Re: teaching vectors

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 17:46 -0500 10/2/02, Raeghan Graessle wrote:
> I am looking for a creative way to teach vectors
> to my conceptual physics class (high school level).
> Any suggestions?
Here are some suggestions:

The most intuitive vectors are displacement vectors. Let the students
construct different paths from point A to point B, and note that, no
matter what multiple (straight-line) path they follow, if they end up
at B after starting from A, they have "displaced" themselves along
the straight line connecting A and B. That is, when they say how far
the are from A, they don't mean how long a route they traveled, but
what is the "as the crow flies" distance and direction.

Playing with Etch-a-Sketches are another way to visualize vectors.
Although the knobs only allow the cursor to move up and down or right
and left, the simultaneous combination of the two motions will enable
them to construct any path they want.

Velocity vectors are a bit more complicated, but can be shown with
relative motion. Have them pull a toy truck across a long sheet of
wide paper that is moving perpendicular tot he direction of the
truck, and note how the motion of the truck appears relative to the
floor. Interactive Physics can help here.

Try force as a vector by showing how things move under the influence
of forces in different directions, like pushing on a door
perpendicular to its face, or along its face, toward the hinges, etc.
Push something across the table with the force parallel to the table,
and then increase the angle gradually and see how much harder it is
to push when the force is not in the direction you want the object to
move.

They should be doing these things themselves.

How much more do you want them to learn about vectors? Addition and
Subraction? Multiplication? Balancing forces? Torques?

Hugh
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Hugh Haskell
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<mailto:hhaskell@mindspring.com>

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