ResultantForce 2025-03-08 17:04:23 2025-06-02 00:47:52 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) \usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The resultant force is simply the sum of the total external forces acting on a body. $$ \mathbf{F}_{res} = \sum_{i=1}^{n}\mathbf{ F}_{i} = \mathbf{ F}_1 + \mathbf{ F}_2 + ...$$ Geometrically, the resultant force $\mathbf{R}$ of two forces $\mathbf{P}$ and $\mathbf{Q}$ is shown in Figure 1. The law of the parallelogram of forces states that given two vectors, the resultant force of using these vectors as sides to a parallelogram is the diagonal of the parallelogram. \begin{figure}[h] \centering \includegraphics{ResultantForceFig1.png} {\tiny Figure 1: Resultant force and the law of the parallelogram of forces. } \end{figure} \begin{thebibliography}{9} [1] Brooke, William; Wilcox, Hugh. "Engineering Mechanics". Ginn and Company, Boston, 1929. \\ [2] Ling, Samuel et al. "University physics". Volume 1. OpenStax College, Houston, 2021. \\ \end{thebibliography}