# Relationship between equilibrant and resultant force

### AP_Equilibrant_Lab

resultant is a single force calculated as the vector sum of the forces exerted on the on the force table by examining the equilibrant, which is a single force that . the % difference between the magnitude of the force measured on the table and. Use spring balances to demonstrate the relationships between the resultant and the equilibrant. Aim: Demonstrate the relationship between the resultant force. Question: How do the Equilibrant and Resultant vectors relate to each It says, " A force equal to but opposite in direction to the resultant is.

Draw your first vector from a point chosen so that all the drawn vectors will fit within the confines of your paper. The first vector should appear as a line whose length and direction have been drawn with reference to your established scales.

RESULTANT FORCE AND EQUILIBRIUM FORCE

The starting point is located at the "tail" of the vector. The end of the vector should be adorned with an arrow tip. This is the "head" of the second vector. The graphical method of adding vectors is accomplished by drawing them in a sequential "head-to-tail" chain.

### equilibrant - Wiktionary

Additional vectors may be added to each previously drawn vector. Starting from the head of the first vector, construct the second vector following the same procedure used to construct the first vector. The staring point tail for the second vector will begin at the arrow-tip head of the first vector. The end of the second vector should also be adorned with an arrow-tip. This is the head of the second vector. The graphical method of adding vectors is accomplished by drawing them in a sequential "head-to-tail" chain, preserving both length magnitude and orientation direction.

Additional vectors may be added to each previously drawn vector in turn. The order in which vectors are placed added is irrelevant. As long as all of the vectors are drawn to the appropriate length and in their proper orientation, the sum resultant will be the same. Once all of the concurrent vectors have been drawn, it is time to construct the equilibrant vector or vector "equalizer". This is accomplished by drawing a line from the head of the last vector to the tail of the first vector.

An arrow-tip is placed at the end of this line, that is, at the tail of the first vector drawn in the chain.

This is the equilibrant anti-sum of all the vectors you have drawn in the chain. Coplanar force systems have all the forces acting in in one plane. They may be concurrent, parallel, non-concurrent or non-parallel. All of these systems can be resolved by using graphic statics or algebra. A concurrent coplanar force system is a system of two or more forces whose lines of action ALL intersect at a common point. However, all of the individual vectors might not acutally be in contact with the common point.

These are the most simple force systems to resolve with any one of many graphical or algebraic options. A parallel coplanar force system consists of two or more forces whose lines of action are ALL parallel.

This is commonly the situation when simple beams are analyzed under gravity loads. These can be solved graphically, but are combined most easily using algebraic methods.

The last illustration is of a non-concurrent and non-parallel system. This consists of a number of vectors that do not meet at a single point and none of them are parallel. These systems are essentially a jumble of forces and take considerable care to resolve.

## Equilibrant force

Almost any system of known forces can be resolved into a single force called a resultant force or simply a Resultant. The resultant is a representative force which has the same effect on the body as the group of forces it replaces.

A couple is an exception to this It, as one single force, can represent any number of forces and is very useful when resolving multiple groups of forces. One can progressively resolve pairs or small groups of forces into resultants. Then another resultant of the resultants can be found and so on until all of the forces have been combined into one force.

This is one way to save time with the tedious "bookkeeping" involved with a large number of individual forces. Resultants can be determined both graphically and algebraically. The graphical methods that will be discussed in Lecture 8 are the Parallelogram Method and the Triangle Method. It is important to note that for any given system of forces, there is only one resultant.

It is often convenient to decompose a single force into two distinct forces.

These forces, when acting together, have the same external effect on a body as the original force. They are known as components. Finding the components of a force can be viewed as the converse of finding a resultant. There are an infinate number of components to any single force. And, the correct choice of the pair to represent a force depends upon the most convenient geometry.

For simplicity, the most convenient is often the coordinate axis of a structure. This diagram illustrates a pair of components that correspond with the X and Y axis. These are known as the rectangular components of a force. Rectangular components can be thought of as the two sides of a right angle which are at ninety degrees to each other.

## Difference between resultant and equilibrant?

The resultant of these components is the hypotenuse of the triangle. The rectangular components for any force can be found with trigonometrical relationships: There are a few geometric relationships that seem common in general building practice in North America.

These relationships relate to roof pitches, stair pitches, and common slopes or relationships between truss members. Some of these are triangles with sides of ratios ofsqrt3, sqrt2, or Commiting the first three to memory will simplify the determination of vector magnitudes when resolving more difficult problems.