Procedure: Using the
Visualizing Vectors Worksheet, students explore how
the force varies with the angle at which the spring scale is pulled. These
observations lead to an exploration of vectors.
Besides the variation of force within the range, there is another issue illustrated
in the picture. The angle at which the spring scale is placed, with respect to the
tong arm, will also affect the result. If students try this measurement several
times, with various orientations of the scale, they are likely to make two
important discoveries:
The measurements depend on the angle of the scale relative to the arm.
The measured force is smallest when the scale is perpendicular to the arm.
In the graphic, we see how vectors can be used to represent and explain these two
observations. A vector has a magnitude, just like an ordinary number, and also a
direction, showing which way it leads. The magnitude of a force vector is just the
amount of force; in other words, the reading on the spring scale. The direction of
each force vector is the direction of the spring scale away from the arm. Vector A
represents the force measured on a spring scale that is perpendicular to the arm,
while B is the force measured at an oblique angle.
Now we can express observations 1 and 2 in the language of vectors:
The magnitude of the force vector depends on its direction.
The magnitude is least when the force vector is perpendicular to the arm.
Procedure: Using the
Visualizing Vectors Worksheet, students explore how
the force varies with the angle at which the spring scale is pulled. These
observations lead to an exploration of vectors.
In the graphic, we see how vectors can be used to represent and explain these two
observations. A vector has a magnitude, just like an ordinary number, and also a
direction, showing which way it leads. The magnitude of a force vector is just the
amount of force; in other words, the reading on the spring scale. The direction of
each force vector is the direction of the spring scale away from the arm. Vector A
represents the force measured on a spring scale that is perpendicular to the arm,
while B is the force measured at an oblique angle.
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