Addition of vectors
Addition and Resolution of Vectors
Equilibrium of a Particle
When a set of forces act on an object in such a way that the lines of action of the forces pass through a common point, the forces are described as concurrent forces. When these forces lie in the same geometric plane, the forces are also described as coplanar forces. A single
G equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and
F2 , as shown. This resultant force is obtained by a process of vector addition of the original force vectors and produces the same effect as the combined effect produced by all the original forces. Conversely, a set of concurrent forces can be balanced exactly by a single force that acts at the common point of concurrence of the forces. Such a force is
known as the equilibrant FE of that set of forces and it is equal in magnitude but acts in exactly opposite direction to the resultant of the set of forces. A particle is considered to be in (static) equilibrium under the action of a set of forces when the vector sum of all the forces is zero.
In this laboratory experiment, the student will be introduced to methods of addition of vectors. Using a force table, the student will determine the magnitudes and directions of applied concurrent forces, find the resultant force of a given set of vectors, investigate the relationship between the resultant force and the equilibrant force of a given set of forces, and compute the rectangular x- and y-components of known forces and their resultant force.
The force table apparatus used in this experiment has a horizontally mounted circular table and the rim of this table is calibrated in degrees, from 0° to 360°. Forces of any chosen magnitude can be applied to a central ring (placed around a central pin at the center of the circular table) at any preferred angle by means of strings passing over a pulley and attached to a