Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

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7 Spaces Of Interest - Overview

Triadic Unit Mesh

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COHN - Natures Engineering Of The Human Body

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Differential Calculus

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Painting

The Screw - The PjProblemStrings

Figure 132.1 illustrates a jack screw. This machine belongs to the class of simple machines called the *screw*. Some common members of this group are the micrometer, the foodprocessor used to grind meat, the rigger's vice and the friction brake.

(a) Physicists say, the screw is a type of an inclined plane. What simple experiment shows that the screw is an adaptation of the inclined plane?

(b) What is the theoretical mechanical advantage of the jack screw of 132.1 if R = 24 and p = 1/4?

(c) Why is it that most of the theoretical mechanical advantage of the jack screw is lost to friction?

(d) Write the PjProblemStrings at play with respect to the jack screw of figure 132.1

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

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

(a) A *screw* is an adaptation of an inclined plane. A simple experiment that supports this fact is as follows:

Cut a sheet of paper in the shape of a right triangle to represent an inclined plane. Wind the right triangle paper around a cylindrical pencil by turning the pencil such that the hypotenuse of the right triangle forms a spiral thread as shown in figure 132.2.

(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 jack screw in figure 132.1:

T.M.A = 2πR/p where p is the pitch of the screw.

So, T.M.A = (2 x 3.14x 24)/(1/4) = 602.88.

(c) The Jack screw has much friction loss because the threads are cut such that the force used to overcome friction is greater than the force used to do useful work so that the load does not slip down when the effort is released.

(d) 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* at effort, linear at load. PjProblemStrings S_{7}P_{4}A_{42} at effort and S_{7}P_{4}A_{41} at load

static equilibrium at load when effort is released. 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