Expressions Of Pj Problems

Pj Problems - Overview

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7 Spaces Of Interest - Overview

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COHN - Natures Engineering Of The Human Body

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Differential Calculus

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Painting

Wheel And Axle - The PjProblemStrings

Figure 131.1 illustrates a brace with a screwdriver bit driving a screw. This machine belongs to the class of simple machines called the *wheel and axle*. Some common members of this group are the doorknob and the steering wheel of automobiles.

(a) Physicists say, the wheel and axle is a type of lever. What type of lever is the brace and bit of figure 131.1 ?

(b) What is the theoretical mechanical advantage of the brace and bit of figure 131.1?

(c) Write the PjProblemStrings at play with respect to the brace and bit of figure 131.1?

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

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

(a) The machine illustrated in figure 131.1 is a second class lever. The resistance is between the fulcrum and the effort as indicated the the top view illustration (131.1B).

Notable: a wheel and axle has the axle rigidly attached to the wheel and the axle rotates with the wheel.

(b) The *theoretical mechanical advantage* (T.M.A) ignores the effect of *friction*. TMA = distance effort moves/distance resistance moves = Resistance/effort.

So, for the machine in figure 131.1:

T.M.A = 5/(1/4) = 20.

The ratio of the diameters of the circumferences of the wheel and axle indicates the mechanical advantage.

(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.

Forces at play of type *push*. PjProblemStrings S_{7}P_{3}A_{32}

Motion at play, *rotational*. PjProblemStrings S_{7}P_{4}A_{42}

static equilibrium at the fulcrum. PjProblemStrings S_{7}P_{7}A_{71}

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