http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Scarswell3Physics Book - User contributions [en]2026-05-01T17:35:12ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=19189Spring Potential Energy2015-12-06T03:40:21Z<p>Scarswell3: </p>
<hr />
<div>This topic covers Spring Potential Energy.<br />
<br />
==Spring Potential Energy==<br />
<br />
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.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
'''<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
'''s<sup>2</sup>'''= <sup>m</sup>&frasl;<sub>k<sub>s</sub></sub>(<sup>2GM</sup>&frasl;<sub>R</sub> +v<sup>2</sup>)=s<sup>2</sup> = <sup>9</sup>&frasl;<sub>2.8x10<sup>5</sup></sub>(<sup>2G8.0x10<sup>20</sup></sup>&frasl;<sub>8.7x10<sup>5</sup></sub>+226<sup>2</sup>) <br />
<br />
'''s<sup>2</sup>'''=5.58 m<br />
<br />
'''s'''=2.36 m<br />
<br />
==Connectedness==<br />
<br />
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.<br />
<br />
[[File:rubberband.jpg|thumb|Rubber bands hold elastic potential energy]]<br />
<br />
==History==<br />
<br />
<br />
Elastic Potential Energy stemmed from the ideas of Robert Hooke, a 17th century British physicist who studied the relationship between forces applied to springs and elasticity. Hooke’s Law, which is a principle that states that the that the force needed to extend or compress a spring by a distance is proportional to that distance. <br />
<br />
== See also ==<br />
<br />
Spring potential energy is related to [[Hooke's Law]] and [[Potential Energy]].<br />
<br />
===Further reading===<br />
<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html<br />
<br />
===External links===<br />
<br />
[http://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy]<br />
<br />
==References==<br />
#http://www.universetoday.com/55027/hookes-law/<br />
#http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html<br />
#http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html<br />
#Chabay and Bruce A. Sherwood. Matter & Interactions. 4th ed.<br />
<br />
[[Category:Energy]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=19115Spring Potential Energy2015-12-06T03:32:35Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==Spring Potential Energy==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
'''<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
'''s<sup>2</sup>'''= <sup>m</sup>&frasl;<sub>k<sub>s</sub></sub>(<sup>2GM</sup>&frasl;<sub>R</sub> +v<sup>2</sup>)=s<sup>2</sup> = <sup>9</sup>&frasl;<sub>2.8x10<sup>5</sup></sub>(<sup>2G8.0x10<sup>20</sup></sup>&frasl;<sub>8.7x10<sup>5</sup></sub>+226<sup>2</sup>) <br />
<br />
'''s<sup>2</sup>'''=5.58 m<br />
<br />
'''s'''=2.36 m<br />
<br />
==Connectedness==<br />
<br />
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.<br />
<br />
==History==<br />
<br />
<br />
Elastic Potential Energy stemmed from the ideas of Robert Hooke, a 17th century British physicist who studied the relationship between forces applied to springs and elasticity. Hooke’s Law, which is a principle that states that the that the force needed to extend or compress a spring by a distance is proportional to that distance. <br />
<br />
== See also ==<br />
<br />
Spring potential energy is related to [[Hooke's Law]] and [[Potential Energy]].<br />
<br />
===Further reading===<br />
<br />
#http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html<br />
<br />
===External links===<br />
<br />
[http://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy]<br />
<br />
==References==<br />
#http://www.universetoday.com/55027/hookes-law/<br />
#http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html<br />
#http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html<br />
#Chabay and Bruce A. Sherwood. Matter & Interactions. 4th ed.<br />
<br />
[[Category:Energy]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18902Spring Potential Energy2015-12-06T03:15:26Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
'''<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
'''s<sup>2</sup>'''= <sup>m</sup>&frasl;<sub>k<sub>s</sub></sub>(<sup>2GM</sup>&frasl;<sub>R</sub> +v<sup>2</sup>)=s<sup>2</sup> = <sup>9</sup>&frasl;<sub>2.8x10<sup>5</sup></sub>(<sup>2G8.0x10<sup>20</sup></sup>&frasl;<sub>8.7x10<sup>5</sup></sub>+226<sup>2</sup>) <br />
<br />
'''s<sup>2</sup>'''=5.58 m<br />
<br />
'''s'''=2.36 m<br />
<br />
==Connectedness==<br />
<br />
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.<br />
<br />
==History==<br />
<br />
<br />
Elastic Potential Energy stemmed from the ideas of Robert Hooke, a 17th century British physicist who studied the relationship between forces applied to springs and elasticity. Hooke’s Law, which is a principle that states that the that the force needed to extend or compress a spring by a distance is proportional to that distance. <br />
<br />
== See also ==<br />
<br />
Spring potential energy is closely related to [[Hooke's Law]].<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
[http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html] Elastic Potential Energy]<br />
<br />
<br />
==References==<br />
#http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html<br />
#http://www.universetoday.com/55027/hookes-law/<br />
#http://www.scienceclarified.com/everyday/Real-Life-Physics-Vol-2/Oscillation-Real-life-applications.html<br />
#Chabay and Bruce A. Sherwood. Matter & Interactions. 4th ed.<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18512Spring Potential Energy2015-12-06T02:37:32Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
'''<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
'''s<sup>2</sup>'''= <sup>m</sup>&frasl;<sub>k<sub>s</sub></sub>(<sup>2GM</sup>&frasl;<sub>R</sub> +v<sup>2</sup>)=s<sup>2</sup> = <sup>9</sup>&frasl;<sub>2.8x10<sup>5</sup></sub>(<sup>2G8.0x10<sup>20</sup></sup>&frasl;<sub>8.7x10<sup>5</sup></sub>+226<sup>2</sup>) <br />
<br />
'''s<sup>2</sup>'''=5.58 m<br />
<br />
'''s'''=2.36 m<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18470Spring Potential Energy2015-12-06T02:32:22Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup> =<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
s<sup>2</sup> = <sup>m</sup>&frasl;<sub>k<sub>s</sub></sub>(<sup>2GM</sup>&frasl;<sub>R</sub> +v<sup>2</sup>)=s<sup>2</sup> = <sup>9</sup>&frasl;<sub>2.8x10<sup>5</sup></sub>(<sup>2G8.0x10<sup>20></sup></sup>&frasl;<sub>8.7x10<sup>5</sup></sub>+226<sup>2</sup>) <br />
s<sup>2</sup>=5.58 m<br />
s=2.36 m<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18390Spring Potential Energy2015-12-06T02:21:48Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R)</sub>=0<br />
<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup> =<sup>1</sup>&frasl;<sub>2</sub>mv<sub>esc</sub><sup2</sup> +(-G*<sup>Mm</sup>&frasl;<sub>R</sub>)<br />
<br />
s<sup>2</sup> = <sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub> +v<sup>2</sup> <br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18363Spring Potential Energy2015-12-06T02:17:56Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc</sub><sup>2</sup> + (-G*<sup>Mm</sup>&frasl;<sub>R</sub>=0<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2</sup> +(-G<sup>Mm</sup>&frasl;<sub>R</sub<br />
<br />
s<sup>2</sup> = <sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub> +v<sup>2</sup> <br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18349Spring Potential Energy2015-12-06T02:16:21Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub>=<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc</sub><sup>2</sup> + (-G<sup>Mm</sup>&frasl;<sub></sub>R</sub>=0<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2</sup> +(-G<sup>Mm</sup>&frasl;<sub>R</sub<br />
<br />
s<sup>2</sup> = <sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub> +v<sup>2</sup> <br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18335Spring Potential Energy2015-12-06T02:14:26Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sup> kg and radius 8.7x10<sup>5</sup> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sup> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub> =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2 +(-G<sup>Mm</sup>&frasl;<sub>(R</sub>=0<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2</sup> +(-G<sup>Mm</sup>&frasl;<sub>R</sub<br />
<br />
s<sup>2</sup> = <sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub> +v<sup>2</sup> <br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18285Spring Potential Energy2015-12-06T02:08:58Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20</sub> kg and radius 8.7x10<sup>5</sub> m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5</sub> N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i</sub>+U<sub>i</sub> =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2 +(-G<sup>Mm</sup>&frasl;<sub>(R</sub>=0<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>(2</sub>k<sub>ss<sup>2 =<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2 +(-G<sup>Mm</sup>&frasl;<sub>(R</sub<br />
<br />
s<sup>2</sub> = <sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub> +v<sup>2</sub> <br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18232Spring Potential Energy2015-12-06T02:03:25Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
<br />
where:<br />
<br />
'''k<sub>s</sub>'''= spring constant<br />
<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
'''k<sub>s'''= 200 N/m<br />
<br />
'''s'''= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
'''k<sub>s'''= 0.6 N/m<br />
<br />
'''s'''= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
A package of mass 9 kg sits on an airless asteroid with mass 8.0x10<sup>20 kg and radius 8.7x10<sup>5 m. Your goal is to launch the package so that it will never come back and when it is very far away it will have a speed of 226 m/s. You have a spring whose stiffness is 2.8x10<sup>5 N/m. How much must you compress the spring?<br />
<br />
The initial condition for escape from the asteroid is:<br />
<br />
K<sub>i+U<sub>i=<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2 +(-G<sup>Mm</sup>&frasl;<sub>(R</sub>=0<br />
<br />
Potential energy of the spring equals the total energy in the system.<br />
<br />
<sup>1</sup>&frasl;<sub>(2</sub>k<sub>ss<sup>2=<sup>1</sup>&frasl;<sub>(2</sub>mv<sub>esc<sup>2 +(-G<sup>Mm</sup>&frasl;<sub>(R</sub<br />
<br />
s<sup>2=<sup>m</sup>&frasl;<sub>(k<sub>s</sub>(<sup>2GM</sup>&frasl;<sub>(k<sub>R</sub>+v<sup>2<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=18026Spring Potential Energy2015-12-06T01:40:09Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
k<sub>s= 200 N/m<br />
s= 1.5 m<br />
<br />
'''U<sub>s'''=(0.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (0.5)(200 N/m)(1.5 m)<sup>2<br />
<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
A horizontal spring with stiffness 0.6 N/m has a relaxed length of 10 cm. A mass of 25 g is attached and you stretch the spring to a length of 20 cm. The mass is released and moves with little friction. What is the speed of the mass at the moment when the spring returns to its relaxed length of 10cm?<br />
<br />
k<sub>s= 0.6 N/m<br />
s= 0.1 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2<br />
<br />
'''U<sub>s'''= (.5)(0.6 N/m)(0.1 m)<sup>2<br />
<br />
'''U<sub>s'''= 0.003 J<br />
<br />
Potential Energy is Converted into Kinetic Energy (K):<br />
<br />
'''U<sub>s'''= K<br />
<br />
'''K'''=(0.5)mv<sup>2<br />
<br />
'''U<sub>s'''=(0.5)mv<sup>2<br />
<br />
0.003 J=(0.5)(0.025 kg)v<sup>2<br />
<br />
'''v<sup>2'''=<sup>(0.003 J)</sup>&frasl;<sub>((0.5)(0.025 kg)</sub><br />
<br />
'''v<sup>2'''=0.24 J/kg*s<br />
<br />
'''v'''=0.49 m/s<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13376Spring Potential Energy2015-12-05T04:19:29Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
If a spring's spring constant is 200 N/m and it is stretched 1.5 meters from rest, what is the potential spring energy?<br />
<br />
k<sub>s= 200 N/m<br />
s= 1.5 m<br />
<br />
'''U<sub>s'''=(.5)k<sub>ss<sup>2<br />
'''U<sub>'''s= (.5)(200 N/m)(1.5 m)<sup>2<br />
'''U<sub>s'''= 225 J<br />
<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13357Spring Potential Energy2015-12-05T04:11:39Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is:<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
<br />
[[File:spring.jpg|thumb|Spring Potential Energy]]<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13351Spring Potential Energy2015-12-05T04:07:56Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is [[File:spring.jpg]]<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=File:Spring.jpg&diff=13349File:Spring.jpg2015-12-05T04:05:38Z<p>Scarswell3: Scarswell3 uploaded a new version of &quot;File:Spring.jpg&quot;</p>
<hr />
<div></div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13344Spring Potential Energy2015-12-05T04:04:41Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Spring Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is [[File:[[File:.jpg]]]]<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13341Spring Potential Energy2015-12-05T04:03:25Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is [[File:]]<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13335Spring Potential Energy2015-12-05T03:59:01Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13316Spring Potential Energy2015-12-05T03:52:26Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is<br />
<br />
'''U<sub>s</sub>=<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup>'''<br />
where:<br />
'''k<sub>s</sub>'''= spring constant<br />
'''s<sup>2</sup>'''= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
An oscillating spring can be modeled by the following:<br />
from __future__ import division <br />
from visual import *<br />
from visual.graph import *<br />
scene.width=600<br />
scene.height = 760<br />
g = 9.8<br />
mball = .2<br />
Lo = 0.3 <br />
ks = 12 <br />
deltat = 1e-3<br />
t = 0 <br />
ceiling = box(pos=(0,0,0), size = (0.5, 0.01, 0.2))<br />
ball = sphere(pos=(0,-0.3,0), radius=0.025, color=color.yellow)<br />
spring = helix(pos=ceiling.pos, color=color.green, thickness=.005, coils=10, radius=0.01)<br />
spring.axis = ball.pos - ceiling.pos<br />
vball = vector(0.02,0,0)<br />
ball.p = mball*vball<br />
scene.autoscale = 0 <br />
scene.center = vector(0,-Lo,0) <br />
while t < 10: <br />
rate(1000) <br />
L_vector = (mag(ball.pos) - Lo)* ball.pos.norm()<br />
Fspring = -ks * L_vector<br />
Fgrav = vector(0,-mball * g,0)<br />
Fnet = Fspring + Fgrav<br />
ball.p = ball.p + Fnet * deltat<br />
ball.pos = ball.pos + (ball.p/mball) * deltat<br />
spring.axis = ball.pos-ceiling.pos <br />
t = t + deltat<br />
<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=File:Spring.jpg&diff=13240File:Spring.jpg2015-12-05T03:21:40Z<p>Scarswell3: </p>
<hr />
<div></div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13231Spring Potential Energy2015-12-05T03:19:05Z<p>Scarswell3: /* A Mathematical Model */</p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is<br />
<br />
U<sub>s</sub>=<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup><br />
where:<br />
k<sub>s</sub>= spring constant[[File:]]<br />
s<sup>2</sup>= stretch measured from the equilibrium point;<br />
<br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13224Spring Potential Energy2015-12-05T03:17:21Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is<br />
<br />
U<sub>s</sub>=<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup><br />
where:<br />
k<sub>s</sub>= spring constant[[File:Example.jpg]]<br />
s<sup>2</sup>= stretch measured from the equilibrium point;<br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=13181Spring Potential Energy2015-12-05T03:03:54Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
Elastic Potential Energy is the energy stored in elastic materials due to their deformation. Often this refers to the stretching or compressing of a spring.<br />
<br />
===A Mathematical Model===<br />
The formula for Ideal Spring Energy is<br />
<br />
U<sub>s</sub>=<br />
<sup>1</sup>&frasl;<sub>2</sub>k<sub>s</sub>s<sup>2</sup><br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Inelastic_Collisions&diff=1404Inelastic Collisions2015-11-25T21:05:36Z<p>Scarswell3: </p>
<hr />
<div>claimed by scarswell3</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=1403Main Page2015-11-25T21:04:26Z<p>Scarswell3: /* Collisions */</p>
<hr />
<div>__NOTOC__<br />
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br />
<br />
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#Pick a specific topic from intro physics<br />
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== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Categories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Interactions===<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
*[[Newton's Second Law of Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Theory===<br />
<div class="mw-collapsible-content"><br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[General Relativity]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Notable Scientists===<br />
<div class="mw-collapsible-content"><br />
*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Joseph Henry]]<br />
*[[Michael Faraday]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Marie Curie]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
*[[Oliver Heaviside]]<br />
*[[Rosalind Franklin]]<br />
*[[Erwin Schrödinger]]<br />
*[[Enrico Fermi]]<br />
*[[Robert J. Van de Graaff]]<br />
*[[Charles de Coulomb]]<br />
*[[Hans Christian Ørsted]]<br />
*[[Philo Farnsworth]]<br />
*[[Niels Bohr]]<br />
*[[Georg Ohm]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Properties of Matter===<br />
<div class="mw-collapsible-content"><br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Density]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Contact Interactions===<br />
<div class="mw-collapsible-content"><br />
* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[Vectors]]<br />
* [[Kinematics]]<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Curving Motion]]<br />
* [[Multi-particle Analysis of Momentum]]<br />
* [[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Angular Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[The Moments of Inertia]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
* [[Right Hand Rule]]<br />
* [[Angular Velocity]]<br />
* [[Predicting a Change in Rotation]]<br />
* [[Conservation of Angular Momentum]]<br />
*[[Total Angular Momentum]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Energy===<br />
<div class="mw-collapsible-content"><br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
*[[Spring Potential Energy]]<br />
*[[Internal Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Collisions===<br />
<div class="mw-collapsible-content"><br />
*[[Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Fields===<br />
<div class="mw-collapsible-content"><br />
* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Potential Difference of point charge in a non-Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
**[[Moving Point Charge]]<br />
**[[Non-Coulomb Electric Field]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Simple Circuits===<br />
<div class="mw-collapsible-content"><br />
*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
*[[Ohm's Law]]<br />
*[[RC]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
*[[Surface Charge Distributions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Maxwell's Equations===<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Faraday's Law]]<br />
**[[Inductance]]<br />
**[[Lenz's Law]]<br />
***[[Lenz Effect and the Jumping Ring]]<br />
*[[Ampere-Maxwell Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Radiation===<br />
<div class="mw-collapsible-content"><br />
*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
*[[Lenses]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Sound===<br />
<div class="mw-collapsible-content"><br />
*[[Doppler Effect]]<br />
</div><br />
</div><br />
*[[blahb]]<br />
</div><br />
</div><br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=983Spring Potential Energy2015-11-20T01:56:17Z<p>Scarswell3: </p>
<hr />
<div>Work in progress by scarswell3<br />
This topic covers Gravitational Potential Energy.<br />
<br />
==The Main Idea==<br />
<br />
State, in your own words, the main idea for this topic<br />
Electric Field of Capacitor<br />
<br />
===A Mathematical Model===<br />
<br />
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.<br />
<br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Which Category did you place this in?]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=982Spring Potential Energy2015-11-20T01:54:23Z<p>Scarswell3: </p>
<hr />
<div>This topic covers Gravitational Potential Energy.<br />
Contents<br />
<br />
1 The Main Idea<br />
1.1 A Mathematical Model<br />
1.2 A Computational Model<br />
2 Examples<br />
2.1 Simple<br />
2.2 Middling<br />
2.3 Difficult<br />
3 Connectedness<br />
4 History<br />
5 See also<br />
5.1 Further reading<br />
5.2 External links<br />
6 References<br />
<br />
The Main Idea<br />
<br />
State, in your own words, the main idea for this topic Electric Field of Capacitor<br />
A Mathematical Model<br />
<br />
What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net<br />
where p is the momentum of the system and F is the net force from the surroundings.<br />
A Computational Model<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript<br />
Examples<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
Simple<br />
Middling<br />
Difficult<br />
Connectedness<br />
<br />
How is this topic connected to something that you are interested in?<br />
How is it connected to your major?<br />
Is there an interesting industrial application?<br />
<br />
History<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
See also<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
Further reading<br />
<br />
Books, Articles or other print media on this topic<br />
External links<br />
<br />
Internet resources on this topic<br />
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<br />
This section contains the the references you used while writing this page</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Charged_Ring&diff=981Charged Ring2015-11-20T01:51:55Z<p>Scarswell3: </p>
<hr />
<div>Short Description of Topic<br />
<br />
==The Main Idea==<br />
<br />
State, in your own words, the main idea for this topic<br />
Electric Field of Capacitor<br />
<br />
===A Mathematical Model===<br />
<br />
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.<br />
<br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Electric Fields]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Spring_Potential_Energy&diff=980Spring Potential Energy2015-11-20T01:50:48Z<p>Scarswell3: Created page with "work in progress by scarswell3"</p>
<hr />
<div>work in progress by scarswell3</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=979Main Page2015-11-20T01:50:21Z<p>Scarswell3: /* Energy */</p>
<hr />
<div>__NOTOC__<br />
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br />
<br />
Looking to make a contribution?<br />
#Pick a specific topic from intro physics<br />
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.<br />
#Copy and paste the default [[Template]] into your new page and start editing.<br />
<br />
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
<br />
== Organizing Catagories ==<br />
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
===Interactions===<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Detecting Interactions]]<br />
*[[Fundamental Interactions]] <br />
*[[System & Surroundings]] <br />
*[[Newton's First Law of Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Theory===<br />
<div class="mw-collapsible-content"><br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Quantum Theory]]<br />
*[[General Relativity]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Notable Scientists===<br />
<div class="mw-collapsible-content"><br />
*[[Albert Einstein]]<br />
*[[Ernest Rutherford]]<br />
*[[Michael Faraday]]<br />
*[[James Maxwell]]<br />
*[[Robert Hooke]]<br />
*[[Marie Curie]]<br />
*[[Carl Friedrich Gauss]]<br />
*[[Nikola Tesla]]<br />
*[[Andre Marie Ampere]]<br />
*[[Sir Isaac Newton]]<br />
*[[J. Robert Oppenheimer]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Properties of Matter===<br />
<div class="mw-collapsible-content"><br />
*[[Mass]]<br />
*[[Charge]]<br />
*[[Spin]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Contact Interactions===<br />
<div class="mw-collapsible-content"><br />
* [[Young's Modulus]]<br />
* [[Friction]]<br />
* [[Tension]]<br />
* [[Hooke's Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[Vectors]]<br />
* [[Kinematics]]<br />
* Predicting Change in one dimension<br />
* [[Predicting Change in multiple dimensions]]<br />
* [[Momentum Principle]]<br />
* [[Curving Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Angular Momentum===<br />
<div class="mw-collapsible-content"><br />
* [[The Moments of Inertia]]<br />
* [[Rotation]]<br />
* [[Torque]]<br />
* [[Right Hand Rule]]<br />
* Predicting a Change in Rotation<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Energy===<br />
<div class="mw-collapsible-content"><br />
*[[Predicting Change]]<br />
*[[Rest Mass Energy]]<br />
*[[Kinetic Energy]]<br />
*[[Potential Energy]]<br />
*[[Work]]<br />
*[[Thermal Energy]]<br />
*[[Conservation of Energy]]<br />
*[[Electric Potential]]<br />
*[[Energy Transfer due to a Temperature Difference]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Point Particle Systems]]<br />
*[[Spring Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Collisions===<br />
<div class="mw-collapsible-content"><br />
*[[Collisions]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Fields===<br />
<div class="mw-collapsible-content"><br />
* [[Electric Field]] of a<br />
** [[Point Charge]]<br />
** [[Electric Dipole]]<br />
** [[Capacitor]]<br />
** [[Charged Rod]]<br />
** [[Charged Ring]]<br />
** [[Charged Disk]]<br />
** [[Charged Spherical Shell]]<br />
*[[Electric Potential]] <br />
**[[Potential Difference in a Uniform Field]]<br />
**[[Sign of Potential Difference]]<br />
*[[Electric Force]]<br />
*[[Polarization]]<br />
*[[Magnetic Field]]<br />
**[[Right-Hand Rule]]<br />
**[[Direction of Magnetic Field]]<br />
**[[Bar Magnet]]<br />
**[[Magnetic Force]]<br />
**[[Hall Effect]]<br />
**[[Lorentz Force]]<br />
**[[Biot-Savart Law]]<br />
**[[Integration Techniques for Magnetic Field]]<br />
**[[Sparks in Air]]<br />
**[[Motional Emf]]<br />
**[[Detecting a Magnetic Field]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Simple Circuits===<br />
<div class="mw-collapsible-content"><br />
*[[Components]]<br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
*[[Node Rule]]<br />
*[[Loop Rule]]<br />
*[[Power in a circuit]]<br />
*[[Ammeters,Voltmeters,Ohmmeters]]<br />
*[[Current]]<br />
*[[Ohm's Law]]<br />
*[[RC]]<br />
*[[Circular Loop of Wire]]<br />
*[[RL Circuit]]<br />
*[[LC Circuit]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Maxwell's Equations===<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
**[[Electric Fields]]<br />
**[[Magnetic Fields]]<br />
*[[Faraday's Law]]<br />
**[[Inductance]]<br />
*[[Ampere-Maxwell Law]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Radiation===<br />
<div class="mw-collapsible-content"><br />
*[[Producing a Radiative Electric Field]]<br />
*[[Sinusoidal Electromagnetic Radiaton]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
===Sound===<br />
<div class="mw-collapsible-content"><br />
*[[Doppler Effect]]<br />
</div><br />
</div><br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* An overview of [[VPython]]</div>Scarswell3http://www.physicsbook.gatech.edu/index.php?title=Charged_Ring&diff=978Charged Ring2015-11-20T01:45:05Z<p>Scarswell3: </p>
<hr />
<div>Short Description of Topic- claimed by scarswell3<br />
<br />
==The Main Idea==<br />
<br />
State, in your own words, the main idea for this topic<br />
Electric Field of Capacitor<br />
<br />
===A Mathematical Model===<br />
<br />
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.<br />
<br />
===A Computational Model===<br />
<br />
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]<br />
<br />
==Examples==<br />
<br />
Be sure to show all steps in your solution and include diagrams whenever possible<br />
<br />
===Simple===<br />
===Middling===<br />
===Difficult===<br />
<br />
==Connectedness==<br />
#How is this topic connected to something that you are interested in?<br />
#How is it connected to your major?<br />
#Is there an interesting industrial application?<br />
<br />
==History==<br />
<br />
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br />
<br />
== See also ==<br />
<br />
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br />
<br />
===Further reading===<br />
<br />
Books, Articles or other print media on this topic<br />
<br />
===External links===<br />
<br />
Internet resources on this topic<br />
<br />
==References==<br />
<br />
This section contains the the references you used while writing this page<br />
<br />
[[Category:Electric Fields]]</div>Scarswell3