Date: Wed, 3 Dec 1997 22:15:42 -0800
Message-Id: <v01520d01b0ab75ec1fc3@[205.179.255.74]>
To: pinhole@exploratorium.edu
From: mafifi@redshift.com (Marc Afifi)
Subject: Re: vector components
Interesting question, though it seems like a question of semantics. Have
your students concluded that gravity is not responsible for avalanches?
I suggest the following approach.
Ask the students the following questions:
1. What keeps the object on the plane? Ans. Its weight.
2. What accelerates the object along the plane? Ans. Its weight.
3. What gives an object its weight? Ans. Gravity, F=mg
Therefore, since mass is not a vector quantity, the only possible
explanantion for this accelerating force along the plane is that the
component of its weight which is parallel to the plane is what is producing
the acceleration of the object along the plane. As the plane's angle of
inclination increases its acceleration along the plane increases until the
plane is 90 degrees at which point the acceleration of the object is equal
to the acceleration due to gravity. What else but gravity could produce
this effect?
Another way of looking at it is to think in terms of potential energy. The
object wants to lower its potential energy which is PE=mgh. Again, g is the
only vector quantity in the equation. Consequently, it seems that we _can_
think of the acceleration due to gravity as having perpendicular components
for ease of understanding. Of course, we all know that gravity wants to
accelerate objects radially toward the center of the Earth but that doesn't
help us understand the motion of objects down an inclined plane, which gets
in the way of the radial acceleration. Remember, vectors are just a
convenient method of analysis...they're not real, and that is perhaps the
most important lesson here.
-Marc
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Favorite Oakland Raiders motto: Marc Afifi
Pacific Grove HS
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