Detecting Interactions: Difference between revisions
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Claimed by Kristen Sparks | Claimed by Kristen Sparks | ||
== | ==Detecting Interactions== | ||
Detecting whether an interaction has taken place is a simple, yet fundamental, skill necessary to the analysis of any physics problem. The importance of this skill will especially be seen when working with problems that call for the identification of multiple forces acting on a system. | Detecting whether an interaction has taken place is a simple, yet fundamental, skill necessary to the analysis of any physics problem. The importance of this skill will especially be seen when working with problems that call for the identification of multiple forces acting on a system. | ||
=== | ===Mathematical Model=== | ||
There are two main conditions that, if observed, would allow one to conclude that an interaction has taken place: change in direction or change in speed. Since velocity consists of both speed and direction, an observed change in velocity would indicate the existence of an interaction. | There are two main conditions that, if observed, would allow one to conclude that an interaction has taken place: change in direction or change in speed. Since velocity consists of both speed and direction, an observed change in velocity would indicate the existence of an interaction. | ||
Since a change in velocity also indicates a change in momentum, we can apply the Momentum Principle to this situation as demonstrated here: | |||
'''No Net Interaction''' | |||
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} = 0</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} = 0</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | ||
=== | '''Nonzero Net Interaction''' | ||
<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} ≠ 0</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | |||
===Application in VPython=== | |||
Detection an interaction is often the first step to trying to troubleshoot VPython code. If you're trying to model a net force acting on an object, but you do not see that object changing in speed or direction, then there is likely an issue with your force equations, momentum update, or position update. | Detection an interaction is often the first step to trying to troubleshoot VPython code. If you're trying to model a net force acting on an object, but you do not see that object changing in speed or direction, then there is likely an issue with your force equations, momentum update, or position update. Instead of qualitatively looking for such an interaction, one can also add a "print" command within a "while" loop to check for changes in velocity or momentum. This will, however, slow down the code, so make sure to delete the print command from the while loop when finished troubleshooting. | ||
==Examples== | ==Examples== | ||
=== | ===Change in direction=== | ||
=== | [[File:Change_of_direction.jpg]] | ||
=== | ===Change in speed=== | ||
[[File:Change_of_speed.jpg]] | |||
===Uniform motion (no net interaction)=== | |||
[[File:Uniform_motion.jpg]] | |||
==History== | ==History== | ||
| Line 29: | Line 39: | ||
== See also == | == See also == | ||
Speed and Velocity [http://www.physicsbook.gatech.edu/Speed_and_Velocity] | |||
Momentum Principle [http://www.physicsbook.gatech.edu/Momentum_Principle] | |||
VPython Animation [http://www.physicsbook.gatech.edu/VPython_Animation] (for those having trouble modeling interactions in VPython) | |||
===External links=== | ===External links=== | ||
Newton's laws of motion (Wikipedia) [https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion] | |||
==References== | ==References== | ||
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Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Wiley. ISBN: 978-1118875865 | Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Wiley. ISBN: 978-1118875865 | ||
[[Category: | [[Category: Interactions]] | ||
Latest revision as of 22:57, 17 April 2016
Claimed by Yahia Ali (Spring 2016)
Claimed by Kristen Sparks
Detecting Interactions
Detecting whether an interaction has taken place is a simple, yet fundamental, skill necessary to the analysis of any physics problem. The importance of this skill will especially be seen when working with problems that call for the identification of multiple forces acting on a system.
Mathematical Model
There are two main conditions that, if observed, would allow one to conclude that an interaction has taken place: change in direction or change in speed. Since velocity consists of both speed and direction, an observed change in velocity would indicate the existence of an interaction.
Since a change in velocity also indicates a change in momentum, we can apply the Momentum Principle to this situation as demonstrated here:
No Net Interaction
[math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} = 0 }[/math] where p is the momentum of the system and F is the net force from the surroundings.
Nonzero Net Interaction
[math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} ≠ 0 }[/math] where p is the momentum of the system and F is the net force from the surroundings.
Application in VPython
Detection an interaction is often the first step to trying to troubleshoot VPython code. If you're trying to model a net force acting on an object, but you do not see that object changing in speed or direction, then there is likely an issue with your force equations, momentum update, or position update. Instead of qualitatively looking for such an interaction, one can also add a "print" command within a "while" loop to check for changes in velocity or momentum. This will, however, slow down the code, so make sure to delete the print command from the while loop when finished troubleshooting.
Examples
Change in direction
Change in speed
Uniform motion (no net interaction)
History
Isaac Newton summarized the relationship between a change in velocity and the presence of an interaction in his First Law of Motion, which says that, when viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
See also
Speed and Velocity [1] Momentum Principle [2] VPython Animation [3] (for those having trouble modeling interactions in VPython)
External links
Newton's laws of motion (Wikipedia) [4]
References
Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Wiley. ISBN: 978-1118875865