Conservation of Energy - Revision history

Claudiatiller7: /* Main Ideas */

2023-04-17T01:10:23Z

Main Ideas

← Older revision		Revision as of 21:10, 16 April 2023
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	==Main Ideas==		==Main Ideas==
	~~CLAUDIA TILLER~~
	* The law of conservation of energy states that the '''total amount of energy''' of a system '''before and after''' an interaction between objects in '''conserved'''.		* The law of conservation of energy states that the '''total amount of energy''' of a system '''before and after''' an interaction between objects in '''conserved'''.
	* This only applies to '''isolated systems''' (no outside forces acting on the system).		* This only applies to '''isolated systems''' (no outside forces acting on the system).

Claudiatiller7: /* Main Ideas */

2023-04-17T01:10:08Z

Main Ideas

← Older revision		Revision as of 21:10, 16 April 2023
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	==Main Ideas==		==Main Ideas==
			CLAUDIA TILLER
	* The law of conservation of energy states that the '''total amount of energy''' of a system '''before and after''' an interaction between objects in '''conserved'''.		* The law of conservation of energy states that the '''total amount of energy''' of a system '''before and after''' an interaction between objects in '''conserved'''.
	* This only applies to '''isolated systems''' (no outside forces acting on the system).		* This only applies to '''isolated systems''' (no outside forces acting on the system).

Enguyentu3: /* How does it relate to things we want to study? */ Improved readability.

2023-04-08T21:43:04Z

How does it relate to things we want to study?: Improved readability.

← Older revision		Revision as of 17:43, 8 April 2023
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	<br>		<br>
	: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} </math>     [e.5]		: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} </math>     [e.5]
	~~The~~ Law of Conservation of Energy tells us that the total energy in the universe is constant.		Furthermore, the Law of Conservation of Energy tells us that the total energy in the universe is constant.
	: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} = \text{Some Constant} </math>     [e.6]		: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} = \text{Some Constant} </math>     [e.6]
	However, when considering the surroundings in [e.5] and [e.6] for systems that are not the entire universe, we run into an important problem:		However, when considering the surroundings in [e.5] and [e.6] for systems that are not the entire universe, we run into an important problem:

Enguyentu3: Corrected/Clarified My Contributions.

2023-04-08T21:02:18Z

Corrected/Clarified My Contributions.

← Older revision		Revision as of 17:02, 8 April 2023
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	===What does it mean?===		===What does it mean?===
	Since The Law of Conservation of Energy states energy cannot be created or destroyed, this means that the total energy in the universe is constant and does not change in value.		Since The Law of Conservation of Energy states energy cannot be created or destroyed, this means that the total energy in the universe is constant and does not change in value, assuming there is nothing beyond the universe.
	<br>		<br>
	Therefore, in equation format:    <math>~~\Delta~~ E_{total, universe} = 0</math>     ~~[e.1]~~		:Therefore, in equation format:
			::[e.1]     <math>E_{total, universe} = \text{Some Constant}</math>
			::[e.2]     <math>\Delta E_{total, universe} = 0</math>

	==Mathematical Model==		==Mathematical Model==
			===Conservation of Energy===
			::[e.1]     <math> E_{total, universe} = \text{Some Constant} </math>
			::[e.2]     <math> \Delta E_{total, universe} = 0 </math>

	[~~e.1~~] ~~   <math>\Delta E_{total, universe}~~ = ~~0</math>~~		===Conservation of Energy & [[The Energy Principle]]===
	~~<br>~~		::[e.3]     <math> \Delta E_{system} + \Delta E_{surroundings} = 0 </math>
	[e.3]  ~~  <math>\Delta E_{total, universe} = \Delta E_{system} + \Delta E_{surroundings}</math>~~
	~~<br> <br>~~
	~~[e.1] & [e.3]:~~
	~~<br>~~
	~~:[e.4]~~    <math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	===Isolated System===		===Isolated System===
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	[[File:Graphspring.gif]]		[[File:Graphspring.gif]]

	====Useful Energy Formulas====		===Useful Energy Formulas===

	'''[[Kinetic Energy]]'''		'''[[Kinetic Energy]]'''
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	In Physics, we separate what we are looking at into a system and its surroundings. This is a zero-sum separation where what we are interested in is included in the system and everything else in the universe is lumped into the system's surroundings.		In Physics, we separate what we are looking at into a system and its surroundings. This is a zero-sum separation where what we are interested in is included in the system and everything else in the universe is lumped into the system's surroundings.
	<br>		<br>
	: In equation format:    Universe = System + Surroundings     [e.2]		: In equation format:    Universe = System + Surroundings     [e.4]
	This division of the universe into a system and its surroundings can also be applied to the total energy in the universe.		This division of the universe into a system and its surroundings can also be applied to the total energy in the universe.
	<br>		<br>
	: ~~Therefore~~:    <math>~~\Delta~~ E_{total, universe} = ~~\Delta~~ E_{system} + ~~\Delta~~ E_{surroundings}</math>     [e.3]		: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} </math>     [e.5]
	~~When trying to apply the~~ Law of Conservation of Energy to [e.3], we run into an important problem:		The Law of Conservation of Energy tells us that the total energy in the universe is constant.
			: In equation format:    <math>E_{total, universe} = E_{system} + E_{surroundings} = \text{Some Constant} </math>     [e.6]
			However, when considering the surroundings in [e.5] and [e.6] for systems that are not the entire universe, we run into an important problem:
	<br>		<br>
	: When considering a system, is that it is highly time inefficient, and essentially impossible, to consider and factor in everything in the universe that is not included in the system. Therefore, this means that we can only find completely accurate values by applying the Law of Conservation of Energy to isolated systems in which the system has no net external force and does not exchange matter and energy with its surroundings. Nevertheless, applying the Law of Conservation of Energy to closed systems, in which matter is not able to enter or leave but energy can, we can get close approximations by identifying the main actors in the surroundings that influence our system.		: When considering the system's surroundings, is that it is highly time inefficient, and essentially impossible, to consider and factor in everything in the universe that is not included in the system. Therefore, this means that we can only find completely accurate energy values by applying the Law of Conservation of Energy to isolated systems in which the system has no net external force and does not exchange matter and energy with its surroundings. In this case, the Law of Conservation of Energy tells us that the energy within the isolated system is constant. Nevertheless, applying the Law of Conservation of Energy to closed systems, in which matter is not able to enter or leave but energy can, we can get close approximations by identifying the main actors in the surroundings that influence our system.

	===How does it related to [[The Energy Principle]]?===		===How does it related to [[The Energy Principle]]?===
	Since the Law of Conservation of Energy says energy cannot be created or destroyed, [[The Energy Principle]] tells us that the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy. Therefore, [[The Energy Principle]] can be generalized in terms of conservation of energy.		Since the Law of Conservation of Energy says energy cannot be created or destroyed, [[The Energy Principle]] tells us that the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy. Therefore, [[The Energy Principle]] can be generalized in terms of conservation of energy.
	<br>		<br>
	:Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>     [e.4]		: Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>     [e.3]

	==History==		==History==

Enguyentu3: Made the Example Questions Collapsable to Make the Solutions Optionally Visible.

2023-04-08T19:03:51Z

Made the Example Questions Collapsable to Make the Solutions Optionally Visible.

← Older revision		Revision as of 15:03, 8 April 2023
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	==Examples==		==Examples==
			To view the solution, click '''Expand''' at the top right of each question.

	===Easy===		===Easy===
	A ball is at rest on a table with 50 J of potential energy. It then rolls off the table, and at one point in time as it falls, the ball has 30 J of kinetic energy.
			<div class="toccolours mw-collapsible mw-collapsed">

			====Question 1====
			A ball is at rest on a table with 50 J of potential energy. It then rolls off the table, and at one point in time as it falls, the ball has 30 J of kinetic energy.
	'''What is the potential energy of the ball at that instant?'''		'''What is the potential energy of the ball at that instant?'''

			<div class="mw-collapsible-content">

	[[File:EasyEnergyConservation.png]]		[[File:EasyEnergyConservation.png]]
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	0 J + 50 J = 30 J + U<sub>final</sub> <br>		0 J + 50 J = 30 J + U<sub>final</sub> <br>
	U<sub>final</sub> = 20 J		U<sub>final</sub> = 20 J

			</div>
			</div>

	===Medium===		===Medium===
	A ball is at rest 50 m above the ground. You then drop the ball.		<div class="toccolours mw-collapsible mw-collapsed">

			====Question 1====
			A ball is at rest 50 m above the ground. You then drop the ball.
	'''What is its speed before hitting the ground?'''		'''What is its speed before hitting the ground?'''

			<div class="mw-collapsible-content">

	[[File:ballcalc.jpg\|400px]]		[[File:ballcalc.jpg\|400px]]

			</div>
			</div>

	===Hard===		===Hard===
	The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. The coefficient of friction between the tires and the road is 0.72.		<div class="toccolours mw-collapsible mw-collapsed">

			====Question 1====
			The driver of an SUV (m = 1700 kg) isn’t paying attention and rear ends a car (m = 950 kg) on level ground at a red light. On impact, both drivers lock their brakes. The SUV and car stick together and travel a distance of 8.2 m before they come to a stop. The coefficient of friction between the tires and the road is 0.72.
	'''How fast was the SUV traveling just before the collision?'''		'''How fast was the SUV traveling just before the collision?'''

			<div class="mw-collapsible-content">

	[[File:collidecars.jpg\|600px]]		[[File:collidecars.jpg\|600px]]

			</div>
			</div>

	==Connectedness==		==Connectedness==

Enguyentu3: Updated with main references.

2023-04-08T06:47:17Z

Updated with main references.

← Older revision		Revision as of 02:47, 8 April 2023
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	# "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>.		# "Conservation of Energy & Momentum Problem: Collision of Two Cars at a Stoplight." University of Wisconsin- Green Bay Physics. Web. 2 Dec. 2015. <http://www.uwgb.edu/fenclh/problems/energy/6/>.
	# "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.		# "Law of Conservation of Mass Energy." Law of Conservation of Mass Energy. Web. 3 Dec. 2015. <http://www.chemteam.info/Thermochem/Law-Cons-Mass-Energy.html>.
	# "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>		# "Law of Conservation of Energy" New York University. Web. 18 Apr. 2018. <http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html>.
	# "Law of Conversation of Energy" ME Mechanical. Web. 18 Apr. 2018. <https://me-mechanicalengineering.com/law-of-conservation-of-energy/>		# "Law of Conversation of Energy" ME Mechanical. Web. 18 Apr. 2018. <https://me-mechanicalengineering.com/law-of-conservation-of-energy/>.
			# "Law of conservation of energy" University of Calgary. Web. 8 Apr. 2023. <https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy>.
			# "Basic Definitions" LibreTexts Chemistry. Web. 8 Apr. 2023. <https://chem.libretexts.org/Bookshelves/General_Chemistry/General_Chemistry_Supplement_(Eames)/Thermochemistry/Basic_Definitions#:~:text=A%20closed%20system%20does%20not,is%20approximately%20an%20isolated%20system.>

	[[Category:Energy]]		[[Category:Energy]]

Enguyentu3: Mostly finalized the Connectedness Section and Contributed to the Mathematical Model and Main Ideas sections.

2023-04-08T06:42:05Z

Mostly finalized the Connectedness Section and Contributed to the Mathematical Model and Main Ideas sections.

← Older revision		Revision as of 02:42, 8 April 2023
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	** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.		** Isolated: An object sliding across a rough floor (system = the object AND the floor). There is no work done on the system because all the forces are contained in the system.
	[[File:canonfire.jpg\|800px\|center]]		[[File:canonfire.jpg\|800px\|center]]

			===What does it mean?===
			Since The Law of Conservation of Energy states energy cannot be created or destroyed, this means that the total energy in the universe is constant and does not change in value.
			<br>
			Therefore, in equation format:    <math>\Delta E_{total, universe} = 0</math>     [e.1]

	==Mathematical Model==		==Mathematical Model==

	===~~Formulas===~~		[e.1]    <math>\Delta E_{total, universe} = 0</math>
			<br>
			[e.3]    <math>\Delta E_{total, universe} = \Delta E_{system} + \Delta E_{surroundings}</math>
			<br> <br>
			[e.1] & [e.3]:
			<br>
			:[e.4]    <math>\Delta E_{system} + \Delta E_{surroundings} = 0</math>

	===~~=Conservation of Energy=~~===		===Isolated System===
	* <b> ΔE = W + Q </b> (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)		* <b> ΔE = W + Q </b> (if no heat transfer indicated, Q = 0; if no external forces acting on system, W = 0)
	* <b> ΔE = K + U </b> (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)		* <b> ΔE = K + U </b> (The total energy is the sum of the kinetic and potential energies. From this, you can infer that for an isolated system, any change in kinetic energy will correspond in an equal but opposite change in the potential energy and vice versa.)
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	==Connectedness==		==Connectedness==
	~~Earlier~~, we ~~learned about~~ [[The Energy Principle]]. Since the Law of Conservation of Energy says energy cannot be created or destroyed, ~~the~~ Energy Principle tells us that the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy. Therefore, ~~the~~ Energy Principle can be generalized in terms of conservation of energy.
	~~<br>~~ <br>		===How does it relate to things we want to study?===
	Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>		In Physics, we separate what we are looking at into a system and its surroundings. This is a zero-sum separation where what we are interested in is included in the system and everything else in the universe is lumped into the system's surroundings.
			<br>
			: In equation format:    Universe = System + Surroundings     [e.2]
			This division of the universe into a system and its surroundings can also be applied to the total energy in the universe.
			<br>
			: Therefore:    <math>\Delta E_{total, universe} = \Delta E_{system} + \Delta E_{surroundings}</math>     [e.3]
			When trying to apply the Law of Conservation of Energy to [e.3], we run into an important problem:
			<br>
			: When considering a system, is that it is highly time inefficient, and essentially impossible, to consider and factor in everything in the universe that is not included in the system. Therefore, this means that we can only find completely accurate values by applying the Law of Conservation of Energy to isolated systems in which the system has no net external force and does not exchange matter and energy with its surroundings. Nevertheless, applying the Law of Conservation of Energy to closed systems, in which matter is not able to enter or leave but energy can, we can get close approximations by identifying the main actors in the surroundings that influence our system.

			===How does it related to [[The Energy Principle]]?===
			Since the Law of Conservation of Energy says energy cannot be created or destroyed, [[The Energy Principle]] tells us that the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy. Therefore, [[The Energy Principle]] can be generalized in terms of conservation of energy.
			<br>
			:Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>     [e.4]

	==History==		==History==

	<b>Who:</b> Many physicists contributed to the knowledge of energy, however it is most notably ~~atributed~~ to Julius Robert Mayer		<b>Who:</b> Many physicists contributed to the knowledge of energy, however it is most notably attributed to Julius Robert Mayer
	<br>		<br>
	<b>What:</b> Most formally discovered the law of conservation of energy		<b>What:</b> Most formally discovered the law of conservation of energy

Enguyentu3: Added clarification to Connectedness section.

2023-04-08T03:59:32Z

Added clarification to Connectedness section.

← Older revision		Revision as of 23:59, 7 April 2023
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	==Connectedness==		==Connectedness==
	Earlier, we learned about [[The Energy Principle]]. Since the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy, the Energy Principle can be generalized in terms of conservation of energy.		Earlier, we learned about [[The Energy Principle]]. Since the Law of Conservation of Energy says energy cannot be created or destroyed, the Energy Principle tells us that the only way for a system to gain or lose energy is from its surroundings losing or gaining the same amount of energy. Therefore, the Energy Principle can be generalized in terms of conservation of energy.
	<br> <br>		<br> <br>
	Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>		Written in equation form, [[The Energy Principle]] in terms of the Law of Conservation of Energy is:    <math>{\Delta E_{system}+\Delta E_{surroundings}=0}</math>

Enguyentu3: Improved Format and sections Connectedness & Intro

2023-04-08T03:19:53Z

Improved Format and sections Connectedness & Intro

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Enguyentu3: Claimed Page for "Wiki Resource Submission Assignment" and Improved formatting of page, code, and equations.

2023-04-08T02:26:35Z

Claimed Page for "Wiki Resource Submission Assignment" and Improved formatting of page, code, and equations.

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