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http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Jmorcos3 Physics Book - User contributions [en] 2026-04-24T12:06:40Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=738 Kinetic Energy 2015-11-13T21:24:36Z

<p>Jmorcos3: /* Connectedness */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can continuously be converted back and forth between potential and kinetic energy without loss. This is an excellent visualization of energy that can be demonstrated with vpython. The spring will oscillate up and down constantly converting between [[Elastic Potential Energy]] and Kinetic Energy. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is moving through space at constant velocity. It is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What is the proton's velocity?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><br /> <br /> ==Connectedness==<br /> Kinetic energy is very important is baseball. When a batter hits a ball, kinetic energy from the bat is transferred into the ball such that the ball flies out into the field. Assuming solid contact between the ball and the bat, the amount of kinetic energy transferred to the ball is directly proportional to the kinetic energy of the bat. As this is a non-relativistic application, there are only two variables to consider when calculating the kinetic energy of the bad: m and v. While a heaver bat would have greater kinetic energy than a bat of smaller mass traveling at the same velocity, heavier bats are more difficult to swing quickly and generally have lower velocity. Hence, batters must try to choose the a bat that they can swing very fast that still has reasonable mass to it to try to maximize kinetic energy (<math>\frac{1}{2}mv²</math>).<br /> <br /> ==History==<br /> <br /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=737 Kinetic Energy 2015-11-13T21:23:51Z

<p>Jmorcos3: /* Connectedness */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can continuously be converted back and forth between potential and kinetic energy without loss. This is an excellent visualization of energy that can be demonstrated with vpython. The spring will oscillate up and down constantly converting between [[Elastic Potential Energy]] and Kinetic Energy. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is moving through space at constant velocity. It is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What is the proton's velocity?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><br /> <br /> ==Connectedness==<br /> Kinetic energy is very important is baseball. When a batter hits a ball, kinetic energy from the bat is transferred into the ball such that the ball flies out into the field. Assuming solid contact between the ball and the bat, the amount of kinetic energy transferred to the ball is directly proportional to the kinetic energy of the bat. As this is a non-relativistic application, there are only two variables to consider when calculating the kinetic energy of the bad: m and v. While a heaver bat would have greater kinetic energy than a bat of smaller mass traveling at the same velocity, heavier bats are more difficult to swing quickly and generally have lower velocity. Hence, batters must try to choose the a bat that they can swing very fast that still has reasonable mass to it to try to maximize kinetic energy (<br /> <br /> ==History==<br /> <br /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=736 Kinetic Energy 2015-11-13T21:18:26Z

<p>Jmorcos3: /* Difficult */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can continuously be converted back and forth between potential and kinetic energy without loss. This is an excellent visualization of energy that can be demonstrated with vpython. The spring will oscillate up and down constantly converting between [[Elastic Potential Energy]] and Kinetic Energy. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is moving through space at constant velocity. It is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What is the proton's velocity?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=735 Kinetic Energy 2015-11-13T21:18:01Z

<p>Jmorcos3: /* Difficult */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can continuously be converted back and forth between potential and kinetic energy without loss. This is an excellent visualization of energy that can be demonstrated with vpython. The spring will oscillate up and down constantly converting between [[Elastic Potential Energy]] and Kinetic Energy. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is moving through space at constant velocity. It is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=734 Kinetic Energy 2015-11-13T21:16:04Z

<p>Jmorcos3: /* A Computational Model */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can continuously be converted back and forth between potential and kinetic energy without loss. This is an excellent visualization of energy that can be demonstrated with vpython. The spring will oscillate up and down constantly converting between [[Elastic Potential Energy]] and Kinetic Energy. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=733 Kinetic Energy 2015-11-13T21:14:57Z

<p>Jmorcos3: /* A Computational Model */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[Conservation of Energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=732 Kinetic Energy 2015-11-13T21:14:47Z

<p>Jmorcos3: /* A Mathematical Model */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> ===A Computational Model===<br /> By [[conservation of energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=731 Kinetic Energy 2015-11-13T21:13:59Z

<p>Jmorcos3: /* A Computational Model */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By [[conservation of energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> By [[conservation of energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=730 Kinetic Energy 2015-11-13T21:13:40Z

<p>Jmorcos3: /* A Mathematical Model */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By [[conservation of energy]], energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=729 Kinetic Energy 2015-11-13T21:11:22Z

<p>Jmorcos3: /* History */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, whom described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=728 Kinetic Energy 2015-11-13T21:10:17Z

<p>Jmorcos3: /* History */</p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, who described it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=727 Kinetic Energy 2015-11-13T21:09:41Z

<p>Jmorcos3: </p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> Kinetic energy can be traced all the way back to Aristotle who first proposed the concept of actuality and potentiality (actuality being kinetic energy and potentiality being [[Potential Energy]]). The connection between energy and mv² was first developed by Gottfried Leibniz and Johann Bernoulli, describing it as the "living force." William Gravesande tested this by dropping weights from different heights into a block of clay, discovering a proportionality between penetration depth and impact velocity squared. William Thomson is credited for devising the term "kinetic energy" in the mid 1800's.<br /> <br /> == See also ==<br /> <br /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=726 Kinetic Energy 2015-11-13T20:53:54Z

<p>Jmorcos3: </p> <hr /> <div>== Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=725 Kinetic Energy 2015-11-13T20:53:15Z

<p>Jmorcos3: /* See also */</p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9 <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br /> <br /> ==References==<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=724 Kinetic Energy 2015-11-13T20:53:01Z

<p>Jmorcos3: /* See also */</p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> [[Potential Energy]]<br> <br /> [[Rest Mass Energy]]<br> <br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br><br /> <br /> ==References==<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=723 Kinetic Energy 2015-11-13T20:51:24Z

<p>Jmorcos3: /* A Computational Model */</p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<br /> <br /> ===A Computational Model===<br /> <br /> https://trinket.io/glowscript/87a35d5778<br /> <br /> ==Examples==<br /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> [[Rest Mass Energy]]<br> <br /> [[Potential Energy]]<br> <br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> ==References==<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=722 Kinetic Energy 2015-11-13T20:43:17Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of Joules (J). KE is also given in units of kilo Joules (kJ). <math>1 kJ = 1000 J</math>. <math>1 J = 1 kg*(m²/s²)</math>. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv²</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<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 /> ===Simple===<br /> A ball is rolling along a frictionless surface at a constant <math>19 m/s</math>. The ball has mass <math>12 kg</math>. What is the kinetic energy of the ball in Joules?<br> <br /> <br>Solution:<br><br /> #Because the ball's velocity is far less than the speed of light, we can use the simplified kinetic energy formula.<br> <br /> #<math>KE=\frac{1}{2}mv²</math><br> <br /> #<math>KE=\frac{1}{2}(12 kg)*(19 m/s)²</math><br> <br /> #Hence, KE = <math>2166 J</math> or <math>2.166 kJ</math><br><br /> ===Middling===<br /> An electron is moving through space at a constant <math>2.9X10^8 m/s</math>. The electron has mass <math>9.1X10^-31 kg</math>. What is the kinetic energy of the ball in Joules?<br><br /> <br>Solution:<br><br /> #Because the electron's velocity is close to the speed of light, we must use the relativistic kinetic energy formula.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>KE=(9.1X10^-31 kg)(3X10^8 m/s)²(\frac{1}{\sqrt{1-\frac{(2.9X10^8 m/s)²}{(3X10^8 m/s)²}}} -1)</math><br><br /> #Hence, KE = <math>2.38X10^-13 J</math> or <math>2.38X10^-16 kJ</math><br><br /> ===Difficult===<br /> An proton is found to have kinetic energy <math>2.38X10^-15 J</math>. The proton has mass <math>1.67X10^-27 kg</math>. What velocity would the proton have to be moving at to have this kinetic energy?<br><br /> <br>Solution:<br><br /> #Because we are dealing with a subatomic particle, we should probably use the relativistic kinetic energy formula as the approximate kinetic energy formula may be very inaccurate if the particle is moving at a velocity near the speed of sound.<br> <br /> #<math>KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²}=(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math><br><br /> #<math>\frac{KE}{mc²} + 1=\frac{1}{\sqrt{1-\frac{v²}{c²}}}</math><br><br /> #<math>\frac{1}{\frac{KE}{mc²} + 1}=\sqrt{1-\frac{v²}{c²}}</math><br><br /> #<math>1-\frac{v²}{c²}=(\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>\frac{v²}{c²}=1 - (\frac{1}{\frac{KE}{mc²} + 1})²</math><br><br /> #<math>v²=c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)</math><br><br /> #<math>v=\sqrt{c²*(1 - (\frac{1}{\frac{KE}{mc²} + 1})²)}</math><br><br /> #<math>v=c*\sqrt{1 - (\frac{1}{\frac{KE}{mc²} + 1})²}</math><br><br /> #<math>v=3X10^8 m/s*\sqrt{1 - (\frac{1}{\frac{(2.38X10^-15 J)}{(1.67X10^-27 kg)(3X10^8 m/s)²} + 1})²}</math><br><br /> #v = <math>2.999X10^8 m/s</math>. This means that the proton is moving very close to the speed of light and hence our choice to use the relativistic kinetic energy equation was a good one.<br><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 /> [[Rest Mass Energy]]<br> <br /> [[Potential Energy]]<br> <br /> <br /> ===Further reading===<br /> <br /> Matter and Interactions By Ruth W. Chabay, Bruce A. Sherwood - Chapter 9<br> <br /> <br /> ===External links===<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> ==References==<br /> <br /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br> <br /> https://en.wikipedia.org/wiki/Kinetic_energy<br> <br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=166 Kinetic Energy 2015-10-20T07:10:12Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of kilo Joules (kJ). Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model|A Computational Model]] for this demo.<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 /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=165 Kinetic Energy 2015-10-20T07:08:36Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of kilo Joules (kJ). Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> By conservation of energy, energy can be converted but it cannot be created nor destroyed. Hence, in an isolated system, energy can be converted back and forth between potential and kinetic energy continuously without loss. This is an excellent visualization of energy that can be demonstrated with vpython. See [[#A Computational Model]] for this demo.<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 /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=164 Kinetic Energy 2015-10-20T07:03:18Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of kilo Joules (kJ). Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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 /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=163 Kinetic Energy 2015-10-20T06:59:25Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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 /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Energy]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=162 Kinetic Energy 2015-10-20T06:59:08Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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 /> http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy<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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=161 Kinetic Energy 2015-10-20T06:57:09Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules. Other types of energy include [[Rest Mass Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=160 Kinetic Energy 2015-10-20T06:56:34Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules. Other types of energy include [[Rest Energy]] and [[Potential Energy]].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=159 Kinetic Energy 2015-10-20T06:55:52Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules. Other types of energy include [Rest Energy] and [Potential Energy].<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=158 Kinetic Energy 2015-10-20T06:54:56Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy. --A WORK IN PROGRESS BY JASON MORCOS--<br /> <br /> == Kinetic Energy==<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules.<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=157 Kinetic Energy 2015-10-20T06:52:43Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> --A WORK IN PROGRESS BY JASON MORCOS--<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules.<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (<math>3X10^8 m/s</math>), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=156 Kinetic Energy 2015-10-20T06:51:29Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> --A WORK IN PROGRESS BY JASON MORCOS--<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules.<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{\sqrt{1-\frac{v²}{c²}}} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (3e8 m/s), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=113 Kinetic Energy 2015-10-19T15:56:56Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> --A WORK IN PROGRESS BY JASON MORCOS--<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules.<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{sqrt(1-\frac{v²}{c²})} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (3e8 m/s), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=112 Kinetic Energy 2015-10-19T14:56:40Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> --A WORK IN PROGRESS BY JASON MORCOS--<br /> Objects in motion have energy associated with them. This energy of motion is called kinetic energy. Kinetic energy, often abbreviated as KE, is usually given in the standard S.I. units of (kilo) Joules.<br /> <br /> ===A Mathematical Model===<br /> The relativistic equation for kinetic energy according to Einstein's Theory of Relativity is <math> KE=mc²(\frac{1}{sqrt(1-\frac{v²}{c²})} -1)</math>. However, for cases where an object's velocity is far less than the speed of light (3e8 m/s), one can use the simplified kinetic energy formula: <math>KE=\frac{1}{2}mv^2</math>. In most cases the simplified kinetic energy formula gives a result with only minimal error. However, for near light speed calculations, such as those involving subatomic particles such as electrons, protons, or photons, the relativistic equation must be used. Usually we think of the simplified kinetic energy formula as the way to calculate the kinetic energy of an average object.<br /> <br /> <br> <br /> <br /> h<br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=109 Kinetic Energy 2015-10-19T14:36:11Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> --A WORK IN PROGRESS BY JASON MORCOS--<br /> Energy is based in whole on Einstein's principle of E=MC^2. At its base it is the concept of how objects interact with their surroundings, their natural energy, or rest energy, the energy that they create when in motion(Kinetic energy) and how energy can change given different interactions which are based on einsteins principle. <br /> <br /> ===A Mathematical Model===<br /> There are <math>E=lambdamc^2</math> and <br /> <math> E=mc^2</math> which reprsents the rest energy. taken together the kinetic energy becomes the overall energy- rest energy. Due to the complexity of this equation, it maybe easier to use the equation <math> 1/2mv^2</math> if the object is not traveling near the speed of light. This equation is applicable to everyday object that we see and more applicable for the "average" situation. <br /> <br> <br /> <br /> h<br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=108 Kinetic Energy 2015-10-19T14:35:52Z

<p>Jmorcos3: </p> <hr /> <div>The energy of motion is kinetic energy.<br /> <br /> == Kinetic Energy==<br /> <br /> Energy is based in whole on Einstein's principle of E=MC^2. At its base it is the concept of how objects interact with their surroundings, their natural energy, or rest energy, the energy that they create when in motion(Kinetic energy) and how energy can change given different interactions which are based on einsteins principle. <br /> <br /> ===A Mathematical Model===<br /> There are <math>E=lambdamc^2</math> and <br /> <math> E=mc^2</math> which reprsents the rest energy. taken together the kinetic energy becomes the overall energy- rest energy. Due to the complexity of this equation, it maybe easier to use the equation <math> 1/2mv^2</math> if the object is not traveling near the speed of light. This equation is applicable to everyday object that we see and more applicable for the "average" situation. <br /> <br> <br /> <br /> h<br /> <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>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=107 Main Page 2015-10-19T14:34:55Z

<p>Jmorcos3: /* 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 /> *Fundamental Interactions<br /> '''Fundamental interactions''', are the most basic interactions in physical systems.<br /> There are four conventionally accepted fundamental interactions: '''Gravitational, Electromagnetic, Strong force, and Weak force.'''<br /> <br /> The '''Garvitational Interaction''' is the ''Interaction'' that a planet or some other large body that has it's own gravitational field can exert<br /> on the System from the Surroundings. The '''Gravitational Interaction''' from the Earth onto an object that is within Earth's gravitational field<br /> is 9.81 meters per second squared (m/s^2).<br /> <br /> The '''Electromagnetic Interaction''' is the ''Interaction'' that charged particles can exert on the System from the Surroundings. Here we use<br /> '''Coulomb's Constant''' (8.98*10^9 n/m^2 (newtons*meters squared)) to describe the ''Interaction'' between electrically charged particles.<br /> <br /> The '''Strong Force''' is the ''Interaction'' between subatomic particles of matter. The strong force binds quarks together in clusters to<br /> make more-familiar subatomic particles, such as protons and neutrons. It also holds together the atomic nucleus.<br /> <br /> The '''Weak force''' is the ''Interaction'' that governs the decay of unstable subatomic particles such as mesons. It also initiates the <br /> nuclear fusion reaction that fuels the Sun.<br /> <br /> *System & Surroundings. <br /> A '''System''' is a part of the universe that we choose to study. The '''Surroundings''' are everything else that ''surrounds'' the '''System'''.<br /> <br /> For further refrence, see: ''Thinking about Physics Thinking'' by Professor Michael Schatz[https://youtu.be/lr_89uaChps?t=1m4s]<br /> <br /> I don't know how grading this works, so I'll just leave my signature with timestamp here. --[[User:Austinrocket|Austinrocket]] ([[User talk:Austinrocket|talk]]) 23:17, 18 October 2015 (EDT)<br /> </div><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 /> </div><br /> </div><br /> <br /> <div class="toccolours mw-collapsible mw-collapsed"><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 /> </div><br /> </div><br /> <br /> <div class="toccolours mw-collapsible mw-collapsed"><br /> ===Angular Momentum===<br /> <div class="mw-collapsible-content"><br /> * The Moments of Inertia<br /> * Rotation<br /> * Torque<br /> * Predicting a Change in Rotation<br /> </div><br /> </div><br /> <br /> <div class="toccolours mw-collapsible mw-collapsed"><br /> ===Energy===<br /> <div class="mw-collapsible-content"><br /> *Predicting Change<br /> *[[Rest Mass Energy]]<br /> *[[Kinetic Energy]]<br /> *Potential Energy<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 /> ** [[Charged Rod]]<br /> ** [[Charged Loop]]<br /> ** [[Charged Spherical Shell]]<br /> *Magnetic<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 /> </div><br /> </div><br /> <br /> <div class="toccolours mw-collapsible mw-collapsed"><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 /> *Ampere-Maxwell Law<br /> </div><br /> </div><br /> <br /> <div class="toccolours mw-collapsible mw-collapsed"><br /> ===Radiation===<br /> <div class="mw-collapsible-content"><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]]</div>

Jmorcos3 http://www.physicsbook.gatech.edu/index.php?title=Kinetic_Energy&diff=106 Kinetic Energy 2015-10-19T14:33:49Z

<p>Jmorcos3: Created page with "Energy is based in whole on Einstein's principle of E=MC^2. At its base it is the concept of how objects interact with their surroundings, their natural energy, or rest energy..."</p> <hr /> <div>Energy is based in whole on Einstein's principle of E=MC^2. At its base it is the concept of how objects interact with their surroundings, their natural energy, or rest energy, the energy that they create when in motion(Kinetic energy) and how energy can change given different interactions which are based on einsteins principle.<br /> <br /> A Mathematical Model[edit]<br /> There are E=lambdamc2 and E=mc2 which reprsents the rest energy. taken together the kinetic energy becomes the overall energy- rest energy. Due to the complexity of this equation, it maybe easier to use the equation 1/2mv2 if the object is not traveling near the speed of light. This equation is applicable to everyday object that we see and more applicable for the "average" situation. <br /> h<br /> <br /> <br /> What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.<br /> <br /> A Computational Model[edit]<br /> How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript<br /> <br /> Examples[edit]<br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> Simple[edit]<br /> Middling[edit]<br /> Difficult[edit]<br /> Connectedness[edit]<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 /> History[edit]<br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> See also[edit]<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[edit]<br /> Books, Articles or other print media on this topic<br /> <br /> External links[edit]<br /> Internet resources on this topic<br /> <br /> References[edit]<br /> This section contains the the references you used while writing this page</div>

Jmorcos3