Posts Tagged ‘Science’

Poisson’s Equation

Friday, September 18th, 2009

How to Solve Poisson’s Equation

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A detailed tutorial on the solving of Poisson’s Equation. Step by step tutorial including several examples of how to solve Poisson’s Equation for reference.

 

 

 

 

 

Overview

 

 

 

Poisson’s Equation is a partial differential equation. It is used in sections of math that deal with engineering and physics. The formula is named after Siméon-Denis Poisson. There are a few different ways of expressing it. In general terms, this equation is expressed as: \Delta\varphi=f

However, in certain branches of math, it is written as {\nabla}^2 \varphi = f..

A third way of expressing it is used in Cartesian coordinates, and it is written as:

\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} \right)\varphi(x,y,z) = f(x,y,z).

Chemical Equations

Friday, September 18th, 2009

How to Balance Chemical Equations?

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A detailed tutorial on the Balancing Chemical Equations. Step by Step example of balancing a chemical equation.

Overview

The law of conservation of mass states that the quantity of each element does not change in a chemical reaction. Therefore each side of the chemical equation must represent the same quantity of any particular element.

You balance a chemical equation by changing the scalar number for each molecular formula, until the quantities of each element on the left side of the equation match the quantites of each element on the right side.

Newtons 3rd Law of Motion: Reciprocal Actions

Wednesday, September 16th, 2009

Newtons 3rd Law of Motion Explained

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A detailed explanation of Newtons 3rd Law of Motion: Reciprocal Actions. Step by step tutorial including several examples of how to apply Newtons 3rd Law of Motion: Reciprocal Actions for reference.

Overview

Newton’s third law basically states that for every action there is an equal and opposite reaction.  This also applies to forces.  Whenever there is a force, there is a reaction force equal in magnitude in the exact opposite direction.

Friction on an Incline Plane

Tuesday, September 15th, 2009

How to calculate the force of friction on an incline plane?

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A detailed tutorial on the solving for Friction on an Incline Plane. Step by step tutorial including several examples of how to solve for Friction on an Incline Plane for reference.

Overview

The force of friction, F_f, can be defined as \mu multiplied by the normal force, N.
F_f = \mu * N

N is equal to the opposing force perpindicular to the surface.  In the case of an inclined plane, the opposing force to the surface would be the perpindicular component of gravity acting on the object.  To get this component, you must complete the triangle and solve for the normal force.  Once you have the normal force you can multiply by the coefficient of friction to get the force of friction.

Exponential Growth and Decay

Tuesday, September 15th, 2009

Introduction to Exponential Growth and Decay

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A detailed tutorial on the solving of exponential growth and decay or half-life. Step by step tutorial including several examples of how to solve exponential growth and decay or half-life for reference.

Overview

Exponential growth and decay, sometimes called half-life, is very similar to compound interest – not in what you\’re solving for, but in the way the equations are set up and how you solve them. This is the exponential growth and decay (or half-life) formula:

N(t) = Nsub(o) * e^kt

Where N(t) represents the population at time t, which tells us that t stands for time. Nsub(o) represents the initial population, and k represents the constant. Normally you are required to solve for the constant as well as the population at time t.

Newtons 1st Law of Motion: Law of Inertia

Friday, September 11th, 2009

Newtons 1st Law of Motion Explained

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A detailed tutorial on the solving of Newtons 1st Law of Motion: Law of Inertia. Step by step tutorial including several examples of how to solve Newtons 1st Law of Motion: Law of Inertia for reference.

Overview

Newton’s first law of motion states that an object at rest will remain at rest while an object in motion will remain in motion if there are no external forces acting on the object.  This means that if you dropped a ball in deep space where there are no external forces in action, the ball would remain where you dropped it and would not fall to the ground.  This also means that if you threw that ball in space, the ball would not slow down until it hit something or it encountered some other force to change its velocity.

Avogadros Number

Thursday, September 10th, 2009

What is Avogadros Number?

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A detailed tutorial on Avogadros Number and its relation to a Mole. Step by step tutorial including several examples of how to use Avogadros Number.

Overview

The Avagadro number is the number of elementary entities (atoms or molecules) in one mole.
One mole is the number of atoms in exactly 12 grams of carbon-12:
N_A = 6.03 \times 10^{23}
Avogadros number is used to convert the number of atoms into grams.
Just remember, you need Avagadros if you’re going to make guacaMOLE.

Newtons 2nd Law of Motion: F=ma

Thursday, September 10th, 2009

Newtons 2nd Law of Motion Explained

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A detailed tutorial on the solving of Newtons 2nd Law of Motion: F=ma. This video gives several detailed examples of how to use Newton’s 2nd law.

Overview

Newton’s second law states that force applied to a body produces a porportional acceleration expressed by the formula

F = m \times a,

where F is the force applied, m is the mass of the body, and a is the body’s acceleration. If the body is subject to multiple forces at the same time, then the acceleration is proportional to the vector sum (the net force):

F_1 + F_2 + \cdots + F_n = F_{net} = m \times a

Scientific Notation

Thursday, September 3rd, 2009

How to Use Scientific Notation

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This video explains each part of scientific notation and lays it out in an easy to read format. It explains the basic concept of exponents and what multiplication by 10 does to a number, then moves onto how to solve scientific notation and how to convert regular numbers into scientific notation. Many examples are provided.

Overview

Scientific notation is a shorthand for very big and very small numbers. It consists of a number multiplied by 10 to the nth power. This power is very often a small, positive number. You use scientific notation by moving the decimal over n number of spaces and filling in any empty spaces with the number zero. To convert a number into scientific notation, move the decimal point until you create a number that is less than 10 but bigger than 0. An easier way to remember it is leave only one number before your decimal point. The number of decimal points you moved over is the number you put as the exponent. An example is 2.468 * 10^8. Move the decimal point over 6 spaces. Your number is 246800000. Now take the number 4928400000. To convert this to scientific notation, we want to create the number 4.9284. We moved the decimal point 9 spaces to get that number, so in scientific notation it is 4.9284 * 10^9.

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