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
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:
S7P3A32 (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 (S7) 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 S7P3A32
Motion at play, rotational at effort, linear at load. PjProblemStrings S7P4A42 at effort and S7P4A41 at load
static equilibrium at load when effort is released. PjProblemStrings S7P7A71
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 = x2 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