Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

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States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

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Chemical Reactions

Electromagnetism

Continuity

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Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

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Faith, Love, Charity

Photosynthesis

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Systems

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Tools

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Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Calculating Vickers Hardness Number

**(a)** What is *technological hardness*?
**(b)** What is *Vickers hardness*?
**(c)** A Vickers hardness test made on a steel specimen with a load of 30 kg produces an impression whose diagonal measure is 0.654 mm. Calulate the Vickers hardness number and determine the load that should be used if the hardness of an area 0.050 mm in diameter, in the same piece of steel, is to be measured.

**The strings**:
S_{7}P_{3}A_{32} (force - push).
**The math**:

Pj Problem of Interest is of type *force* (push).
**(a)** In general *hardness*, is the strength of the surface of a material. In many instances, the surface strength of a material is significantly different from that of the bulk (e.g. surface-hardened steel).*Technological hardness* is the resistance of a material to permanent deformation of its surface. The deformation may be a *scratching impression*, *mechanical wear*, *indentation*, or *cutting*.
**(b)** *Indenters* of various geometric shapes are used to test the hardness of the surface of a material. Some of the commonly used shapes are: sphere, cone and pyramid. *Vickers hardness* is the hardness measured by a square-based pyramid indenter.
**(c)** As an indenter penetrates the surface of a material, the area over which the force of the indenter acts, increases with the depth of penetration, Consequently, the *hardness* can be expressed only in terms of force and area. As figure 1.1 shows, the Vickers hardness is expressed in terms of force and area as follows:

Vickers hardness, Hv = P/A = P/d^{2}(2 sin α/2). Where A = d^{2}/(2 sin α/2) and α is the angle between two opposite faces of the pyramid; P is expressed in kilograms and A is expressed in millimeter.

Hv = (1.8544)(30/(0.654)^{2}) = 130.

Load P, to be used for area A = 0.050 mm with same hardness, P = [130(0.050)^{2}]/1.8544 = 0.175225 kg = 175 g.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings