FORCES & VECTORS
PRELAB
PURPOSE
You will learn to relate vectors (or arrows) and vector arithmetic to physical situations involving forces.
EQUIPMENT
force table, weights, protractor, ring with strings.
RELEVANT EQUATIONS
Components of a vector: Fx = F cos θ
Fy = F sin θ
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 length (magnitude).
There are two basic methods to add force vectors: graphical and analytical. You will learn to apply both of these methods in this experiment.
In the graphical method the force vectors are accurately drawn 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 (beginning) contacts the tip (arrow) 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. (See Figure 5-1.)
Figure 5-1: Graphical Representation of Forces
Scale: 1 cm = 10 N
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° reference line. In all cases, the positive x-axis
will represent the 0° line of the force table. Measure the angular
directions of all vectors counterclockwise from the positive x-axis.
Print out and complete the
Prelab questions.