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# Chapter 2 Force Vectors

## Scalar and Vectors

In mechanics, commonly used terms like force, speed, velocity, and work can be classified as either scalar or vector quantities. A scalar is a…

## Vector Operations

Vectors are physical quantities that have both magnitude and direction. The vector operations include addition, subtraction, and scalar…

## Introduction to force

Consider water flowing from a nozzle to a turbine vane. As the water hits the turbine vane, it exerts a force that causes it to move along the flow…

## Force Classification

Forces play a crucial role in the study of physics and engineering. They are essential in describing the motion, behavior, and equilibrium of objects…

## Vector Addition of Forces

When understanding the effects of multiple forces acting on an object, vector addition is a crucial concept to grasp. This mathematical concept can…

## Two-Dimensional Force System

A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be…

## Two-Dimensional Force System: Problem Solving

Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector…

## Scalar Notation

Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be…

## Cartesian Vector Notation

Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector…

## Direction Cosines of a Vector

Direction cosines, which help describe the orientation of a vector with respect to the coordinate axes, are an essential concept in the field of…

## Three-Dimensional Force System

In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and…

## Three-Dimensional Force System:Problem Solving

A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is…

## Position Vectors

A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It…

## Force Vector along a Line

Quite often in three-dimensional statics problems, the direction of a force is specified by two points through which its line of action passes.…

## Dot Product

The dot product is an essential concept in mathematics and physics. In engineering, the dot product of any two vectors is the product of the…

## Dot Product: Problem Solving

The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes…

## Cross Product

The cross product is a fundamental concept in vector algebra that is a vector operation on two different vectors to obtain a third vector. Unlike the…

## Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

In this paper, we present a complete workflow for the biomechanical analysis of atherosclerotic plaque in the coronary vasculature. With…

## External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

A neuron will fire an action potential when its membrane potential exceeds a certain threshold. In typical activity of the brain, this occurs as a…

## Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

It is well known that the flow field over a delta wing is dominated by a pair of counter rotating leading edge vortices (LEV). However, their…

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