PURPOSE

You will learn to relate vectors (or arrows) and vector arithmetic to physical situations involving forces.

MATERIALS force table, weights, protractor, ring with strings.

RELEVANT EQUATIONS

Components of a vector:                                F_x = F cos q

                                                                        F_y = F sin q

Magnitude and direction: 

DISCUSSION

A force has both direction and magnitude. As such, it is a vector quantity that can be represented as an arrow with an angle (direction) and a scale (magnitude).

When forces are to be added, there are two basic methods: graphical and analytical. You will learn to apply both of these methods in this experiment.

In the graphical method the force vectors are accurately laid out to scale on a graph, with directions drawn relative to a reference line. To add one force to another, the second force is transported without changing its orientation so that its tail contacts the tip of the first vector. The sum, or resultant vector is then drawn from the origin to the tip of the last vector, and its magnitude and direction measured according to the scale.

In the analytical method, the two forces are resolved into their components using the equations given above, the respective x- and y-components added together, and then the magnitude and direction of the resultant determined from the equations above.

In this experiment, you will represent all forces as arrows drawn to scale, using the positive x-axis of your graphs as the 0.0° reference line. In all cases, the positive x-axis will represent the 0.0° line of the force table. Measure the angular directions of all vectors counterclockwise from the positive x-axis.