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

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Levers - The PjProblemStrings

*Levers* are simple machines. Figure 128.1 illustrates a 6-inch file scraper (brown) being used to pry up the lid of a can.

(a) Name the other types of simple machines.

(b) What type of lever is the file scraper illustrated in figure 128.1?

(c) The blue arrows associated with the file scraper are

implicitly PjProblemStrings. Make them explicit.

(d) What is the mechanical advantage of the file scraper,

given that MN is 1 inch and NQ is 5 inches?

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

Pj Problem of Interest is of type *force* (push/pull).

(a) There are six explicit types of simple machines (lever, inclined plane, block and tackle, wheel and axle, screw and gear). However, physicists group simple machines into levers and inclined planes since block and tackle, wheel and axle and gears can be considered as levers while screws can be considered as inclined planes.

(b) There are three types of levers: first class, second class and third class.
*First Class*: *fulcrum* is located between *resistance* and *effort*
*Second Class*: *fulcrum* is at one end, *effort* at the other end and *resistance* is somewhere between the fulcrum and the effort.
*Third Class* : *fulcrum* is at one end, *resistance* is at the other end and *effort* is somewhere between the fulcrum and the resistance.

So, the file scraper illustrated in figure 128.1 is a *first class lever*.

(c) Assuming a multi-matter-multi-dynamic space (S_{7}) because of the dynamism of atoms of materials and the fact that there are several matter in the space.

Both the *resistance* and *effort* arrows are linearly directed *forces* (push).

So, the PjProblemStrings S_{7}P_{3}A_{32} and S_{7}P_{4}A_{41} are implied.

There is *static equilibrium* at the fulcrum

So, the PjProblemString (S_{7}P_{7}A_{71}) is implied.

(d) *Mechanical Advantage* is essentially the *gain in effort* or the *loss in effort*. In other words, *gain in effort* implies the *Resistance* overcomed is greater than the *Effort* applied while *loss in effort* implies the *Resistance* overcomed is less than the *Effort* applied.

Mathematical equation for Mechanical Advantage (M.A):

M.A = Reistance/Effort = *L/l*

Where *L* = length of *effort arm* (NQ)
*l* = length of *resistance arm* (MN).

So, for the file scraper of figure 128.1, M.A = 5/1 = 5

That is the *effort* can overcome a *resistance* that is five times the effort applied.

*First Class* and *Second Class* levers provide M.A > 1.
*Third Class* levers provide fractional M.A. They are often used to speed up *resistance* at the expense of *effort*. In other words, *effort* applied is greater than *resistance* overcomed because of the desire to overcome the *resistance* speedily.

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