Physics Book - User contributions [en]

Real Systems

2016-11-27T13:24:22Z

Cstanek3:

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

Assuming there is no relative kinetic energy (none based on diagram) and no change in chemical energy (there is no change in substance), the change in thermal energy of the clay can be found. Finding the change in thermal energy is important because you can determine whether there was enough energy to change the temperature of the clay or whether there is enough energy given off by the clay to change the temperature of a surrounding substance by a degree. Problems like this show the importance of analyzing real systems versus point particle systems.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

This topic interests me because from one single system you can mathematically determine the other forms of energy that can occur in various physical interaction. From the other forms of energy, you can determine whether there is enough energy to maybe change the temperature of another substance via thermal energy or even change the substance that is in the system given a big enough change in chemical energy.

'''How is it connected to your major?'''

As a chemical engineering major, the application of Real Systems is largely used for the majority of mathematics in my major dealing with energy balances. From only analyzing a system from a point particle method, one would only be able to find the change in the translational kinetic energy. In my major, it is very important to consider the entire system in order to find important values such as the change in thermal and kinetic energy because these values are often associated with the amount of work and heat produced in many chemical engineering processes.

'''Is there an interesting industrial application?'''

There is an absolute overload of interesting industrial applications for the analysis of real systems. In fact, the analysis of real systems in terms of energy balances is the entirety of what I've done in my chemical engineering classes thus far (I am currently a second year). There are many interesting (depending on your taste) uses of the real system analysis on a multitude of different turbines and chemical reactors.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-11-27T00:07:32Z

Cstanek3:

This topic has been claimed by cstanek3 on November 26.

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

Assuming there is no relative kinetic energy (none based on diagram) and no change in chemical energy (there is no change in substance), the change in thermal energy of the clay can be found. Finding the change in thermal energy is important because you can determine whether there was enough energy to change the temperature of the clay or whether there is enough energy given off by the clay to change the temperature of a surrounding substance by a degree. Problems like this show the importance of analyzing real systems versus point particle systems.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

This topic interests me because from one single system you can mathematically determine the other forms of energy that can occur in various physical interaction. From the other forms of energy, you can determine whether there is enough energy to maybe change the temperature of another substance via thermal energy or even change the substance that is in the system given a big enough change in chemical energy.

'''How is it connected to your major?'''

As a chemical engineering major, the application of Real Systems is largely used for the majority of mathematics in my major dealing with energy balances. From only analyzing a system from a point particle method, one would only be able to find the change in the translational kinetic energy. In my major, it is very important to consider the entire system in order to find important values such as the change in thermal and kinetic energy because these values are often associated with the amount of work and heat produced in many chemical engineering processes.

'''Is there an interesting industrial application?'''

There is an absolute overload of interesting industrial applications for the analysis of real systems. In fact, the analysis of real systems in terms of energy balances is the entirety of what I've done in my chemical engineering classes thus far (I am currently a second year). There are many interesting (depending on your taste) uses of the real system analysis on a multitude of different turbines and chemical reactors.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Potential Energy of Macroscopic Springs

2016-11-27T00:07:12Z

Cstanek3:

Ideal Spring
==The Key Concept==
Studying macroscopic springs pulls us out of the theoretical atomic realm and into the physical world of springs. The potential energy of a spring changes as the end of the coil varies in its relative distance from the location of its affixed base.

==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.
<math> \Delta U\approx \Delta mgy </math>

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:59:08Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Key Concept==
Studying macroscopic springs pulls us out of the theoretical atomic realm and into the physical world of springs. The potential energy of a spring changes as the end of the coil varies in its relative distance from the location of its affixed base.

==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.
<math> \Delta U\approx \Delta mgy </math>

'''Bold text'''

===A Mathematical Model===

== A VPython Example ==

https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:54:34Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Key Concept==
Studying macroscopic springs pulls us out of the theoretical atomic realm and into the physical world of springs. The potential energy of a spring changes as the end of the coil varies in its relative distance from the location of its affixed base.

==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.

'''Bold text'''

===A Mathematical Model===

== A VPython Example ==

https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:54:10Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Key Concept==
Studying macroscopic springs pulls us out of the theoretical atomic realm and into the physical world of springs. The potential energy of a spring changes as the end of the coil varies in its relative distance from the location of its affixed base.

==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.

<math>\Delta U\approx \Delta mgy<math>

'''Bold text'''

===A Mathematical Model===

== A VPython Example ==

<embed><https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action><embed>

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:53:38Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Key Concept==
Studying macroscopic springs pulls us out of the theoretical atomic realm and into the physical world of springs. The potential energy of a spring changes as the end of the coil varies in its relative distance from the location of its affixed base.

==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.

<math>\Delta U\approx \Delta mgy<math>

'''Bold text'''

===A Mathematical Model===

== A VPython Example ==

[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:49:27Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.

[[math]]
\Delta U\approx \Delta mgy
[[math]]

'''Bold text'''

===A Mathematical Model===

{{Us = 0.5*ks*s^2}}
<img src="https://latex.codecogs.com/gif.latex?\Delta&space;U\approx&space;\Delta&space;mgy" title="\Delta U\approx \Delta mgy" />

== A VPython Example ==

[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:46:29Z

Cstanek3: /* Terms and Definitions */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.
* Gravitational potential energy relates the vertical position of an object to the surface of the Earth.
[[math]]
\Delta U\approx \Delta mgy
[[math]]

'''Bold text'''

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==

[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:42:58Z

Cstanek3: /* The Main Idea */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==Terms and Definitions==

'''Potential Energy''' - the energy stored in a body or system that results inherently from its relative position to another object
* A change in potential energy occurs when there is a change in the separation distance between the two objects.

'''Bold text'''

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==

[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:39:14Z

Cstanek3: /* A VPython Example */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==

[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result Macroscopic Spring in Action]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:36:40Z

Cstanek3: /* A VPython Example */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:36:28Z

Cstanek3: /* A VPython Example */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==
[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result]
<?php
// do php stuff

include('fileOne.html');
include('fileTwo.html');

?>

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:34:24Z

Cstanek3: /* Examples */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

== A VPython Example ==
[https://trinket.io/glowscript/4b759aa77a?outputOnly=true&start=result]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:31:03Z

Cstanek3: /* Examples */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

==Examples==
<iframe src="https://trinket.io/embed/glowscript/4b759aa77a?outputOnly=true&start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

[[<iframe src="https://trinket.io/embed/glowscript/4b759aa77a?outputOnly=true&start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:29:02Z

Cstanek3: /* Examples */

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

==Examples==
[<iframe src="https://trinket.io/embed/glowscript/4b759aa77a?outputOnly=true&start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]

[[<iframe src="https://trinket.io/embed/glowscript/4b759aa77a?outputOnly=true&start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>]]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-26T23:27:55Z

Cstanek3:

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

==Examples==
<iframe src="https://trinket.io/embed/glowscript/4b759aa77a?outputOnly=true&start=result" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]

Potential Energy of Macroscopic Springs

2016-11-08T19:55:32Z

Cstanek3:

Ideal Spring
'''Claimed by Carolyn Stanek 11/8/2016
'''
==The Main Idea==

Since real springs have limits as to stretching or compressing, ideal Springs are used for a both real macroscopic spring and for spring-like interatomic bonds.

===A Mathematical Model===

{Us = 0.5*ks*s^2}

==Examples==
[[File:img13.gif]]

==Connectedness==
#How is this topic connected to something that you are interested in?
This is the first law of thermodynamics where every energy related goes around with this law, where energy is neither made or destroyed.
It is very interesting how energy is just there and is transformed into other energies such as chemical energy that the food in the student center has will transform into kinetic energy when playing tennis after school.

#How is it connected to your major?
As my major is Chemical Engineering, thermodynamics has many materials in common because of calculating the energy balances toward a reaction. The first law of thermodynamics To work out thermodynamic problems you will need to isolate a certain portion of the universe, the system, from the remainder of the universe, the surroundings.

#Is there an interesting industrial application?
There was an interesting industrial application where we can calculate the energy required by the machine to pump the fluid out.

==History==

*'''William Rankinet'''
**The term potential energy was introduced e, although it has links to Greek philosopher Aristotle's concept of potentiality.
**Scottish engineer and physicist
** links to Greek philosopher Aristotle's concept of potentiality

== See also ==

Potential Energy
Ideal Spring
Spring stretch.

===Further reading===

[[Potential Energy:https://en.wikipedia.org/wiki/Potential_energy]]

==References==

[https://en.wikipedia.org/wiki/William_John_Macquorn_Rankine]
[https://en.wikipedia.org/wiki/Spring]