Spring Potential Energy - Revision history

Ss87: Added tables to the main idea sections that include common mistakes made when conceptualizing springs, and added a few more examples to the connectedness section

2025-11-19T10:27:10Z

Added tables to the main idea sections that include common mistakes made when conceptualizing springs, and added a few more examples to the connectedness section

@@ Line 1: / Line 1: @@
-CLAIMED BY Taraji Long Fall 2019 11/15/2019
+'''Shlesh Sakpal (Ss87) Fall 2025 11/19/2025'''
 This topic covers Spring Potential Energy.
@@ Line 167: / Line 168: @@
      t = t + deltat
      rate(1000)
 ==Examples==
@@ Line 254: / Line 318: @@
 Because springs are all around us, from Slinkies to parts in automobiles, spring potential energy is useful in everyday life. One example of this is a trampoline.  Without potential spring energy to allow for bounce, a trampoline would simply be a boring stretch of fabric.  Spring potential is also used to absorb shock in vehicles.  This allows for a smoother ride while traveling over bumps in the road. An extreme example of spring energy we commonly come across is the mechanism for garage doors. These doors contain large springs that allow them to open and close. These springs can lift an average of 400 pounds, giving them a huge amount of potential energy.
 [[File:trampoline.jpg|thumb|Trampoline Potential Energy]]

Gharrigan3 at 09:20, 5 December 2022

2022-12-05T09:20:56Z

@@ Line 55: / Line 55: @@
 https://trinket.io/glowscript/3146b836dc
-'''An hanging oscillating spring:'''
+'''A hanging oscillating spring:'''
   from __future__ import division
@@ Line 88: / Line 88: @@
 [[File:Animated-mass-spring-faster.gif|200 px]]
 ==Examples==
@@ Line 168: / Line 247: @@
 '''Energy graph'''
-The energy graph of a oscillating spring continuously switches between kinetic and potential energy because springs are continuously returning to equilibrium.
+The energy graph of a oscillating spring continuously switches between kinetic and potential energy because springs are continuously returning to equilibrium. The following is an example of a computational model of a hanging spring with an initial force in the positive x direction. As seen below, the energies the spring contains will always equal out to zero despite each fluctuating individually.
-[[File:energy2456.jpg|500 px|Example of Potential Energy Graph]]
+[[File:Spring energy.jpg]]
 ==Connectedness==
-Because springs are all around us, from Slinkies to parts in automobiles, spring potential energy is useful in everyday life. One example of this is a trampoline.  Without potential spring energy to allow for bounce, a trampoline would simply be a boring stretch of fabric.  Spring potential is also used to absorb shock in vehicles.  This allows for a smoother ride while traveling over bumps in the road.
+Because springs are all around us, from Slinkies to parts in automobiles, spring potential energy is useful in everyday life. One example of this is a trampoline.  Without potential spring energy to allow for bounce, a trampoline would simply be a boring stretch of fabric.  Spring potential is also used to absorb shock in vehicles.  This allows for a smoother ride while traveling over bumps in the road. An extreme example of spring energy we commonly come across is the mechanism for garage doors. These doors contain large springs that allow them to open and close. These springs can lift an average of 400 pounds, giving them a huge amount of potential energy.
 [[File:trampoline.jpg|thumb|Trampoline Potential Energy]]

Ilee305 at 17:22, 13 November 2020

2020-11-13T17:22:46Z

← Older revision		Revision as of 13:22, 13 November 2020
Line 6:		Line 6:
	[[File:spring2456.png\|thumb\|500 px\| Spring Potential Energy]]		[[File:spring2456.png\|thumb\|500 px\| Spring Potential Energy]]

	Spring potential energy, also known as elastic potential energy,is the stored energy in a spring, that can potentially be converted into kinetic energy. The energy stored in the spring is due to the deformation of the spring, often from stretching and compressing. The force excreted to stretch or compress a spring is known as Hooke's law, '''F<sub>s</sub> = -k<sub>x</sub>s''', where '''F<sub>s</sub>''' is force, '''x''' is the displacement, and '''-k<sub>s</sub>''' is the spring constant. The spring constant being unique for every spring depends on factors such as material and thickness of coiled wire. If a spring is not stretched or compressed, then it is at equilibrium. At equilibrium a spring has no potential energy, assuming there is no force being applied to the spring.		Spring potential energy, also known as elastic potential energy,is the stored energy in a spring, that can potentially be converted into kinetic energy. The energy stored in the spring is due to the deformation of the spring, often from stretching and compressing. The force excreted to stretch or compress a spring is known as Hooke's law, '''F<sub>s</sub> = -k<sub>s</sub>x''', where '''F<sub>s</sub>''' is force, '''x''' is the displacement, and '''-k<sub>s</sub>''' is the spring constant. The spring constant being unique for every spring depends on factors such as material and thickness of coiled wire. If a spring is not stretched or compressed, then it is at equilibrium. At equilibrium a spring has no potential energy, assuming there is no force being applied to the spring.

Tlong44: /* See also */

2019-11-25T04:59:20Z

Tlong44: /* The Main Idea */

2019-11-25T04:55:59Z

The Main Idea

← Older revision		Revision as of 00:55, 25 November 2019
Line 49:		Line 49:
	spring.axis = box.pos - spring.pos		spring.axis = box.pos - spring.pos
	t = t+ deltat		t = t+ deltat

			[[File:spring2457.png\|500 px\| Oscillating Spring on Floor]]

	Link to Simulation:		Link to Simulation:
Line 85:		Line 87:
	t = t + deltat		t = t + deltat

	[[File:Animated-mass-spring-faster.gif\|~~300~~ px]]		[[File:Animated-mass-spring-faster.gif\|200 px]]

	==Examples==		==Examples==

Tlong44: /* The Main Idea */

2019-11-25T04:51:13Z

The Main Idea

← Older revision		Revision as of 00:51, 25 November 2019
Line 6:		Line 6:
	[[File:spring2456.png\|thumb\|500 px\| Spring Potential Energy]]		[[File:spring2456.png\|thumb\|500 px\| Spring Potential Energy]]

	Spring potential energy, also known as elastic potential energy,is the stored energy in a spring, that can potentially be converted into kinetic energy. The energy stored in the spring is due to the deformation of the spring, often from stretching and compressing. The force excreted to stretch or compress a spring is known as Hooke's law, '''F<sub>s</sub> = -k<sub>x</sub>s''', where '''F<sub>s</sub>''' is force, '''x''' is the displacement, and '''-k<sub>s</sub>''' is the spring constant. The spring constant being unique for every spring depends on factors such as material and thickness of coiled wire.		Spring potential energy, also known as elastic potential energy,is the stored energy in a spring, that can potentially be converted into kinetic energy. The energy stored in the spring is due to the deformation of the spring, often from stretching and compressing. The force excreted to stretch or compress a spring is known as Hooke's law, '''F<sub>s</sub> = -k<sub>x</sub>s''', where '''F<sub>s</sub>''' is force, '''x''' is the displacement, and '''-k<sub>s</sub>''' is the spring constant. The spring constant being unique for every spring depends on factors such as material and thickness of coiled wire. If a spring is not stretched or compressed, then it is at equilibrium. At equilibrium a spring has no potential energy, assuming there is no force being applied to the spring.

Tlong44: /* Examples */

2019-11-25T04:47:52Z

Examples

← Older revision		Revision as of 00:47, 25 November 2019
Line 163:		Line 163:

	'''s'''=2.36 m		'''s'''=2.36 m

			===Graphing===
			'''Energy graph'''

			The energy graph of a oscillating spring continuously switches between kinetic and potential energy because springs are continuously returning to equilibrium.

			[[File:energy2456.jpg\|500 px\|Example of Potential Energy Graph]]

	==Connectedness==		==Connectedness==

Tlong44: /* Connectedness */

2019-11-25T04:36:10Z

Connectedness

← Older revision		Revision as of 00:36, 25 November 2019
Line 166:		Line 166:
	==Connectedness==		==Connectedness==

	Because springs are all around us, from Slinkies to parts in automobiles, spring potential energy is useful in everyday life. One example of this is a trampoline. Without potential spring energy to allow for bounce, a trampoline would simply be a boring stretch of fabric. Spring potential is also used to absorb shock in vehicles. This allows for a smoother ride while traveling over bumps in the road.		Because springs are all around us, from Slinkies to parts in automobiles, spring potential energy is useful in everyday life. One example of this is a trampoline. Without potential spring energy to allow for bounce, a trampoline would simply be a boring stretch of fabric. Spring potential is also used to absorb shock in vehicles. This allows for a smoother ride while traveling over bumps in the road.

	[[File:~~rubberband~~.jpg\|thumb\|~~Rubber bands hold elastic potential energy~~]]		[[File:trampoline.jpg\|thumb\|Trampoline Potential Energy]]

	==History==		==History==

Tlong44: /* The Main Idea */

2019-11-25T04:32:16Z

The Main Idea

← Older revision		Revision as of 00:32, 25 November 2019
Line 4:		Line 4:
	==The Main Idea==		==The Main Idea==

	[[File:~~Animated-mass-spring-faster~~.~~gif~~\|~~300~~ px]]		[[File:spring2456.png\|thumb\|500 px\| Spring Potential Energy]]

			Spring potential energy, also known as elastic potential energy,is the stored energy in a spring, that can potentially be converted into kinetic energy. The energy stored in the spring is due to the deformation of the spring, often from stretching and compressing. The force excreted to stretch or compress a spring is known as Hooke's law, '''F<sub>s</sub> = -k<sub>x</sub>s''', where '''F<sub>s</sub>''' is force, '''x''' is the displacement, and '''-k<sub>s</sub>''' is the spring constant. The spring constant being unique for every spring depends on factors such as material and thickness of coiled wire.


	Elastic potential energy, also known as spring potential energy, is the energy stored in elastic materials due to their deformation. This is most often seen in the stretching or compressing of springs.

	===A Mathematical Model===		===A Mathematical Model===
	The formula for ~~Ideal~~ Spring ~~Force is~~:		The formula for Force of a Spring:

	'''F<sub>s</sub> = -k<sub>s</sub>s		'''F<sub>s</sub> = -k<sub>s</sub>x

	The formula for ~~Ideal~~ Spring Energy is:		The formula for Spring Potential Energy:

	'''U<sub>s</sub> = <sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''		'''U<sub>s</sub> = <sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>x<sup>2</sup>'''

	where:		where:
Line 21:		Line 23:
	'''k<sub>s</sub>''' = spring constant		'''k<sub>s</sub>''' = spring constant

	'''s<sup>2</sup>''' = stretch measured from the equilibrium point;		'''x<sup>2</sup>''' = stretch measured from the equilibrium point;


	~~[[File~~:~~spring.jpg\|thumb\|Spring Potential Energy]]~~		===A Computational Model===
			'''An oscillating spring on the floor:'''

	===~~A Computational Model~~===		GlowScript 2.9 VPython
	An oscillating spring ~~can be modeled by the following~~:		display(width=600,height=600,center=vector(6,0,0),background=color.black)
			mbox=2
			L0 = vector(9,0,0)
			ks = 1
			deltat = .01
			t = 0
			wall=box(pos=vector(0,1,0),size=vector(0.2,3,2),color=color.cyan)
			floor=box(pos=vector(7.2,-0.6,0),size=vector(14,0.2,4),color=color.cyan)
			box=box(pos=vector(12,0,0),size=vector(1,1,1),color=color.red)
			pivot=vector(0,0,0)
			spring=helix(pos=pivot,axis=box.pos-pivot,radius=0.4,constant=1,thickness=0.1,coils=20,color=color.orange)
			box.p = vector(0,0,0)
			while (t<50):
			rate(100)
			s = wall.pos - box.pos
			Fspring=(L0-box.pos)*(ks)
			box.p= box.p +Fspring*deltat
			box.pos = box.pos + box.p*deltat
			spring.axis = box.pos - spring.pos
			t = t+ deltat

			Link to Simulation:
			https://trinket.io/glowscript/3146b836dc

			'''An hanging oscillating spring:'''

	from __future__ import division		from __future__ import division
	from visual import *		from visual import *
	from visual.graph import *		from visual.graph import *
	scene.width=600		scene.width=600
	scene.height = 760		scene.height = 760
	g = 9.8		g = 9.8
	mball = .2		mball = .2
	Lo = 0.3		Lo = 0.3
	ks = 12		ks = 12
	deltat = 1e-3		deltat = 1e-3
	t = 0		t = 0
	ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))		ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))
	ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)		ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)
	spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)		spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)
	spring.axis = ball.pos - ceiling.pos		spring.axis = ball.pos - ceiling.pos
	vball = vector(0.02,0,0)		vball = vector(0.02,0,0)
	ball.p = mball*vball		ball.p = mball*vball
	scene.autoscale = 0		scene.autoscale = 0
	scene.center = vector(0,-Lo,0)		scene.center = vector(0,-Lo,0)
	while t < 10:		while t < 10:
	rate(1000)		rate(1000)
	L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()		L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()
Line 58:		Line 85:
	spring.axis = ball.pos-ceiling.pos		spring.axis = ball.pos-ceiling.pos
	t = t + deltat		t = t + deltat

			[[File:Animated-mass-spring-faster.gif\|300 px]]

	==Examples==		==Examples==

Tlong44 at 00:27, 16 November 2019

2019-11-16T00:27:12Z

← Older revision		Revision as of 20:27, 15 November 2019
Line 1:		Line 1:
	CLAIMED BY ~~MOLLY BUTLER FALL 2017~~		CLAIMED BY Taraji Long Fall 2019 11/15/2019
	This topic covers Spring Potential Energy.		This topic covers Spring Potential Energy.

← Older revision		Revision as of 00:59, 25 November 2019
Line 190:		Line 190:

	http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html		http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html

			https://www.khanacademy.org/science/ap-physics-1/ap-work-and-energy/spring-potential-energy-and-hookes-law-ap/a/spring-force-and-energy-ap1

			https://openstax.org/books/university-physics-volume-1/pages/8-1-potential-energy-of-a-system

	===External links===		===External links===