Rest Mass Energy: Difference between revisions

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== Rest Mass Energy==
== Rest Mass Energy==
By: Shiv Tailor


Work In Progress - Shiv Tailor  HAI SHIV <3 -Alice
Rest mass energy is the energy an object has when is not moving nor is it in a potential field. The famous equation


<math> E=mc^2</math>
Rest mass energy is the energy an object has when is neither moving nor is it in a potential field. The famous equation
::<math> E=mc^2</math>
demonstrates the mass energy equivalence where
::''E'' is the internal energy in joules
::''m'' is the mass in kilograms
::''c'' is the speed of light in a vacuum (approximately <math>3.00 \times 10^{8} {\rm \ m/s}</math>)


demonstrates the mass energy equivalence. What this equation means is that the Internal Energy (E) in Joules is
This relationship was shown by Albert Einstein in 1905.[[File:Albert Einstein Head.jpeg|200px|thumb|right|Albert Einstein in 1947]]
equal to the mass (m) in kilograms times the speed of light (c) in meters per second squared.


This incredible relationship was shown by Albert Einstein in 1905.[[File:https://upload.wikimedia.org/wikipedia/commons/d/d3/Albert_Einstein_Head.jpg]]


===A Mathematical Model===
===A Mathematical Model===
There are <math>E=\lambda mc^2</math> and
<math> E=mc^2</math> which reprsents the rest energy. taken together the kinetic energy becomes the overall energy- rest energy. Due to the complexity of this equation, it maybe easier to use the equation <math> 1/2mv^2</math> if the object is not traveling near the speed of light. This equation is applicable to everyday object that we see and more applicable for the "average" situation.
<br>


h
This is a very simple equation but it can be rewritten in many ways.


<math> E/(c^2)=m</math>


What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
This is especially important because it says that all the energy, regardless of form, can be equated to mass


===A Computational Model===
===A Computational Model===


How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
The best way to visualize this mass-energy equivalence to think about a pan on a stove. As the pan heats up one would see that the pan gets hotter,
and one could infer that the internal energy of the pan goes up. This change in energy can be equated to mass. This is shown in the examples.


==Examples==
==Examples==
Line 32: Line 33:


===Simple===
===Simple===
What is the rest mass energy of an object that weighs 7 kg and is going 40 mi/h?
Since it asks for rest mass energy, we ignore the movement.
<math>E = mc^2</math>
<math>E = (7 {\rm \ kg})*(3e8 {\rm \ m/s})^2</math>
<math>E = 6.3e17 {\rm \ J}</math>
===Middling===
===Middling===
  What is the mass of an object that has a rest mass energy of 1e16 J
and is traveling through a medium where the speed of light is 2e8 m/s?
The rest mass energy always uses the speed of light in a vacuum (c) which is ~3e8 m/s.
<math>E = mc^2</math>
<math>m = \frac{E}{c^2}</math>
<math>m = \frac{1e16 {\rm \ J}}{3e8 {\rm \ m/s}^2}</math>
<math>m = 0.11 {\rm \ kg}</math>
===Difficult===
===Difficult===


==Connectedness==
A pot with mass 0.5 kg is filled with 1.2 kg of water. After some time 10,000 kJ of heat have been added to the pot
#How is this topic connected to something that you are interested in?
and 40,000 kJ of heat have been added to the water. Ignoring evaporation what is the mass of the pot and the water?
#How is it connected to your major?
 
#Is there an interesting industrial application?
Initial rest mass energy:
 
<math>E_i = m_i c^2</math>
 
<math>E_i = (1.5 {\rm \ kg})*(3e8 {\rm \ m/s})^2</math>
 
<math>E_i= 1.35e17 {\rm \ J}</math>
 
Final rest mass energy:
 
<math>E_f = (10,000 {\rm \ kJ})*(1000 {\rm \ J/kJ}) + (40,000 {\rm \ kJ})*(1000 {\rm \ J/kJ}) + 1.35e17 {\rm \ J}</math>
 
<math>E_f = 1.3500000005e17 {\rm \ J}</math>
 
<math>m_f = \frac{E_f}{c^2}</math>
 
<math>m_f = \frac{1.3500000005e17 {\rm \ J}}{3e8 {\rm \ m/s}^2}</math>
 
<math>m_f = 1.5000000006 {\rm \ kg}</math>
 
**note: The mass change is almost 0. Why?**


==History==
==History==


Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
Mass-energy equivalence was proposed by Albert Einstein in 1905 in his paper ''Does the Inertia of a Body Depend upon its Energy Content


== See also ==
== See also ==


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


===Further reading===
===Further reading===


Books, Articles or other print media on this topic
https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
 
===External links===
 
Internet resources on this topic


==References==
==References==


This section contains the the references you used while writing this page
http://einsteinpapers.press.princeton.edu/vol2-trans/186


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

Latest revision as of 22:31, 4 December 2015

Provide a brief summary of the page here

Rest Mass Energy

By: Shiv Tailor


Rest mass energy is the energy an object has when is neither moving nor is it in a potential field. The famous equation

[math]\displaystyle{ E=mc^2 }[/math]

demonstrates the mass energy equivalence where

E is the internal energy in joules
m is the mass in kilograms
c is the speed of light in a vacuum (approximately [math]\displaystyle{ 3.00 \times 10^{8} {\rm \ m/s} }[/math])

This relationship was shown by Albert Einstein in 1905.

Albert Einstein in 1947


A Mathematical Model

This is a very simple equation but it can be rewritten in many ways.

[math]\displaystyle{ E/(c^2)=m }[/math]

This is especially important because it says that all the energy, regardless of form, can be equated to mass

A Computational Model

The best way to visualize this mass-energy equivalence to think about a pan on a stove. As the pan heats up one would see that the pan gets hotter, and one could infer that the internal energy of the pan goes up. This change in energy can be equated to mass. This is shown in the examples.

Examples

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

Simple

What is the rest mass energy of an object that weighs 7 kg and is going 40 mi/h?

Since it asks for rest mass energy, we ignore the movement.

[math]\displaystyle{ E = mc^2 }[/math]

[math]\displaystyle{ E = (7 {\rm \ kg})*(3e8 {\rm \ m/s})^2 }[/math]

[math]\displaystyle{ E = 6.3e17 {\rm \ J} }[/math]

Middling

 What is the mass of an object that has a rest mass energy of 1e16 J
and is traveling through a medium where the speed of light is 2e8 m/s?

The rest mass energy always uses the speed of light in a vacuum (c) which is ~3e8 m/s.

[math]\displaystyle{ E = mc^2 }[/math]

[math]\displaystyle{ m = \frac{E}{c^2} }[/math]

[math]\displaystyle{ m = \frac{1e16 {\rm \ J}}{3e8 {\rm \ m/s}^2} }[/math]

[math]\displaystyle{ m = 0.11 {\rm \ kg} }[/math]

Difficult

A pot with mass 0.5 kg is filled with 1.2 kg of water. After some time 10,000 kJ of heat have been added to the pot
and 40,000 kJ of heat have been added to the water. Ignoring evaporation what is the mass of the pot and the water?

Initial rest mass energy:

[math]\displaystyle{ E_i = m_i c^2 }[/math]

[math]\displaystyle{ E_i = (1.5 {\rm \ kg})*(3e8 {\rm \ m/s})^2 }[/math]

[math]\displaystyle{ E_i= 1.35e17 {\rm \ J} }[/math]

Final rest mass energy:

[math]\displaystyle{ E_f = (10,000 {\rm \ kJ})*(1000 {\rm \ J/kJ}) + (40,000 {\rm \ kJ})*(1000 {\rm \ J/kJ}) + 1.35e17 {\rm \ J} }[/math]

[math]\displaystyle{ E_f = 1.3500000005e17 {\rm \ J} }[/math]

[math]\displaystyle{ m_f = \frac{E_f}{c^2} }[/math]

[math]\displaystyle{ m_f = \frac{1.3500000005e17 {\rm \ J}}{3e8 {\rm \ m/s}^2} }[/math]

[math]\displaystyle{ m_f = 1.5000000006 {\rm \ kg} }[/math] 

**note: The mass change is almost 0. Why?**

History

Mass-energy equivalence was proposed by Albert Einstein in 1905 in his paper Does the Inertia of a Body Depend upon its Energy Content

See also

See the energy section of this wiki.

Further reading

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

References

http://einsteinpapers.press.princeton.edu/vol2-trans/186

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