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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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