Physics Book - User contributions [en]

Electric Motors

2017-11-30T01:07:31Z

Jpricelight: /* Further reading */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

[[File:nano.jpg]]
This image shows the schematic for a nano-scale system that generates power from acoustic vibrations.

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

Michael Faraday also discovered the operating principle of electromagnetic generators between the year 1831-1832.The principle, later coined as Faraday's Law, simply put is that an electromotive force is generated in a conduction which encircles a changing magnetic flux. The first generators that were made were disk generators and direct current generators. Later come alternating current generators. As science had developed so to have the generator technology. Generators are now designed in both DC homopolar and MHD generators, as well as AC induction, linear electric, variable speed constant frequency generators. They exist on vehicles, bicycles, sailboats, and are essential components to every aspect of our daily life.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

"How Self-Powered Nanotech Machines Work"
https://www.scientificamerican.com/article/how-self-powered-nanotech-works/

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-30T01:06:06Z

Jpricelight: /* History */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

[[File:nano.jpg]]
This image shows the schematic for a nano-scale system that generates power from acoustic vibrations.

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

Michael Faraday also discovered the operating principle of electromagnetic generators between the year 1831-1832.The principle, later coined as Faraday's Law, simply put is that an electromotive force is generated in a conduction which encircles a changing magnetic flux. The first generators that were made were disk generators and direct current generators. Later come alternating current generators. As science had developed so to have the generator technology. Generators are now designed in both DC homopolar and MHD generators, as well as AC induction, linear electric, variable speed constant frequency generators. They exist on vehicles, bicycles, sailboats, and are essential components to every aspect of our daily life.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:38:31Z

Jpricelight: /* Connectedness */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

[[File:nano.jpg]]
This image shows the schematic for a nano-scale system that generates power from acoustic vibrations.

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:37:00Z

Jpricelight: /* Connectedness */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

[[File:nano.jpg]]

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

File:Nano.jpg

2017-11-29T23:36:05Z

Jpricelight:

Electric Motors

2017-11-29T23:35:15Z

Jpricelight: /* Connectedness */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:34:47Z

Jpricelight: /* Connectedness */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
a. Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.
b. Generators are connected to my everyday life because the provide energy to the power-grid that ultimately allows the United States to function in the manner that it does. Something as simple as turning on a lite bulb or charging a cell phone would simply not be possible without generates. I guess I could say I am interested in maintaining the quality of life I have right now, so I am definitely definitely interested in generators.

'''How is it connected to your major?'''
a. Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.
b. Generators are related to my material science and engineering because scientists are now looking to harvest power, "generate power", from nano-scale systems. Researchers are doing this with many different materials and synthesis methods. The idea behind nano-scale thermoelectric, magnetic, and/or electric power generation is a hot research topic among leading material science researchers in the field.

'''Is there an interesting industrial application?'''
a. Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:
b. The industrial applications of generators are endless. The generators can be coal, water, or nuclear based and the construction of each one of these is a huge part of industry. Then there is the actual generation and allocation of power, which involves the entire power grid. All of this is super fascinating because there are rising concerns about the potential affects of the destruction of the power grid. These affects could have detrimental affects on all aspects of life. Unless you live of the grid, chances are your life would be turned upside down.

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:04:15Z

Jpricelight: /* Generators */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

Check out this awesome video to help understand the different between AC and DC

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

'''How is it connected to your major?'''
Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

'''Is there an interesting industrial application?'''
Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:03:29Z

Jpricelight: /* Generators */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

[[Media:"https://www.youtube.com/watch?v=SAvYvfg41FU"]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

'''How is it connected to your major?'''
Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

'''Is there an interesting industrial application?'''
Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T23:00:02Z

Jpricelight: /* Generators */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

<iframe width="560" height="315" src="https://www.youtube.com/watch?v=SAvYvfg41FU" frameborder="0" allowfullscreen></iframe>

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

'''How is it connected to your major?'''
Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

'''Is there an interesting industrial application?'''
Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T22:57:12Z

Jpricelight: /* A Mathematical Model */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as...
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

'''How is it connected to your major?'''
Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

'''Is there an interesting industrial application?'''
Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T22:56:46Z

Jpricelight: /* The Main Idea */

This page covers electric motors

Claimed by Komal Hirani: khirani6

[[File:Motors01CJC.jpg|thumb|Various Electric Motors]]

==The Main Idea==
===Electric Motors===

Motors convert electrical energy into mechanical energy. Our everyday routines heavily rely upon the electric motors in common applications such as refrigerator compressors, water pumps, elevators, clocks, and cars. Electric motors are a common application of the torque that a magnetic field exerts on a current-carrying coil. In order for motors to function the way that they do, the current-carrying coil needs to turn continuously. In order for the current-carrying coil to turn in such a way, you need to make electrical connections to the coil in such a way that just as it is coming to its stable position, you reverse the direction of the current. A simple way to achieve this continuos motion is through a "split-ring commutator" that automatically changes the direction of the current through the coil at just the right moment. Metal tabs make contact between the battery and the commutator, which allows current to flow and for the motor to rotate.

Below is a picture that shows the overall design of a single-loop motor driven by direct current (DC):

[[File:Qn_38_Magnetic1.png]]

===A Mathematical Model===
A motor's mechanical output is calculated as follows:
:<math>P_{em} = F\times{v}</math> (watts).
with Force (F) expressed in Newtons and velocity (v) expressed in meters per second.

To calculate the motor's efficiency, you divide the mechanical output power by the electrical input power:
:<math>\eta = \frac{P_m}{P_e}</math>

===Generators===
Commercial generators rotate a loop of wire in a magnetic field. This is the ideal construction because it is much easier to arrange and it experiences very low friction on the axle. The magnitude of the magnetic force on a charge carrier q is F=qvBsinθ. Additionally, the magnetic force is uniform throughout the wire, thus motional emf is the force multiplies by the length, divided by the charge… emf=2vBwsinθ. This equations can also be written as emf=wB(hw)sin(wt). The current inside of this type of current varies in a sinusoidal. This type of current is known as alternating current or AC. AC is what comes out of the wall while direct current or DC is what flows through a battery. Direct current is one-direction current, while alternating current in bi-directional.

[[File:it.gif]]

===A Mathematical Model===

Calculate the work done on a generator...

When a loop is rotated through a small angle ∆θ, we move each end a short distance [h/2 ∆θ], thus...
∆W=2[IwBsinθ][h/2 ∆θ]
dividing this result by ∆t....

dW/dt=2[IwBsinθ][h/2 dθ/dt]=I[Bwhωsinθ]

this can be rewritten as
dW/dt=I[RI]=RI^2

This calculation give the power dissipated in the resistor at this instant. Essentially this tells that a generator is not "generating" something from nothing. Instead it is converting mechanical power into electrical power.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''
Motors are heavily used in robotics, which is something that I have been interested in ever since I was on my high school's robotics team. In robotics, we heavily rely upon motors to power the robot and allow the robot to perform as it is supposed to. I am interested in going into the robotics industry, particularly the electronic component of the industry, so knowing how motors work is very useful to me.

'''How is it connected to your major?'''
Even though I'm a Computer Science major, I want to eventually go into the robotics industry. In robotics, when coding for any robot, you need to know how the electronic components of the robot are able to produce energy for the robot to function. You need to be able to write code that is able to be translated by the CPU and will allow each controller and motor to function.

'''Is there an interesting industrial application?'''
Like I said, motors are heavily used in robotics in order for robots to properly move and carry out the tasks the robot was programmed to do. Robots such as the robotic arm pictured below need motors in order to generate enough power for the arm to move in different directions:

[[File:stacks_image_5796.png]]

==History==

[[File:Thomas_Davenport.jpg|thumb|Thomas Davenport]]

In the early 1800's, Orstead, Ampere, and Faraday laid down the foundation for building electric motors by introducing the basic principles of electromagnetic induction. In 1820, Orstead had confirmed that there was a relationship between electricity and magnetism. In the same year, Ampere invented the solenoid and discovered Ampere's Law, which helps describe magnetic fields produced by motors and solenoids. In 1821, Faraday successfully converted electrical energy into motion and created the simplest form of the electric motor. In 1832 however, William Sturgeon introduced the first ever commutator DC electronic motor, and later on in 1837, Thomas Davenport created a DC motor for commercial services and received the first US electric motor patent, which is why a lot of people associate him with the first person to invent the electric motor.

== See also ==

[[Direction of Magnetic Field]]

===Further reading===

"Electric Motor"
https://en.wikipedia.org/wiki/Electric_motor#Early_motors

===External links===

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

http://www.howmotorswork.com/history.html

==References==

https://en.wikipedia.org/wiki/Electric_motor#Early_motors

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

https://www.eti.kit.edu/english/1376.php

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html#c1

http://www.edisontechcenter.org/electricmotors.html

http://www.howmotorswork.com/history.html

http://electronics.howstuffworks.com/motor3.htm

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

Electric Motors

2017-11-29T22:41:25Z

Jpricelight: /* Generators */

Electric Motors

2017-11-29T22:41:01Z

Jpricelight: /* The Main Idea */

File:It.gif

2017-11-29T22:38:34Z

Jpricelight: black and white clowns on a couch

black and white clowns on a couch

Electric Motors

2017-11-29T22:37:16Z

Jpricelight: /* Generators */

Electric Motors

2017-11-29T22:34:56Z

Jpricelight: /* The Main Idea */

Main Page

2017-11-29T20:21:28Z

Jpricelight: /* Magnetic forces on charges and currents */

__NOTOC__
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== Resources ==
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<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[Python Syntax]]
</div>
</div>

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

====Vectors and Units====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

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

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
*[[Relativistic Momentum]]
</div>
</div>

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

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Analytical Prediction]]
</div>
</div>

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

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke's Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">

==Main Idea==

*[[Gravitational Force]]
*[[Fluid Mechanics]]
*[[An Application of Gravitational Potential]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
===='''Rama Sambatur - Fall 2017''': The Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Calorific Value(Heat of combustion)]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Quantized energy levels part II]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

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

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

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

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

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

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

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

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy - Claimed by Janki Patel]]
Morgan Kehoe Spring 2017
</div>
</div>

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

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

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

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]

====The Main Idea====
*'''Mathematical Model'''

**In this image, you can see what our equations are based on: [[File:noderule.jpg]]
**The node rules can be written as I_total = I_1 + I_2 and I_total = I_3 + I_4. It is also true that I_1 + I_2 = I_3 + I_4.
**However, each of these currents are different because each point has a different resistance. The current is different for each because it is equal to V/R, and in a parallel circuit, the voltage drop across each point is equal.
**An easy way to know when to use node rule is by seeing if there are three connections or more. That is when node rule is most helpful.

*'''Computational Model'''

**In an electric circuit in series, electrons flow from the negative end of a power source, creating a constant current. This current remains consistent at each point in the circuit in series. Sometimes, a circuit is not simply one constant path and may include parts that are in parallel, where the current must travel down two paths such as this:
**[[File:noderule.jpg]]
**In this case, when the current enters a portion of the circuit where the items are in parallel, the total amount of current in must equal the total amount of current out. Therefore, the currents in each branch of the parallel portion must sum up to the amount of current at any other point in series in the circuit.
**People also call this the "Junction Rule"
**Another important point is that this comes from the Kirchoff's Circuit Laws

====Examples====

*'''Simple'''
**Here is an example of a simple circuit problem: [[File:SimpleNodeRule.jpg]]

*'''Medium'''
**Here is an example of a medium circuit problem: [[File:MediumNodeRule.jpg]]

*'''Difficult'''
**Here is an example of a difficult circuit problem: [[File:DifficultNodeRule.jpg]]

====Connectedness====

*'''To other topics:'''
**Many times when you use Node Rule you will also use the Loop Rule. The Loop Rule states that the sum of voltage will equal zero. So using this concept and the Node Rule, you are usually able to figure out missing variables in circuit problems.

*'''To majors:'''
**Node rule is important in all and any major. More specifically, electrical engineering because of the constant need to look, analyze, and understand circuits. However, in general, any major that involves some sort of circuitry will need this. It is the basis to making an effective circuit.

*'''To industrial application:'''
**If you go into robots, engineering, or really anything that involves wires and batteries. You will need to know this.

====History====

*Basic History
**Gustav Kirchoff was the man who discovered this rule while studying electrical currents. He was also the first person to confirm an electrical impulse moves at the speed of light.

====External Resources and Information====

*Sources like Khan Academy and simple YouTube searches can be very helpful in learning more about this topic.

</div>
</div>

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

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell 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]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

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

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Work Done By A Nonconstant Force

2016-11-30T03:48:24Z

Jpricelight: /* See also */

This page explains the significance and fundamental calculations of work done by non-constant forces. In addition it provides multiple worked examples and analytical models will help readers develop a more thorough understanding.

==The Main Idea==

[https://www.youtube.com/watch?v=RJgf4kvov9g]
[[https://www.youtube.com/watch?v=RJgf4kvov9g]]
Work done by constant force of magnitude 'F' on a point that moves a displacement 'd' in the directional of the force is the product: W=F*d. The SI unit for work is the joule (J) which is equivalent to newton meter. Force is a relationship of the product of mass*acceleration of the object, while displace is a result of the change in final and starting position. It is important to note thatno matter how large or small the magnitude of the force is, no work is done if there is no displacement. The formula W=F*d only holds true when constant force is applied to the system.

Calculus is used to calculate the word in systems where force is non constant. Common systems that deal with non-constant force are with springs and gravity. This is due to the change in spring force and gravitational force respectively. The work done on the system is found by integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''

https://www.youtube.com/watch?v=jTkknXVjBl4

https://www.youtube.com/watch?v=9Be81qfgBVc

==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas

Work Done By A Nonconstant Force

2016-11-30T03:48:12Z

Jpricelight: /* See also */

This page explains the significance and fundamental calculations of work done by non-constant forces. In addition it provides multiple worked examples and analytical models will help readers develop a more thorough understanding.

==The Main Idea==

[https://www.youtube.com/watch?v=RJgf4kvov9g]
[[https://www.youtube.com/watch?v=RJgf4kvov9g]]
Work done by constant force of magnitude 'F' on a point that moves a displacement 'd' in the directional of the force is the product: W=F*d. The SI unit for work is the joule (J) which is equivalent to newton meter. Force is a relationship of the product of mass*acceleration of the object, while displace is a result of the change in final and starting position. It is important to note thatno matter how large or small the magnitude of the force is, no work is done if there is no displacement. The formula W=F*d only holds true when constant force is applied to the system.

Calculus is used to calculate the word in systems where force is non constant. Common systems that deal with non-constant force are with springs and gravity. This is due to the change in spring force and gravitational force respectively. The work done on the system is found by integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''

https://www.youtube.com/watch?v=jTkknXVjBl4
https://www.youtube.com/watch?v=9Be81qfgBVc

==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas

Work Done By A Nonconstant Force

2016-11-29T21:44:32Z

Jpricelight: /* The Main Idea */

This page explains the significance and fundamental calculations of work done by non-constant forces. In addition it provides multiple worked examples and analytical models will help readers develop a more thorough understanding.

==The Main Idea==

[https://www.youtube.com/watch?v=RJgf4kvov9g]
[[https://www.youtube.com/watch?v=RJgf4kvov9g]]
Work done by constant force of magnitude 'F' on a point that moves a displacement 'd' in the directional of the force is the product: W=F*d. The SI unit for work is the joule (J) which is equivalent to newton meter. Force is a relationship of the product of mass*acceleration of the object, while displace is a result of the change in final and starting position. It is important to note thatno matter how large or small the magnitude of the force is, no work is done if there is no displacement. The formula W=F*d only holds true when constant force is applied to the system.

Calculus is used to calculate the word in systems where force is non constant. Common systems that deal with non-constant force are with springs and gravity. This is due to the change in spring force and gravitational force respectively. The work done on the system is found by integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''

https://www.youtube.com/watch?v=jTkknXVjBl4

==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas

Work Done By A Nonconstant Force

2016-11-29T18:59:07Z

Jpricelight:

This page explains the significance and fundamental calculations of work done by non-constant forces. In addition it provides multiple worked examples and analytical models will help readers develop a more thorough understanding.

==The Main Idea==

Work done by constant force of magnitude 'F' on a point that moves a displacement 'd' in the directional of the force is the product: W=F*d. The SI unit for work is the joule (J) which is equivalent to newton meter. Force is a relationship of the product of mass*acceleration of the object, while displace is a result of the change in final and starting position. It is important to note thatno matter how large or small the magnitude of the force is, no work is done if there is no displacement. The formula W=F*d only holds true when constant force is applied to the system.

Calculus is used to calculate the word in systems where force is non constant. Common systems that deal with non-constant force are with springs and gravity. This is due to the change in spring force and gravitational force respectively. The work done on the system is found by integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''

https://www.youtube.com/watch?v=jTkknXVjBl4

==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas

Work Done By A Nonconstant Force

2016-11-29T18:42:52Z

Jpricelight: /* See also */

This page explains the significance and fundamental calculations of work done by non-constant forces.

==The Main Idea==

Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''

https://www.youtube.com/watch?v=jTkknXVjBl4

==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas

Work Done By A Nonconstant Force

2016-11-29T18:40:50Z

Jpricelight:

This page explains the significance and fundamental calculations of work done by non-constant forces.

==The Main Idea==

Basic calculations of work can be solved with a simple formula: force times displacement. However, this formula only works when work is constant. Calculus is essential for the calculation of work in many cases because force is not always a constant. In cases such as springs and gravity, for example, the force applied varies depending on location. By integrating, or finding the area under the curve of force by displacement, we can calculate work without having to use inaccurate approximations.

===A Mathematical Model===

<math> W=\int\limits_{i}^{f}\overrightarrow{F}\bullet\overrightarrow{dr} = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

This means that the work is equal to the integral of the function of the force with respect to the change in the objects position. This is also the same as the summation of the force on an object multiplied by the change in position.

===A Computational Model===

<https://trinket.io/glowscript/49f7c0f35f>

This model shows both the total work and the work done by a spring on a ball attached to a vertical spring. The work done by the spring oscillates because the work is negative when the ball is moving away from the resting state and is positive when the ball moves towards it.

Because gravity causes the ball’s minimum position to be further from the spring’s resting length than its maximum position could be, the work is more negative when the ball approaches its minimum height.

The code works by using small time steps of 0.01 seconds and finding the work done in each time step. Work is the summation of all of the work done in each time step, so another step makes sure the value for work is cumulative.

==Examples==

===Example 1===
A box is pushed to the East, 5 meters by a force of 40 N, then it is pushed to the north 7 meters by a force of 60 N. Calculate the work done on the box.

<math> W = \sum\overrightarrow{F}\bullet\Delta\overrightarrow{r} </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 40N \bullet\ 5m + 60N \bullet\ 7m </math>

<math> W = 620 J </math>

===Example 2===
We know that the formula for force is <math> F=ks </math>, where <math> s </math> is the distance the spring is stretched. If we integrate this with respect to <math> s </math>, we find that <math> W=.5ks^2 </math> is the formula for work.

<math> W=\int\limits_{i}^{f}\overrightarrow{k}\bullet\overrightarrow{ds} = .5ks^2 </math>

Say that we want to find the work done by a horizontal spring with spring constant k=100 N/m as it moves an object 15 cm. Using the formula W=.5ks2 that we derived from F=ks, we can calculate that the work done by the spring is 1.125 J.

<math> W=\int\limits_{0}^{15}100\bullet\overrightarrow{ds}=.5ks^2=.5(100)(0.15^2)=1.125 J </math>

===Example 3===
The earth does work on an asteroid approaching from an initial distance r. How much work is done on the asteroid by gravity before it hits the earth’s surface?

First, we must recall the formula for gravitational force.

Because <math> G </math>, <math> M </math>, and <math> m </math> are constants, we can remove them from the integral. We also know that the integral of <math> -1\over r^2 </math> is <math> 1\over r </math>. We then must calculate the integral of <math> –GMm\over r^2 </math> from the initial radius of the asteroid, <math> R </math>, to the radius of the earth, <math> r </math>.

<math> W=-GMm\bullet\int\limits_{R}^{r}{-1\over r^2}\bullet dr </math>

<math> W=-GMm\bullet({1\over r}-{1\over R}) </math>

Our answer will be positive because the force done by the earth on the asteroid and the direction of the asteroid's displacement are the same.

==Connectedness==
I am most interested in the types of physics problems that accurately model real world situations. Some forces, like gravity near the surface of the earth and some machine-applied forces, are constant. However, most forces in the real world are not.

Because of this, calculating work for non-constant forces is essential to mechanical engineering. For example, when calculating work done by an engine over a distance, the force applied by the engine can vary depending on factors such as user controls.

On an industrial level, the work needed to fill and empty tanks depends on the weight of the liquid, which varies as the tanks fill and empty. Energy conversion in hydroelectric dams depends on the work done by water against turbines, which depends on the flow of water. Windmills work in the same way.

==History==

Gaspard-Gustave de Coriolis, famous for discoveries such as the Coriolis effect, is credited with naming the term “work” to define force applied over a distance. Later physicists combined this concept with Newtonian calculus to find work for non-constant forces.

== See also ==

'''Further Reading'''
[[Work]]

'''External Links'''
https://www.youtube.com/watch?v=jTkknXVjBl4
==References==

[http://www.britannica.com/biography/Gustave-Gaspard-Coriolis]
[http://www.math.northwestern.edu]

[[Category:Energy]]

Created by Justin Vuong
Edited by Chris Mickas