Addition of vectors
Name _____________________ Class ______________
Date _________
Addition and Resolution of Vectors
Equilibrium of a Particle
Overview
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
G equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and
G
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
G
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
Date _________
Addition and Resolution of Vectors
Equilibrium of a Particle
Overview
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
G equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and
G
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
G
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