Detecting Interactions: Difference between revisions
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Since a change in velocity also indicates a change in momentum, we can apply the Momentum Principle to this situation as shown here: | Since a change in velocity also indicates a change in momentum, we can apply the Momentum Principle to this situation as shown here: | ||
'''No Net Interaction''' | '''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''' | '''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. | <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. | ||
Revision as of 22:20, 17 April 2016
Claimed by Yahia Ali (Spring 2016)
Claimed by Kristen Sparks
The Main Idea
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.
A 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 shown 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.
A Computational Model
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.
Examples
Simple
Middling
Difficult
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
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading
External links
Internet resources on this topic
References
Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. 4th ed. Wiley. ISBN: 978-1118875865