME SPEED AS A BALLOON OF
THE SAME SIZE FILLED WITH SAND IF CONTAINED IN A VACUUM?
Replies:
Consider Newton's Universal Law of Gravitation: Fg = GMm/(r*r).
If M is the mass of the earth and m is the mass of your falling body,
we can make some simple conclusions that bear out Galileo's law of
falling bodies which state that all objects fall with the same acceleration
regardless of their mass. First, G is the gravitational constant. The
mass of the earth is a constant. Now, assume that both the empty balloon
and the sand filled balloon are dropped from the same height, the radius
of the earth (for all practical purposes, this will usually be the case
unless you can get booked on the space shuttle). Now Newton's equation
reduces to this form: Fg = (constant)m. Applying this to Newton's
second law we get Fg = ma = (constant)m. Now, in both cases the m is
the mass of our falling body. Dividing through we find that the constant
must be the acceleration of our falling body. As we have already discussed
this constant depends only on the mass of the earth, the radius of the
earth and the universal gravitaional constant. All of these things are
constant, and, therefore, so is the acceleration of gravity, regardless of
the mass of the object! This acceleration, GM/(r*r) can easily be
calculated to be about 9.8 m/s/s.
Nick P. Drozdoff
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Update: June 2012
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