Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
A cable weighing 2 lbs/ft is used to lift a 300 lbs load from the bottom of a well 100 feet deep.
Calculate the work done to raise the load to the surface.
(a) S7P3A31 (Force - Pull).
Pj Problem of interest is of type force. Work problems are generally of type force because force is the doer of work. In the case of white-collar work, intellectual force actuates materiality.
Consider the above diagram (fig. CW.1):
Let W be the work done to raise the load x feet.
Let k be the work done in raising the load h feet.
k = [300 + 2(100 - xavg)]h -------(1). xavg is the representative average of the partitions of the distance BC.
So, the rate of change of k with respect to h is:
k/h = [300 + 2(100 - xavg)] = 500 -2xavg
limit (k/h) as h → 0 = dW/dx (instantaneous change of W with respect to x)
So, limit (k/h) as h → 0 = 500 -2x. Since xavg → x.
So, dW/dx = 500 -2x.
So, W = 500x - x2 + C---------(2). Where C is a constant.
When x = 0, W = 0. So C = 0.
So, W = 500x - x2.
So, for x = 100,
W = 500(100) - (100)(100) = 40,000 ft-lb.
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
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
Derivation Of Heat Equation For A One-Dimensional Heat Flow
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.
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