Spring Force - Revision history

Cnarreddy3: /* History */

2025-12-03T04:55:49Z

History

← Older revision		Revision as of 00:55, 3 December 2025
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	The study of springs began in the early 1600's, during the rapid development of mechanics. Before this time, springs were used in objects like crossbows and bows, but their behavior was understood only through the methods of trial and error, but not mathematically proven.		The study of springs began in the early 1600's, during the rapid development of mechanics. Before this time, springs were used in objects like crossbows and bows, but their behavior was understood only through the methods of trial and error, but not mathematically proven.

	In 1660, Robert Hooke created a linear model of spring force that expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>, and first published this discovery as an encoded phrase "ceiiinosssttuv", later revealed to be: "Ut tensio, sic vis," or “As the extension, so the force.” This would later be recognized as Hooke's Law [3].		In 1660, Robert Hooke created a linear model of spring force that expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>, and first published this discovery as an encoded phrase "ceiiinosssttuv", later revealed to be: "Ut tensio, sic vis," or “As the extension, so the force.” This would later be recognized as Hooke's Law [https://books.google.com/books/about/Lectures_de_Potentia_Restitutiva_Or_of_S.html?id=LAtPAAAAcAAJ].

	Hooke's work had major technological consequences in oscillations and structural vibrations, and currently remains central in physics and engineering.		Hooke's work had major technological consequences in oscillations and structural vibrations, and currently remains central in physics and engineering.

Cnarreddy3: /* History */

2025-12-03T04:54:58Z

History

← Older revision		Revision as of 00:54, 3 December 2025
Line 164:		Line 164:
	The study of springs began in the early 1600's, during the rapid development of mechanics. Before this time, springs were used in objects like crossbows and bows, but their behavior was understood only through the methods of trial and error, but not mathematically proven.		The study of springs began in the early 1600's, during the rapid development of mechanics. Before this time, springs were used in objects like crossbows and bows, but their behavior was understood only through the methods of trial and error, but not mathematically proven.

	In 1660, Robert Hooke created a linear model of spring force that expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>, and first published this discovery as an encoded phrase "ceiiinosssttuv", later revealed to be: "Ut tensio, sic vis," or “As the extension, so the force.” This would later be recognized as Hooke's Law.		In 1660, Robert Hooke created a linear model of spring force that expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>, and first published this discovery as an encoded phrase "ceiiinosssttuv", later revealed to be: "Ut tensio, sic vis," or “As the extension, so the force.” This would later be recognized as Hooke's Law [3].

	Hooke's work had major technological consequences in oscillations and structural vibrations, and currently remains central in physics and engineering.		Hooke's work had major technological consequences in oscillations and structural vibrations, and currently remains central in physics and engineering.

Cnarreddy3 at 04:53, 3 December 2025

2025-12-03T04:53:40Z

← Older revision		Revision as of 00:53, 3 December 2025
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	Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />		Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />
	Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]		Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]
	Hooke, Robert (1678). ''De Potentia Restitutiva''. London. ~~Available at:~~ https://books.google.com/books/about/Lectures_de_Potentia_Restitutiva_Or_of_S.html?id=LAtPAAAAcAAJ		Hooke, Robert (1678). ''Lectures De Potentia Restitutiva''. London. [https://books.google.com/books/about/Lectures_de_Potentia_Restitutiva_Or_of_S.html?id=LAtPAAAAcAAJ]

Cnarreddy3: /* References */

2025-12-03T04:51:40Z

References

← Older revision		Revision as of 00:51, 3 December 2025
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	Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />		Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />
	Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]		Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]
			Hooke, Robert (1678). ''De Potentia Restitutiva''. London. Available at: https://books.google.com/books/about/Lectures_de_Potentia_Restitutiva_Or_of_S.html?id=LAtPAAAAcAAJ


	[[Category: Interactions]]		[[Category: Interactions]]

	--[[User:Arj\|Arj]] ([[User talk:Arj\|talk]]) 23:35, 5 December 2015 (EST)		--[[User:Arj\|Arj]] ([[User talk:Arj\|talk]]) 23:35, 5 December 2015 (EST)

Cnarreddy3: History Section Expansion

2025-12-03T04:48:12Z

History Section Expansion

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	==History==		==History==

	The ~~concept~~ of ~~spring force~~ was ~~first discovered in~~ 1660 by Robert Hooke~~. Hooke's~~ linear model of spring force expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>~~. Hooke originally stated~~ this ~~law in Latin~~: "Ut tensio, sic vis," or “As the extension, so the force.” This ~~insight~~ would ~~lead~~ Hooke ~~to devise plans for a watch with a balance spring~~, ~~that would make pocket watches much more accurate~~.		The study of springs began in the early 1600's, during the rapid development of mechanics. Before this time, springs were used in objects like crossbows and bows, but their behavior was understood only through the methods of trial and error, but not mathematically proven.

			In 1660, Robert Hooke created a linear model of spring force that expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>, and first published this discovery as an encoded phrase "ceiiinosssttuv", later revealed to be: "Ut tensio, sic vis," or “As the extension, so the force.” This would later be recognized as Hooke's Law.

			Hooke's work had major technological consequences in oscillations and structural vibrations, and currently remains central in physics and engineering.

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

Cnarreddy3 at 02:58, 3 December 2025

2025-12-03T02:58:51Z

← Older revision		Revision as of 22:58, 2 December 2025
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	:<math>\vert \vec{F}_{spring} \vert = 6N</math>		:<math>\vert \vec{F}_{spring} \vert = 6N</math>

	===~~2.2~~ Middling===		===Middling===
	Suppose a spring sits at the origin with a spring stiffness of 300 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?		Suppose a spring sits at the origin with a spring stiffness of 300 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?

Cnarreddy3 at 02:58, 3 December 2025

2025-12-03T02:58:29Z

← Older revision		Revision as of 22:58, 2 December 2025
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	'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.		'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.

	==1 The Main Idea==		==The Main Idea==

	The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance. The distance the spring has been stretched is measured relative to the length of the spring at its relaxed length. This length is the length the spring exhibits when the net forces acting upon the spring are zero.		The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance. The distance the spring has been stretched is measured relative to the length of the spring at its relaxed length. This length is the length the spring exhibits when the net forces acting upon the spring are zero.
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	The most important thing to remember about the spring force is that it is a non-constant force. The magnitude of the force varies based on how much the spring is being stretched or compressed, as displayed in the following mathematical model.		The most important thing to remember about the spring force is that it is a non-constant force. The magnitude of the force varies based on how much the spring is being stretched or compressed, as displayed in the following mathematical model.

	===~~1.1~~ A Mathematical Model===		===A Mathematical Model===

	[[File:SpringForceDiagram.png\|right\|300px\|thumb\|L0 is the distance in the relaxed length, while L is the distance of the entire spring. s is the difference between these two variabels.]]		[[File:SpringForceDiagram.png\|right\|300px\|thumb\|L0 is the distance in the relaxed length, while L is the distance of the entire spring. s is the difference between these two variabels.]]
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	These models are linear models of the spring force and not the true force under every scenario. In a real system, the spring will deform when stretched and compressed, and thus change its spring constant; however, in a small enough stretches this deformation will be negligible and the linear representation will be reasonably accurate.		These models are linear models of the spring force and not the true force under every scenario. In a real system, the spring will deform when stretched and compressed, and thus change its spring constant; however, in a small enough stretches this deformation will be negligible and the linear representation will be reasonably accurate.

	===~~1.2~~ A Computational Model===		===A Computational Model===

	A GlowScript model of a spring that prints out the spring force vector[https://trinket.io/glowscript/9c8718bb1a]		A GlowScript model of a spring that prints out the spring force vector[https://trinket.io/glowscript/9c8718bb1a]
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	[[File:stepsize3.png]]		[[File:stepsize3.png]]

	==2 Examples==		==Examples==

	===~~2.1~~ Simple===		===Simple===
	Suppose a spring has been calibrated to have a spring stiffness of 300 N/m. You pull on the spring at rest and observe that it stretches a length of 0.02 m. What is the magnitude of the force exerted by the spring?		Suppose a spring has been calibrated to have a spring stiffness of 300 N/m. You pull on the spring at rest and observe that it stretches a length of 0.02 m. What is the magnitude of the force exerted by the spring?

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	:<math>\vec{F}_{spring} = -(300N/m)(-0.1483m) \langle 0.35, -2.39, 0 \rangle m = \langle 15.57, -106.33, 0 \rangle N</math>		:<math>\vec{F}_{spring} = -(300N/m)(-0.1483m) \langle 0.35, -2.39, 0 \rangle m = \langle 15.57, -106.33, 0 \rangle N</math>

	===~~2.3~~ Difficult===		===Difficult===

	A spring sitting vertically on a table. The spring has a relaxed length of 0.3 m and a spring stiffness of 4 N/m. A 0.8 kg block is stuck atop the spring. You push the block and spring down so the bottom of the block is 0.1 m from the surface of the table. What is the net force acting upon the block at this moment?		A spring sitting vertically on a table. The spring has a relaxed length of 0.3 m and a spring stiffness of 4 N/m. A 0.8 kg block is stuck atop the spring. You push the block and spring down so the bottom of the block is 0.1 m from the surface of the table. What is the net force acting upon the block at this moment?
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	==3 Connectedness==		==Connectedness==

	Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.		Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.
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	Read more: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html#ixzz45Xl3YEy0		Read more: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html#ixzz45Xl3YEy0

	==4 History==		==History==

	The concept of spring force was first discovered in 1660 by Robert Hooke. Hooke's linear model of spring force expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>. Hooke originally stated this law in Latin: "Ut tensio, sic vis," or “As the extension, so the force.” This insight would lead Hooke to devise plans for a watch with a balance spring, that would make pocket watches much more accurate.		The concept of spring force was first discovered in 1660 by Robert Hooke. Hooke's linear model of spring force expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>. Hooke originally stated this law in Latin: "Ut tensio, sic vis," or “As the extension, so the force.” This insight would lead Hooke to devise plans for a watch with a balance spring, that would make pocket watches much more accurate.

	==5 See also==		==See also==

	[[Work Done By A Nonconstant Force]]<br/>		[[Work Done By A Nonconstant Force]]<br/>
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	[[Spring Potential Energy]]<br/>		[[Spring Potential Energy]]<br/>

	===~~5.1~~ External links===		===External links===
	Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]<br />		Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]<br />
	Science Clarified[http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html]<br />		Science Clarified[http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html]<br />
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	==6 References==		==References==

	Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />		Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />

Cnarreddy3: Heading Numberings

2025-12-03T02:57:25Z

Heading Numberings

← Older revision		Revision as of 22:57, 2 December 2025
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	'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.		'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.

	==The Main Idea==		==1 The Main Idea==

	The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance. The distance the spring has been stretched is measured relative to the length of the spring at its relaxed length. This length is the length the spring exhibits when the net forces acting upon the spring are zero.		The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance. The distance the spring has been stretched is measured relative to the length of the spring at its relaxed length. This length is the length the spring exhibits when the net forces acting upon the spring are zero.
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	The most important thing to remember about the spring force is that it is a non-constant force. The magnitude of the force varies based on how much the spring is being stretched or compressed, as displayed in the following mathematical model.		The most important thing to remember about the spring force is that it is a non-constant force. The magnitude of the force varies based on how much the spring is being stretched or compressed, as displayed in the following mathematical model.

	===A Mathematical Model===		===1.1 A Mathematical Model===

	[[File:SpringForceDiagram.png\|right\|300px\|thumb\|L0 is the distance in the relaxed length, while L is the distance of the entire spring. s is the difference between these two variabels.]]		[[File:SpringForceDiagram.png\|right\|300px\|thumb\|L0 is the distance in the relaxed length, while L is the distance of the entire spring. s is the difference between these two variabels.]]
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	These models are linear models of the spring force and not the true force under every scenario. In a real system, the spring will deform when stretched and compressed, and thus change its spring constant; however, in a small enough stretches this deformation will be negligible and the linear representation will be reasonably accurate.		These models are linear models of the spring force and not the true force under every scenario. In a real system, the spring will deform when stretched and compressed, and thus change its spring constant; however, in a small enough stretches this deformation will be negligible and the linear representation will be reasonably accurate.

	===A Computational Model===		===1.2 A Computational Model===

	A GlowScript model of a spring that prints out the spring force vector[https://trinket.io/glowscript/9c8718bb1a]		A GlowScript model of a spring that prints out the spring force vector[https://trinket.io/glowscript/9c8718bb1a]
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	=Accuracy=		====Accuracy====
	If we have a step-size of five seconds, we are assuming that force of the spring is constant for those five seconds. This simplifying assumption decreases the accuracy of our model. Hence, in order to improve the accuracy of the computational model, we can decrease the time step-size. The graphs below display the difference between using a .01 second step-size (left graph) and 1 second step-size (right graph).		If we have a step-size of five seconds, we are assuming that force of the spring is constant for those five seconds. This simplifying assumption decreases the accuracy of our model. Hence, in order to improve the accuracy of the computational model, we can decrease the time step-size. The graphs below display the difference between using a .01 second step-size (left graph) and 1 second step-size (right graph).

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	[[File:stepsize3.png]]		[[File:stepsize3.png]]

	==Examples==		==2 Examples==

	===Simple===		===2.1 Simple===
	Suppose a spring has been calibrated to have a spring stiffness of 300 N/m. You pull on the spring at rest and observe that it stretches a length of 0.02 m. What is the magnitude of the force exerted by the spring?		Suppose a spring has been calibrated to have a spring stiffness of 300 N/m. You pull on the spring at rest and observe that it stretches a length of 0.02 m. What is the magnitude of the force exerted by the spring?

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	:<math>\vert \vec{F}_{spring} \vert = 6N</math>		:<math>\vert \vec{F}_{spring} \vert = 6N</math>

	===Middling===		===2.2 Middling===
	Suppose a spring sits at the origin with a spring stiffness of 300 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?		Suppose a spring sits at the origin with a spring stiffness of 300 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?

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	:<math>\vec{F}_{spring} = -(300N/m)(-0.1483m) \langle 0.35, -2.39, 0 \rangle m = \langle 15.57, -106.33, 0 \rangle N</math>		:<math>\vec{F}_{spring} = -(300N/m)(-0.1483m) \langle 0.35, -2.39, 0 \rangle m = \langle 15.57, -106.33, 0 \rangle N</math>

	===Difficult===		===2.3 Difficult===

	A spring sitting vertically on a table. The spring has a relaxed length of 0.3 m and a spring stiffness of 4 N/m. A 0.8 kg block is stuck atop the spring. You push the block and spring down so the bottom of the block is 0.1 m from the surface of the table. What is the net force acting upon the block at this moment?		A spring sitting vertically on a table. The spring has a relaxed length of 0.3 m and a spring stiffness of 4 N/m. A 0.8 kg block is stuck atop the spring. You push the block and spring down so the bottom of the block is 0.1 m from the surface of the table. What is the net force acting upon the block at this moment?
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	==~~Practical Applications~~==		==3 Connectedness==

	Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.		Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.
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	Read more: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html#ixzz45Xl3YEy0		Read more: http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html#ixzz45Xl3YEy0

	==History==		==4 History==

	The concept of spring force was first discovered in 1660 by Robert Hooke. Hooke's linear model of spring force expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>. Hooke originally stated this law in Latin: "Ut tensio, sic vis," or “As the extension, so the force.” This insight would lead Hooke to devise plans for a watch with a balance spring, that would make pocket watches much more accurate.		The concept of spring force was first discovered in 1660 by Robert Hooke. Hooke's linear model of spring force expressed the force of the spring using the equation <math>F = kx</math>, relating force, <math>F</math> and displacement, <math>x</math>, by some constant <math>k</math>. Hooke originally stated this law in Latin: "Ut tensio, sic vis," or “As the extension, so the force.” This insight would lead Hooke to devise plans for a watch with a balance spring, that would make pocket watches much more accurate.

	== See also ==		==5 See also==

	[[Work Done By A Nonconstant Force]]<br/>		[[Work Done By A Nonconstant Force]]<br/>
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	[[Spring Potential Energy]]<br/>		[[Spring Potential Energy]]<br/>

	===External links===		===5.1 External links===
	Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]<br />		Hyper Physics[http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html]<br />
	Science Clarified[http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html]<br />		Science Clarified[http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html]<br />
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	==References==		==6 References==

	Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />		Ruth W. Chabay, Bruce A. Sherwood (2011). ''Matter & Interactions''. John Wiley & Sons, Inc. p. 64.<br />

Cnarreddy3 at 02:41, 3 December 2025

2025-12-03T02:41:59Z

← Older revision		Revision as of 22:41, 2 December 2025
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	~~claimed~~ by ~~Madhur Bhuyan Spring 2017~~		'''Claimed by Charith Narreddy - Fall 2025'''

	'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.		'''''Spring Force''' is the non-constant, elastic force exerted by a spring upon a system.

Awilson383: /* Middling */

2020-09-14T04:15:57Z

Middling

← Older revision		Revision as of 00:15, 14 September 2020
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	===Middling===		===Middling===
	Suppose a spring sits at the origin with a spring stiffness of 15 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?		Suppose a spring sits at the origin with a spring stiffness of 300 N/m. The spring has a relaxed length of 0.32 m. The spring has a 5 kg mass on the end at position <0.06, -0.41, 0> m. What is the current force exerted by the spring?

	:<math>\vec{F}_{spring} = -k_s s \hat{L}</math>		:<math>\vec{F}_{spring} = -k_s s \hat{L}</math>