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Solving Vector Addition Problems using Three Different Methods

Three different methods are use to compute for the resultant vector of the given vectors, to show the difference between these three methods. The first method is the parallelogram method, the second one is the analytical method and lastly the polygon method.

I. Introduction

The goal of this paper is to answer a problem in vector addition using three methods: Polygon, Analytical, and Parallelogram method. It is hope that these study will will interest not only the students in physics, but also physicist who have been formulated the methods in solving Vector Addition. The fact, as will become clear, is that a variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). This process of adding two or more vectors has already been discussed in an earlier unit. Recall in our discussion of Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors.

The objectives of this paper are: (1) practice the polygon method of vector addition, and (2) compare the graphical results with calculation (analytical solution) to get an idea of how accurate the graphical method used is.

In polygon method, two vectors A and B are added by drawing the arrows which represent the vectors in such a way that the initial point of B is on the terminal point of A. The resultant C = A + B, is the vector from the initial point of A to the terminal point of B. In parallelogram method the resultant R is the diagonal of the parallelogram drawn from the common origin. The vector analytical method is limiting a vector to 2 dimensions when adding components. An example of this is A to the base of x added to...