Mechanics is the branch of science concerned with the behavior of physical bodies when subjected to forces or displacements, and the effects of the bodies on their environment. Mechanics is a physical science incorporating mathematical concepts directly applicable to many fields of engineering such as mechanical, civil, structural and electrical engineering.

Vector analysis is a mathematical tool used in mechanics to explain and predict physical phenomena. The word “vector” comes from the Latin word vectus (or vehere – meaning to carry). A vector is a depiction or symbol showing movement or a force carried from point A to point B.

Statics (or vector mechanics) is the branch of mechanics that is concerned with the analysis of loads (or forces and moments) on physical systems in static equilibrium. Systems that are in static equilibrium are either at rest or the system’s center of mass moves at a constant velocity. Unlike dynamics, where the components of the system are in motion, components of a system in static equilibrium do not move or vary in position relative to one another over time. Problems involving statics use trigonometry to find a solution.

Newton’s First Law states that an object at rest tends to stay at rest or an object in motion tends to stay in motion at a constant velocity, unless acted upon by an external force. In the area of statics Newton’s First Law dictates that the sum of all forces, or net force, and net moment on every part of the system are both zero.

The term “static” means still or unchanging. In relation to vector mechanics the terms “still” or “unchanging” pertain to the system under evaluation. The system may be at rest or may be moving at a constant velocity, but all of the components of the system are still or in equilibrium with each other. However, there are forces within the system usually acted upon by gravity, but all of the forces are balanced.

This course is intended to be a refresher course for statics (vector mechanics). This course is intended for someone who has a general working knowledge of vectors. This course has a lot of sample problems and teaches by showing examples and sample problems.

Learning Objectives

At the conclusion of this course the learner will understand:

How to decompose a force into its vector components
How to determine the equilibrium of a particle
How to determine the equilibrium of a rigid body
How to determine the mechanical advantage of a pulley system
How bodies are subject to moments (or torque)
How to reduce a force couple to a moment
How to reduce a system to a force and a moment
How to determine if a truss is stable
How to determine the axial forces within a truss by the method of joints
How to determine the axial forces within a truss by the method of sections
How to calculate the force of friction between a body and a surface
How the determine the equilibrium of a body when the force of friction acts on the body

Statics: Vector Mechanics

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