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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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