Core - Mechanical Engineering

Chapter 2

Force Vectors

2.1 : Scalar and Vectors

2.1 : 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 physical ...

2.2 : Vector Operations

2.2 : Vector Operations

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

2.3 : Introduction to force

2.3 : 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 of ...

2.4 : Force Classification

2.4 : 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 in ...

2.5 : Vector Addition of Forces

2.5 : 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 be ...

2.6 : Two-Dimensional Force System

2.6 : 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 resolved ...

2.7 : Two-Dimensional Force System: Problem Solving

2.7 : 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 ...

2.8 : Scalar Notation

2.8 : Scalar Notation

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

2.9 : Cartesian Vector Notation

2.9 : Cartesian Vector Notation

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

2.10 : Direction Cosines of a Vector

2.10 : 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 vector ...

2.11 : Three-Dimensional Force System

2.11 : 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 z ...

2.12 : Three-Dimensional Force System:Problem Solving

2.12 : 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 ...

2.13 : Position Vectors

2.13 : 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 is a ...

2.14 : Force Vector along a Line

2.14 : 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. Consider a ...

2.15 : Dot Product

2.15 : 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 magnitudes of ...

2.16 : Dot Product: Problem Solving

2.16 : 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 and ...

2.17 : Cross Product

2.17 : 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 ...

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