Physics Book - User contributions [en]

Mass

2015-12-05T05:06:11Z

Ctam8: Fix grammar issues

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the measurement of the amount of matter a physical body possesses and is an underlying fundamental concept that governs other physical science concepts, such as [[Gravitational Force|gravity]], [[Inertia|inertia]], and [[Rest Mass Energy|rest energy]].

The SI units for mass is kilograms (kg), a base unit in the International System of Units.

==Defining Mass==
One may differentiate between at least seven different aspects of mass, or seven distinct physical approaches to relating mass.[[#References|1]] However, there exists some constant that unifies all widely accepted concepts related to mass. Below are some of these concepts.

===Inertial Mass===
''Main article: [[Inertia]]''

Inertial mass is the measure of some physical body's resistance to changes in motion (the definition of [[Inertia|inertia]]). A physical body's motional resistance is inversely proportional to its inertial mass. Put more simply, under the same force <math>F</math>, a body with mass <math>m</math> will experience greater [[Velocity#Acceleration|acceleration]] than that of a body with mass <math>M</math>, when <math>m < M</math>.

===Gravitational Mass===
''See also: [[Gravitational Force]]''

====Active Gravitational Mass====
Active gravitational mass is the measure of the magnitude of a body's gravitational field at corresponding distances. When other bodies of mass are involved, active gravitational mass may be defined as the [[Gravitational Force|gravitational force]] that other bodies experience at corresponding distances. For surfaces, active gravitational mass may be more formally defined as the measure of a body's [[Gravitational flux|gravitational flux]]. Qualitatively speaking, this just means active gravitational mass determines how strong a body's gravitational field is. A body's active gravitational mass can be demonstrated by allowing a second, smaller test body to free-fall and then measuring the [[Velocity#Acceleration|acceleration]] that the second body experiences. In classical mechanics, this can formally be shown as
::<math>\mathbf{g}=\frac{\mathbf{F}}{m}=-\frac{{\rm d}^2\mathbf{r}}{{\rm d}t^2}=-Gm\frac{\mathbf{\hat{r}}}{|\mathbf{r}|^2},</math>
:where
::'''g''' is the gravitational acceleration caused by active gravitational mass's resulting gravitational field
::'''F''' is the gravitational force on a test body
::'''m''' is the mass of a test body
::'''r''' is the direction vector from the body being measured to the test body
::'''t''' is time
::'''G''' is the universal gravitational constant (<math>6.6740831 \times 10^{-11} {\rm \ N \ m^{2} \ kg^{-2} }</math>)

====Passive Gravitational Mass====
Passive gravitational mass is the measure of how affected an body is by a gravitational field. When the sole force acting on a physical body is a result of its interaction with a gravitational field, passive gravitational mass of a body can be calculated by the formula
::<math>\mathbf{F} = ma</math>.
:Algebraically solving for '''m''' gives:
::<math>m = \frac{\mathbf{F}}{a}</math>
:where
::* ''F'' is the body's weight in the given
::* ''m'' is the body's passive gravitational mass
::* ''a'' is the free-fall acceleration of the body.

====Combining the Gravitational Masses====
The differentiation between active and passive gravitational masses can be bridged by combining the two equations derived above and [[Newton's Third Law of Motion]], which results in the general gravitational force equation
::<math>|\vec{\mathbf{F}}_{grav}|= G \frac{m_1 m_2}{r^2}</math>,
:or in vector form
::<math>\vec{\mathbf{F}}_{grav}= -G \frac{m_1 m_2}{r^2} \mathbf{\hat{r}}</math>.

===Rest Energy of Mass===
'Main article: [[Rest Mass Energy]]''
The mass-energy equivalence states that there exists an intrinsic energy quantity equivalent for any quantity of mass, even when the body of mass has no other form of energy (no [[Kinetic Energy|kinetic]], [[Potential Energy|potential]], elastic, chemical, thermal, or otherwise) and vice versa. This was made famous by Albert Einstein's equation
::<math>E_{rest} = mc^2</math>
:where
::<math>E_{rest}</math> is the rest energy of a body of mass
::''m'' is the mass of the body
::''c'' is the speed of light (approximately <math>3.00 \times 10^{8} {\rm \ m/s}</math> in a vacuum)

This phenomenon can be observed in many processes, including nuclear fusion (the Sun) and the gravitational bending of light.

===Deformation of Spacetime===
''See also: [[Einstein's Theory of Special Relativity]]''
[[ Image:SpacetimeCurvature.jpg | thumb | right | 200px | A 3-D visualization of the planet Earth deforming spacetime. Credit to NASA for the image. ]]
The deformation of spacetime is a relativistic phenomenon that is the result of the existence of mass.[[#References|2]] The manifestation of the deformation of spacetime can be seen with gravitational time dilation. For example, given two hypothetical, isolated bodies of mass '''Small''' and '''Large''' where the masses <math>M_{Small} << M_{Large}</math>, an observer near '''Small''' will observe the passage of time much slower relative to an observer near '''Large'''. In popular culture, Christopher Nolan's science fiction film ''Interstellar'' depicted this phenomenon when astronauts Joe Cooper, Amelia Brand, and Dr. Doyle approach the supermassive black hole Gargantua, while scientist Dr. Romilly remains further from the black hole's spacetime deformation. As a result, in the movie, for every hour the characters Cooper, Brand, and Doyle remain close to the black hole's huge mass and deformation of spacetime, Romilly observes the passage of 23 years of time.

===Quantum Mass===

==Differentiating between Mass and Weight==
In everyday usage, the terms "mass" and "weight" are often interchanged incorrectly. For example, one may state that he or she weighs 100 kg, even though a kilogram is a unit of mass, not weight. Because the majority of humans exist on Earth, where the gravitational field is essentially constant, mass and weight are proportional, so the distinction can be overlooked. However, inconsistencies occur when the gravitational fields are difference. For instance, the mass of a person on both Earth and the Moon will be the same, whereas the weight of a person on Earth and the Moon will be different. This is because weight is actually a measurement of force (typically [[Gravitational Force|gravitational]]) exerted on a body of mass. The equation <math>\mathbf{F} = ma</math> reappears again to describe weight, where '''F''' is an object's weight, ''m'' is the object's mass, and ''a'' is the body's free-fall [[Velocity#Acceleration|acceleration]].

==History==

===Pre-Newtonian Concepts===
The idea about the "amount" of something and its relationship to weight predates recorded history. Humans, at some early prehistoric time, recognized the weight of a group of objects and its direct proportionality to the number of objects in the group. The most direct and widely supported evidence of this is the discovery of [https://en.wikipedia.org/wiki/Weighing_scale weighing scales] in early civilization trade. However, there exists no evidence that any of these civilizations recognized the [[#Mass versus Weight|distinction between mass and weight]], since the effects of [https://en.wikipedia.org/wiki/Gravity_of_Earth Earth's gravity] near the surface ensures that the weight and mass of an object are directly proportional.

== See also ==
* [[Kinds of Matter]]
* [[Gravitational Force]]
* [[Inertia]]
* [[Rest Mass Energy]]
* [[Sir Isaac Newton]]
* [[Einstein's Theory of Special Relativity]]

==References==

# W. Rindler (2006). Relativity: Special, General, And Cosmological. Oxford University Press. pp. 16–18. ISBN 0-19-856731-6.
# A. Einstein, "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg. <https://www.gutenberg.org/etext/5001.>

[[Category:Properties of Matter]]

Mass

2015-12-05T04:57:46Z

Ctam8:

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the measurement of the amount of matter a physical body possesses and is an underlying fundamental concept that governs other physical science concepts, such as [[Gravitational Force|gravity]], [[Inertia|inertia]], and [[Rest Mass Energy|rest energy]].

The SI units for mass is kilograms (kg), a base unit in the International System of Units.

==Defining Mass==
One may differentiate between at least seven different aspects of mass, or seven distinct physical approaches to relating mass.[[#References|1]] However, there exists some constant that unifies all widely accepted concepts related to mass. Below are some of these concepts.

===Inertial Mass===
''Main article: [[Inertia]]''

Inertial mass is the measure of some physical body's resistance to changes in motion (the definition of [[Inertia|inertia]]). A physical body's motional resistance is inversely proportional to its inertial mass. Put more simply, under the same force <math>F</math>, a body with mass <math>m</math> will experience greater [[Velocity#Acceleration|acceleration]] than that of a body with mass <math>M</math>, when <math>m < M</math>.

===Gravitational Mass===
''See also: [[Gravitational Force]]''

====Active Gravitational Mass====
Active gravitational mass is the measure of the magnitude of a body's gravitational field at corresponding distances. When other bodies of mass are involved, active gravitational mass may be defined as the [[Gravitational Force|gravitational force]] that other bodies experience at corresponding distances. For surfaces, active gravitational mass may be more formally defined as the measure of a body's [[Gravitational flux|gravitational flux]]. Qualitatively speaking, this just means active gravitational mass determines how strong a body's gravitational field is. A body's active gravitational mass can be demonstrated by allowing a second, smaller test body to free-fall and then measuring the [[Velocity#Acceleration|acceleration]] that the second body experiences. In classical mechanics, this can formally be shown as
::<math>\mathbf{g}=\frac{\mathbf{F}}{m}=-\frac{{\rm d}^2\mathbf{r}}{{\rm d}t^2}=-Gm\frac{\mathbf{\hat{r}}}{|\mathbf{r}|^2},</math>
:where
::'''g''' is the gravitational acceleration caused by active gravitational mass's resulting gravitational field
::'''F''' is the gravitational force on a test body
::'''m''' is the mass of a test body
::'''r''' is the direction vector from the body being measured to the test body
::'''t''' is time
::'''G''' is the universal gravitational constant (<math>6.6740831 \times 10^{-11} {\rm \ N \ m^{2} \ kg^{-2} }</math>)

====Passive Gravitational Mass====
Passive gravitational mass is the measure of how affected an body is by a gravitational field. When the sole force acting on a physical body is a result of its interaction with a gravitational field, passive gravitational mass of a body can be calculated by the formula
::<math>\mathbf{F} = ma</math>.
:Algebraically solving for '''m''' gives:
::<math>m = \frac{\mathbf{F}}{a}</math>
:where
::* ''F'' is the body's weight in the given
::* ''m'' is the body's passive gravitational mass
::* ''a'' is the free-fall acceleration of the body.

====Combining the Gravitational Masses====
The differentiation between active and passive gravitational masses can be bridged by combining the two equations derived above and [[Newton's Third Law of Motion]], which results in the general gravitational force equation
::<math>|\vec{\mathbf{F}}_{grav}|= G \frac{m_1 m_2}{r^2}</math>,
:or in vector form
::<math>\vec{\mathbf{F}}_{grav}= -G \frac{m_1 m_2}{r^2} \mathbf{\hat{r}}</math>.

===Rest Energy of Mass===
'Main article: [[Rest Mass Energy]]''
The mass-energy equivalence states that there exists an intrinsic energy quantity equivalent for any quantity of mass, even when the body of mass has no other form of energy (no [[Kinetic Energy|kinetic]], [[Potential Energy|potential]], elastic, chemical, thermal, or otherwise) and vice versa. This was made famous by Albert Einstein's equation
::<math>E_{rest} = mc^2</math>
:where
::<math>E_{rest}</math> is the rest energy of a body of mass
::''m'' is the mass of the body
::''c'' is the speed of light (approximately <math>3.00 \times 10^{8} {\rm \ m/s}</math> in a vacuum)

This phenomenon can be observed in many processes, including nuclear fusion (the Sun) and the gravitational bending of light.

===Deformation of Spacetime===
''See also: [[Einstein's Theory of Special Relativity]]''
[[ Image:SpacetimeCurvature.jpg | thumb | right | 200px | A 3-D visualization of the planet Earth deforming spacetime. Credit to NASA for the image. ]]
The deformation of spacetime is a relativistic phenomenon that is the result of the existence of mass.[[#References|2]] The manifestation of the deformation of spacetime can be seen with gravitational time dilation. For example, given two hypothetical, isolated bodies of mass '''Small''' and '''Large''' where the masses <math>M_{Small} << M_{Large}</math>, an observer near '''Small''' will observe the passage of time much slower relative to an observer near '''Large'''. In popular culture, Christopher Nolan's science fiction film ''Interstellar'' depicted this phenomenon when astronauts Joe Cooper, Amelia Brand, and Dr. Doyle approach the supermassive black hole Gargantua, while scientist Dr. Romilly remains further from the black hole's spacetime deformation. As a result, in the movie, for every hour the characters Cooper, Brand, and Doyle remain close to the black hole's huge mass and deformation of spacetime, Romilly observes the passage of 23 years of time.

===Quantum Mass===

==Differentiating between Mass and Weight==
In everyday usage, the terms "mass" and "weight" are often interchanged incorrectly. For example, one may state that they weigh 100 kg, even though kilograms is a unit of mass, not weight. Because the majority of humans exist on Earth, where the gravitational field is essentially constant, mass and weight are proportional, so the distinction can be overlooked. However, inconsistencies occur when the gravitational fields are difference. For instance, the mass of a person on both Earth and the Moon will be the same, whereas the weight of a person on Earth and the Moon will be different. This is because weight is actually a measurement of force (typically [[Gravitational Force|gravitational]]) exerted on a body of mass. The equation <math>\mathbf{F} = ma</math> reappears again to describe weight, where '''F''' is an object's weight, ''m'' is the object's mass, and ''a'' is the body's free-fall [[Velocity#Acceleration|acceleration]].

==History==

===Pre-Newtonian Concepts===
The idea about the "amount" of something and its relationship to weight predates recorded history. Humans, at some early prehistoric time, recognized the weight of a group of objects and its direct proportionality to the number of objects in the group. The most direct and widely supported evidence of this is the discovery of [https://en.wikipedia.org/wiki/Weighing_scale weighing scales] in early civilization trade. However, there exists no evidence that any of these civilizations recognized the [[#Mass versus Weight|distinction between mass and weight]], since the effects of [https://en.wikipedia.org/wiki/Gravity_of_Earth Earth's gravity] near the surface ensures that the weight and mass of an object are directly proportional.

== See also ==
* [[Kinds of Matter]]
* [[Gravitational Force]]
* [[Inertia]]
* [[Rest Mass Energy]]
* [[Sir Isaac Newton]]
* [[Einstein's Theory of Special Relativity]]

==References==

# W. Rindler (2006). Relativity: Special, General, And Cosmological. Oxford University Press. pp. 16–18. ISBN 0-19-856731-6.
# A. Einstein, "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg. <https://www.gutenberg.org/etext/5001.>

[[Category:Properties of Matter]]

Mass

2015-12-05T04:52:49Z

Ctam8: Wrote article

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the measurement of the amount of matter a physical body possesses and is an underlying fundamental concept that governs other physical science concepts, such as [[Gravitational Force|gravity]], [[Inertia|inertia]], and [[Rest Mass Energy|rest energy]].

The SI units for mass is kilograms (kg), a base unit in the International System of Units.

==Defining Mass==
One may differentiate between at least seven different aspects of mass, or seven distinct physical approaches to relating mass.[[#References|1]] However, there exists some constant that unifies all widely accepted concepts related to mass. Below are some of these concepts.

===Inertial Mass===
'''Main article: [[Inertia]]'''

Inertial mass is the measure of some physical body's resistance to changes in motion (the definition of [[Inertia|inertia]]). A physical body's motional resistance is inversely proportional to its inertial mass. Put more simply, under the same force <math>F</math>, a body with mass <math>m</math> will experience greater [[Velocity#Acceleration|acceleration]] than that of a body with mass <math>M</math>, when <math>m < M</math>.

===Gravitational Mass===
'See also: [[Gravitational Force]]''

====Active Gravitational Mass====
Active gravitational mass is the measure of the magnitude of a body's gravitational field at corresponding distances. When other bodies of mass are involved, active gravitational mass may be defined as the [[Gravitational Force|gravitational force]] that other bodies experience at corresponding distances. For surfaces, active gravitational mass may be more formally defined as the measure of a body's [[Gravitational flux|gravitational flux]]. Qualitatively speaking, this just means active gravitational mass determines how strong a body's gravitational field is. A body's active gravitational mass can be demonstrated by allowing a second, smaller test body to free-fall and then measuring the [[Velocity#Acceleration|acceleration]] that the second body experiences. In classical mechanics, this can formally be shown as
::<math>\mathbf{g}=\frac{\mathbf{F}}{m}=-\frac{{\rm d}^2\mathbf{r}}{{\rm d}t^2}=-Gm\frac{\mathbf{\hat{r}}}{|\mathbf{r}|^2},</math>
:where
::'''g''' is the gravitational acceleration caused by active gravitational mass's resulting gravitational field
::'''F''' is the gravitational force on a test body
::'''m''' is the mass of a test body
::'''r''' is the direction vector from the body being measured to the test body
::'''t''' is time
::'''G''' is the universal gravitational constant (<math>6.6740831 \times 10^{-11} {\rm \ N \ m^{2} \ kg^{-2} }</math>)

====Passive Gravitational Mass====
Passive gravitational mass is the measure of how affected an body is by a gravitational field. When the sole force acting on a physical body is a result of its interaction with a gravitational field, passive gravitational mass of a body can be calculated by the formula
::<math>\mathbf{F} = ma</math>.
:Algebraically solving for '''m''' gives:
::<math>m = \frac{\mathbf{F}}{a}</math>
:where
::* ''F'' is the body's weight in the given
::* ''m'' is the body's passive gravitational mass
::* ''a'' is the free-fall acceleration of the body.

====Combining the Gravitational Masses====
The differentiation between active and passive gravitational masses can be bridged by combining the two equations derived above and [[Newton's Third Law of Motion]], which results in the general gravitational force equation
::<math>|\vec{\mathbf{F}}_{grav}|= G \frac{m_1 m_2}{r^2}\</math>,
:or in vector form
::<math>\vec{\mathbf{F}}_{grav}= -G \frac{m_1 m_2}{r^2}\ </math><math>\mathbf{\hat{r}}</math>.

===Rest Energy of Mass===
'Main article: [[Rest Mass Energy]]''
The mass-energy equivalence states that there exists an intrinsic energy quantity equivalent for any quantity of mass, even when the body of mass has no other form of energy (no [[Kinetic Energy|kinetic]], [[Potential Energy|potential]], elastic, chemical, thermal, or otherwise) and vice versa. This was made famous by Albert Einstein's equation
::<math>E_rest = mc^2</math>
:where
::''Erest' is the rest energy of a body of mass
::''m'' is the mass of the body
::''c'' is the speed of light (approximately <math>3.00 \times 10^{8} {\rm \ m/s}</math> in a vacuum)

This phenomenon can be observed in many processes, including nuclear fusion (the Sun) and the gravitational bending of light.

===Deformation of Spacetime===
''See also: [[Einstein's Theory of Special Relativity]]''
[[ Image:SpacetimeCurvature.jpg | thumb | right | 200px | A 3-D visualization of the planet Earth deforming spacetime. Credit to NASA for the image. ]]
The deformation of spacetime is a relativistic phenomenon that is the result of the existence of mass.[[#References|2]] The manifestation of the deformation of spacetime can be seen with gravitational time dilation. For example, given two hypothetical, isolated bodies of mass '''Small''' and '''Large''' where the masses <math>M_{Small} << M_{Large}</math>, an observer near '''Small''' will observe the passage of time much slower relative to an observer near '''Large'''. In popular culture, Christopher Nolan's science fiction film ''Interstellar'' depicted this phenomenon when astronauts Joe Cooper, Amelia Brand, and Dr. Doyle approach the supermassive black hole Gargantua, while scientist Dr. Romilly remains further from the black hole's spacetime deformation. As a result, in the movie, for every hour the characters Cooper, Brand, and Doyle remain close to the black hole's huge mass and deformation of spacetime, Romilly observes the passage of 23 years of time.

===Quantum Mass===

==Differentiating between Mass and Weight==
In everyday usage, the terms "mass" and "weight" are often interchanged incorrectly. For example, one may state that they weigh 100 kg, even though kilograms is a unit of mass, not weight. Because the majority of humans exist on Earth, where the gravitational field is essentially constant, mass and weight are proportional, so the distinction can be overlooked. However, inconsistencies occur when the gravitational fields are difference. For instance, the mass of a person on both Earth and the Moon will be the same, whereas the weight of a person on Earth and the Moon will be different. This is because weight is actually a measurement of force (typically [[Gravitational Force|gravitational]]) exerted on a body of mass. The equation <math>\mathbf{F} = ma</math> reappears again to describe weight, where '''F''' is an object's weight, ''m'' is the object's mass, and ''a'' is the body's free-fall [[Velocity#Acceleration|acceleration]].

==History==

===Pre-Newtonian Concepts===
The idea about the "amount" of something and its relationship to weight predates recorded history. Humans, at some early prehistoric time, recognized the weight of a group of objects and its direct proportionality to the number of objects in the group. The most direct and widely supported evidence of this is the discovery of [https://en.wikipedia.org/wiki/Weighing_scale weighing scales] in early civilization trade. However, there exists no evidence that any of these civilizations recognized the [[#Mass versus Weight|distinction between mass and weight]], since the effects of [https://en.wikipedia.org/wiki/Gravity_of_Earth Earth's gravity] near the surface ensures that the weight and mass of an object are directly proportional.

== See also ==
* [[Kinds of Matter]]
* [[Gravitational Force]]
* [[Inertia]]
* [[Rest Mass Energy]]
* [[Sir Isaac Newton]]
* [[Einstein's Theory of Special Relativity]]

==References==

# W. Rindler (2006). Relativity: Special, General, And Cosmological. Oxford University Press. pp. 16–18. ISBN 0-19-856731-6.
# A. Einstein, "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg. <https://www.gutenberg.org/etext/5001.>

[[Category:Properties of Matter]]

File:SpacetimeCurvature.jpg

2015-12-05T04:03:46Z

Ctam8: A 3-D visualization of the planet Earth deforming spacetime. Credit: NASA

A 3-D visualization of the planet Earth deforming spacetime.
Credit: NASA

Rest Mass Energy

2015-12-05T03:31:30Z

Ctam8: Fix grammar and follow standard wiki formats/standards

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> 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>)

This relationship was shown by Albert Einstein in 1905.[[File:Albert Einstein Head.jpeg|200px|thumb|right|Albert Einstein in 1947]]

===A Mathematical Model===

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

<math> 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>E = mc^2</math>

<math>E = (7 {\rm \ kg})*(3e8 {\rm \ m/s})^2</math>

<math>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>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===

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>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==

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

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

Mass

2015-10-25T02:07:58Z

Ctam8:

This page is about the idea of mass in physics. A work in progress by [http://www.physicsbook.gatech.edu/User:ctam8 Christopher Tam].

==The Main Idea==

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the underlying fundamental concept that governs gravity, inertia, and rest energy. The SI units for mass is kilograms (kg).

===A Mathematical Model===

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

===A Computational Model===

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

==Properties==

===Gravitational Attraction===
One of the intrinsic properties of mass is its gravitational attraction. A body of mass not only attracts other bodies of mass but also is attracted by other bodies of mass.

==Examples==

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

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

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

==History==

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

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

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

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

Mass

2015-10-25T01:35:53Z

Ctam8:

This page is about the idea of mass in physics. A work in progress by [http://www.physicsbook.gatech.edu/User:ctam8 Christopher Tam].

==The Main Idea==

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the underlying fundamental concept that governs gravity, inertia, and rest energy.

===A Mathematical Model===

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

===A Computational Model===

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

==Examples==

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

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

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

==History==

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

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

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

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

Mass

2015-10-25T01:34:14Z

Ctam8: Created page with "This page is about the idea of mass in physics. A work in progress by [www.physicsbook.gatech.edu/User:ctam8 Christopher Tam]. ==The Main Idea== Mass is one of the intrinsi..."

This page is about the idea of mass in physics. A work in progress by [www.physicsbook.gatech.edu/User:ctam8 Christopher Tam].

==The Main Idea==

Mass is one of the intrinsic properties of physical bodies that exist in 3-dimensional space. Mass is the underlying fundamental concept that governs gravity, inertia, and rest energy.

===A Mathematical Model===

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

===A Computational Model===

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

==Examples==

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

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

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

==History==

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

== See also ==

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

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

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

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