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Re: [Phys-l] Motion in 1D, vectors and vector components



To me, the big question (yet to be completely answered) in this thread
can be reworded in terms of the first diagram at
<http://www.av8n.com/physics/img48/pin-connected.png>
if we change the diagram so that the surface on which the anvil rests is
tilted (rotate everything in the diagram, for instance, 20 degrees
counterclockwise relative to the "page", but keeping "toward the bottom
of the page" as the downward direction. Then, given that the anvil is
in equilibrium; given that the frictional force on the anvil is
negligible; given the values for the mass of the anvil and the magnitude
of |F_a> chosen so that it is not clear by inspection whether the simple
straight strut is in tension, compression, or neither; and assuming that
the strut force is not zero (in a special case you might prove that it
is zero but one should still start off with the non-zero assumption) the
question is, in a free body diagram of the anvil, how do you draw the
vector that is or represents the force exerted on the anvil by the
strut? You can't (prior to solving the problem) draw an arrow to scale
to represent the physical geometric vector because you don't know how
long to make the arrow and while you know that it lies along the line
passing through the two pins, you don't know in which of the two
possible directions along that line the arrow should be pointing. The
only complete answer (that I have seen and understood to be a complete
answer telling one how to drag the tip of a pencil around on some
paper--perhaps I missed one) in our recent discussion and references
made in that discussion, to the question as to how to diagrammatically
represent an unknown vector known to be along a specified line, appears
in
<http://www.av8n.com/physics/intro-vector.htm#sec-circuits>
where the unknown vector is the charge flow rate at a point in a
circuit. There, the physical geometrical vector is represented in a
diagram, not by means of a properly oriented arrow with a length drawn
to scale (since we wouldn't known how long to make it or which way to
orient it), but by means of the combination of an arrowhead and, very
close to the arrowhead, a letter with a subscript, namely I_3. The
arrowhead, although not labeled "basis vector" or "e_3" is supposed to
be understood to represent a basis vector and the letter with subscript,
namely I_3 is supposed to be a component value, a.k.a. matrix element,
for the vector, where it is supposed to be understood that in any set of
orthonormal basis vectors in which the basis vector represented by the
arrowhead is one of the basis vectors, the component value (matrix
element) I_3 is the only non-zero matrix element for the geometrical
vector in question (so the geometrical physical vector itself is equal
to the matrix element times the basis vector). I think that this is a
beautiful way to represent an unknown geometrical physical vector on a
diagram while at the same time defining a component value variable
(matrix element) whose value is to be solved for. Should one find that
I_3=-4.00mA, then the reader of a solution that includes both the
diagram and the statement that I_3=-4.00mA should have all the
information that is needed about the geometrical physical vector in
question. I think that this method is an excellent way of representing
an unknown geometrical physical vector in a diagram. The question
remains, how do you (phys-l subscribers) represent an unknown force
(unknown magnitude, direction known to be in one direction or the
direction opposite that one direction) in a free body diagram?