Physics Book - User contributions [en]

Blaise Pascal

2015-12-05T21:05:36Z

Tknight30: /* References */

Short Description of Topic

==Mathematical and Scientific Discoveries==
[[File:BlaisePascal.png]]

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

-In 1631, Pascal's father moved him and his two sisters to Paris, and already at his early age, Blaise showed an amazing aptitude for mathematics and science.

-In 1642, when Pascal was not even 19, he made his first calculator in an effort to help is father with his commissioner of taxes work.

- In 1646, Pascal replicated Evangelista Torricelli's experiment with a tube, bowl, and mercury which led to his discoveries about vacuums.

-Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

- In 1654, Pascal developed a probabilistic argument called Pascal's Wager, to justify God and a virtuous life. This work done by Pascal into the calculus of probabilities helped the formation of calculus.

- Later in 1654, Pascal endured a religious experience which led to him mostly giving up work in mathematics.

- In late 1654, Pascal began writing influential works on philosophy and theology.

- Pascal had poor health from the time he turned 18, and in 1662 Pascal's illness became more violent along with his worsening emotional condition from his sister's death.

- Pascal died on August 19th, 1662 at the young age of 39.

== See also ==
To learn more about Pascal's calculators:
https://en.wikipedia.org/wiki/Pascal%27s_calculator

To further read about Pascal's Trangle:
https://en.wikipedia.org/wiki/Pascal%27s_triangle

to learn more about Pascal's experiment with hydrostatic pressure:
https://en.wikipedia.org/wiki/Pascal%27s_barrel
===Further reading===

To read about Pascal's ''De l'Esprit géométrique'' ("Of the Geometrical Spirit") which is the preface to a geometry textbook "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"):
https://en.wikipedia.org/wiki/Petites_%C3%A9coles_de_Port-Royal

===External links===
http://www.biography.com/people/blaise-pascal-9434176

==References==

https://en.wikipedia.org/wiki/Blaise_Pascal

https://en.wikipedia.org/wiki/Pascal_(unit)

http://www.daerospace.com/HydraulicSystems/HydraulicFluidProp.php

https://en.wikipedia.org/wiki/Pascal%27s_triangle

http://chatafrik.com/special/philosophers/blaise-pascal-men-of-ideas#.VmNQ5XarRD9

Blaise Pascal

2015-12-05T21:05:15Z

Tknight30: /* Mathematical and Scientific Discoveries */

File:BlaisePascal.png

2015-12-05T21:04:41Z

Tknight30:

Blaise Pascal

2015-12-05T20:56:34Z

Tknight30: /* References */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

-In 1631, Pascal's father moved him and his two sisters to Paris, and already at his early age, Blaise showed an amazing aptitude for mathematics and science.

-In 1642, when Pascal was not even 19, he made his first calculator in an effort to help is father with his commissioner of taxes work.

- In 1646, Pascal replicated Evangelista Torricelli's experiment with a tube, bowl, and mercury which led to his discoveries about vacuums.

-Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

- In 1654, Pascal developed a probabilistic argument called Pascal's Wager, to justify God and a virtuous life. This work done by Pascal into the calculus of probabilities helped the formation of calculus.

- Later in 1654, Pascal endured a religious experience which led to him mostly giving up work in mathematics.

- In late 1654, Pascal began writing influential works on philosophy and theology.

- Pascal had poor health from the time he turned 18, and in 1662 Pascal's illness became more violent along with his worsening emotional condition from his sister's death.

- Pascal died on August 19th, 1662 at the young age of 39.

== See also ==
To learn more about Pascal's calculators:
https://en.wikipedia.org/wiki/Pascal%27s_calculator

To further read about Pascal's Trangle:
https://en.wikipedia.org/wiki/Pascal%27s_triangle

to learn more about Pascal's experiment with hydrostatic pressure:
https://en.wikipedia.org/wiki/Pascal%27s_barrel
===Further reading===

To read about Pascal's ''De l'Esprit géométrique'' ("Of the Geometrical Spirit") which is the preface to a geometry textbook "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"):
https://en.wikipedia.org/wiki/Petites_%C3%A9coles_de_Port-Royal

===External links===
http://www.biography.com/people/blaise-pascal-9434176

==References==

https://en.wikipedia.org/wiki/Blaise_Pascal

https://en.wikipedia.org/wiki/Pascal_(unit)

http://www.daerospace.com/HydraulicSystems/HydraulicFluidProp.php

https://en.wikipedia.org/wiki/Pascal%27s_triangle

Blaise Pascal

2015-12-05T20:54:56Z

Tknight30: /* External links */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

-In 1631, Pascal's father moved him and his two sisters to Paris, and already at his early age, Blaise showed an amazing aptitude for mathematics and science.

-In 1642, when Pascal was not even 19, he made his first calculator in an effort to help is father with his commissioner of taxes work.

- In 1646, Pascal replicated Evangelista Torricelli's experiment with a tube, bowl, and mercury which led to his discoveries about vacuums.

-Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

- In 1654, Pascal developed a probabilistic argument called Pascal's Wager, to justify God and a virtuous life. This work done by Pascal into the calculus of probabilities helped the formation of calculus.

- Later in 1654, Pascal endured a religious experience which led to him mostly giving up work in mathematics.

- In late 1654, Pascal began writing influential works on philosophy and theology.

- Pascal had poor health from the time he turned 18, and in 1662 Pascal's illness became more violent along with his worsening emotional condition from his sister's death.

- Pascal died on August 19th, 1662 at the young age of 39.

== See also ==
To learn more about Pascal's calculators:
https://en.wikipedia.org/wiki/Pascal%27s_calculator

To further read about Pascal's Trangle:
https://en.wikipedia.org/wiki/Pascal%27s_triangle

to learn more about Pascal's experiment with hydrostatic pressure:
https://en.wikipedia.org/wiki/Pascal%27s_barrel
===Further reading===

To read about Pascal's ''De l'Esprit géométrique'' ("Of the Geometrical Spirit") which is the preface to a geometry textbook "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"):
https://en.wikipedia.org/wiki/Petites_%C3%A9coles_de_Port-Royal

===External links===
http://www.biography.com/people/blaise-pascal-9434176

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:54:04Z

Tknight30: /* See also */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

-In 1631, Pascal's father moved him and his two sisters to Paris, and already at his early age, Blaise showed an amazing aptitude for mathematics and science.

-In 1642, when Pascal was not even 19, he made his first calculator in an effort to help is father with his commissioner of taxes work.

- In 1646, Pascal replicated Evangelista Torricelli's experiment with a tube, bowl, and mercury which led to his discoveries about vacuums.

-Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

- In 1654, Pascal developed a probabilistic argument called Pascal's Wager, to justify God and a virtuous life. This work done by Pascal into the calculus of probabilities helped the formation of calculus.

- Later in 1654, Pascal endured a religious experience which led to him mostly giving up work in mathematics.

- In late 1654, Pascal began writing influential works on philosophy and theology.

- Pascal had poor health from the time he turned 18, and in 1662 Pascal's illness became more violent along with his worsening emotional condition from his sister's death.

- Pascal died on August 19th, 1662 at the young age of 39.

== See also ==
To learn more about Pascal's calculators:
https://en.wikipedia.org/wiki/Pascal%27s_calculator

To further read about Pascal's Trangle:
https://en.wikipedia.org/wiki/Pascal%27s_triangle

to learn more about Pascal's experiment with hydrostatic pressure:
https://en.wikipedia.org/wiki/Pascal%27s_barrel
===Further reading===

To read about Pascal's ''De l'Esprit géométrique'' ("Of the Geometrical Spirit") which is the preface to a geometry textbook "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"):
https://en.wikipedia.org/wiki/Petites_%C3%A9coles_de_Port-Royal

===External links===
http://www.biography.com/people/blaise-pascal-9434176

https://en.wikipedia.org/wiki/Blaise_Pascal

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:44:04Z

Tknight30: /* History */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

-In 1631, Pascal's father moved him and his two sisters to Paris, and already at his early age, Blaise showed an amazing aptitude for mathematics and science.

-In 1642, when Pascal was not even 19, he made his first calculator in an effort to help is father with his commissioner of taxes work.

- In 1646, Pascal replicated Evangelista Torricelli's experiment with a tube, bowl, and mercury which led to his discoveries about vacuums.

-Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

- In 1654, Pascal developed a probabilistic argument called Pascal's Wager, to justify God and a virtuous life. This work done by Pascal into the calculus of probabilities helped the formation of calculus.

- Later in 1654, Pascal endured a religious experience which led to him mostly giving up work in mathematics.

- In late 1654, Pascal began writing influential works on philosophy and theology.

- Pascal had poor health from the time he turned 18, and in 1662 Pascal's illness became more violent along with his worsening emotional condition from his sister's death.

- Pascal died on August 19th, 1662 at the young age of 39.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:29:59Z

Tknight30: /* Examples */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Here are a couple examples of calculating pressure in pascals.

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:28:49Z

Tknight30: /* Connectedness */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
Pressure and the Pascal relate to some of the classes I will be taking down the road, like fluids. I find fluids and their characteristics to be intriguing, and since I have a co-op with an HVAC company, it helps to have more knowledge on how fluids and pressure affect the HVAC systems.

This is very connected to my major because my major is mechanical engineering, which has several classes pertaining to the understanding of fluids and how they work, as well as pressure and how the two relate.

There are many industrial applications to pressure because there are many reactions that can only take place under high pressure conditions. Some of these are found in the areas of polymerization, separations, oil and gas recovery, and food processing.

==History==

Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:19:12Z

Tknight30: /* Difficult */

Short Description of Topic

==Mathematical and Scientific Discoveries==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.

Pascal also contributed to the field of study of hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids. His main inventions in these areas were the hydraulic press, which involved using hydraulic pressure to multiply force, as well as the syringe. Pascal proved that hydrostatic pressure does not depend on the weight of the fluid but rather on the elevation difference. Pascal also experimented some with barometers, and in 1646 he replicated Evangelista Torricelli's experimentation with barometers. Torricelli's experiment consisted of placing a mercury-filled tube upside down in a bowl of mercury. This is where he made a discovery about vacuums because he questioned what force kept some mercury in the tube and what filled the space above the mercury when the tube of mercury was upside down. This went against Aristotle's declaration of "Everything that is in motion must be moved by something", which caused Pascal to conduct further experimentation. In 1647 Pascal introduced "New Experiments with the Vacuum" which explained basic rules as to what degree liquids could be supported by air pressure, as well as providing reasons why it was a vacuum above the column of liquid in a barometer tube.

Since Pascal made so many contributions to the scientific knowledge of pressure, his last name was used for the SI unit of pressure. The pascal (symbol: Pa) is the derived unit for multiple measurements, including: pressure, internal pressure, stress, Young's Modulus, and ultimate tensile strength.

The Pascal is defined as one newton per square meter. Common units of the pascal are the hectopascal(hPa) = 100 Pa, which is also equal to 1mbar, as well as the kilopascal (1kPa = 1000Pa).

Another unit of measurement called standard atmosphere (atm) is equivalent to 101.325 kPa and is an approximation to the average pressure at sea level at 45° N.
===A Mathematical Model===

:<math>{\rm 1~Pa = 1~\frac{N}{m^2} = 1~\frac{kg}{m \cdot s^2}}</math>
where '''N''' is the newton,'''m''' is the meter, '''kg''' is the kilogram, and '''s''' is the second.

:<math>{\rm P = \frac{F}{A}}</math>
where '''P''' is Pressure in pascals(Pa), '''F''' is the force in newtons (N), and '''A''' is area in meters squared(<math>{\rm {m^2}}</math>).

===A Computational Model===
This a model applicable in Vpython for calculating pressure a box with sides (l & w) puts on the ground it sits on from gravity plus an external force(Fy):

Area = l*w

Fgrav = 9.8

Fnet = Fgrav + Fy

Pressure = Fnet / Area

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
A golf club with a flat face supplies a force of 700 N. The club face has an area of 7.1 x 10-4 m^2. What is the pressure?

P = F/A
P = (700 N/7.1 x 10-4 m^2)
P = 9.86 x 105 N/m^2
P = 9.86 x 105 Pa

===Middling===
A force of 100N is applied to one end of a tube with a radius of 8cm. What is the force resulting at the other end of the tube with a diameter of 6cm?

P1 = P2

(F1)/A1 = (F2)/A2

F2 = (F1*A2)/A1

A1 = pi*(0.08m)^2 = 0.02 m^2

A2 = pi*(0.06m/2)^2 = 2.83e-3 m^2

F2 = (100N*2.83e-3 m^2)/(0.02 m^2)

F2 = 14.15 N

===Difficult===
Calculate the pressure at a depth "h" in a cylinder with an area A and a height h filled with a fluid.

P = pressure, Po = pressure due to the air (atmospheric pressure)

The fluid is at rest,
So we can write:

Fnet = 0
PA – mg – PoA = 0

However we know that:
Mass = density x volume = density x (area x height)
, r = density

M = rV = rAh

So we can substitute:

PA – (rAh)g - PoA = 0

cancel out the Area, A:

P – (rh)g - Po = 0

and the pressure at any depth will be:

P = Po + rgh

In words this says: the pressure at a depth ‘h’ will be the atmospheric pressure(14.7 lbs/in2) + (rgh)

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Pascal created his ''Traité du triangle arithmétique'' ("Treatise on the Arithmetical Triangle") in 1653 while he was living in Paris, France.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T20:09:48Z

Tknight30: /* Middling */

Blaise Pascal

2015-12-05T19:59:48Z

Tknight30: /* Simple */

Blaise Pascal

2015-12-05T19:47:16Z

Tknight30: /* A Computational Model */

Blaise Pascal

2015-12-05T19:41:09Z

Tknight30: /* Mathematical and Scientific Discoveries */

Blaise Pascal

2015-12-05T18:53:54Z

Tknight30: /* History */

Blaise Pascal

2015-12-05T18:47:49Z

Tknight30: /* The Main Idea */

Blaise Pascal

2015-12-05T18:47:13Z

Tknight30: /* The Main Idea */

Short Description of Topic

==The Main Idea==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients.

[[File:PascalsTriangle.png]]

This shows that if you add the two numbers directly above each spot of the next row, the values you get are the order of every coefficient for each increasing degree equation.
===A Mathematical Model===

where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T18:40:26Z

Tknight30: /* The Main Idea */

Short Description of Topic

==The Main Idea==

Blaise Pascal (June 19, 1623 - August 19, 1662) was a French inventor, physicist, and mathematician who went on to make several discoveries in both mathematics and physics. Pascal's earliest work was in natural and applied sciences, where he made important contributions to the study of fluids, as well as better explaining the ideas of pressure and vacuum.
In his teenage years, Pascal started working on calculating machines. Over the course of several years, he developed fifty prototypes, and completely built twenty finished machines. These machines were called Pascal's calculators and established him as one of the first inventors of the mechanical calculator. These machines were capable of addition and subtraction, and even though they failed in becoming a commercial success, they were catalysts in the next 400 years of development of mechanical methods of calculation.
His most well known mathematical contribution is what people refer to as Pascal's Triangle. This "triangle" refers to Pascal's 1653 "Treatise on the Arithmetical Triangle" which describes a convenient tabular presentation for binomial coefficients. [[Media:https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj5hK2Cr8XJAhXB5yYKHbdzAU8QjRwIBw&url=%2Furl%3Fsa%3Di%26rct%3Dj%26q%3D%26esrc%3Ds%26source%3Dimages%26cd%3D%26cad%3Drja%26uact%3D8%26ved%3D0ahUKEwj5hK2Cr8XJAhXB5yYKHbdzAU8QjRwIBw%26url%3Dhttps%253A%252F%252Fen.wikipedia.org%252Fwiki%252FPascal%27s_triangle%26psig%3DAFQjCNEx9otnILO7m23Gr5XbZ_uor-YGFA%26ust%3D1449427139573085&psig=AFQjCNEx9otnILO7m23Gr5XbZ_uor-YGFA&ust=1449427139573085]]

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T18:23:06Z

Tknight30:

Short Description of Topic

==The Main Idea==

State, in your own words, the main idea for this topic

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Blaise Pascal

2015-12-05T18:22:33Z

Tknight30: Blanked the page

Blaise Pascal

2015-12-05T18:22:06Z

Tknight30:

Short Description of Topic

Contents [hide]
1 The Main Idea
1.1 A Mathematical Model
1.2 A Computational Model
2 Examples
2.1 Simple
2.2 Middling
2.3 Difficult
3 Connectedness
4 History
5 See also
5.1 Further reading
5.2 External links
6 References
The Main Idea[edit]
State, in your own words, the main idea for this topic

A Mathematical Model[edit]
What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model[edit]
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples[edit]
Be sure to show all steps in your solution and include diagrams whenever possible

Simple[edit]
Middling[edit]
Difficult[edit]
Connectedness[edit]
How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?
History[edit]
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also[edit]
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading[edit]
Books, Articles or other print media on this topic

External links[edit]
[1]

References[edit]
This section contains the the references you used while writing this page

Category: Which Category did you place this in?

Blaise Pascal

2015-12-02T02:32:23Z

Tknight30: Created page with "This Page was made by Tyler Knight."

This Page was made by Tyler Knight.

Main Page

2015-12-02T02:31:36Z

Tknight30: /* Notable Scientists */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Big Bang Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[Wave-Particle Duality]]
*[[String Theory]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Wolfgang Pauli]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
**[[Solenoid Applications]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electrical Resistance]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers]]
*[[Resistors and Conductivity]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
**[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Gravitational waves]]
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]