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| This page discusses the Momentum Principle and examples of how it is used. | | This page was redundant and has been removed. Its information has been incorporated into the pages below: |
| | | *[[Linear Momentum]] |
| Claimed by hyk96610
| | *[[Newton's Second Law: the Momentum Principle]] |
| | | *[[Impulse and Momentum]] |
| ==The Main Idea==
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| The Momentum Principle is the first fundamental principle of mechanics where it describes the relationship between the change in momentum of a system and the total amount of interaction (or total amount of force) with the surroundings. In terms of the system and surroundings, both can be set in any way necessary, where the system may just include a person or the entire Earth. The Momentum Principle can be used in nearly all situations, and it is always advised to start a problem by first writing out the Momentum Principle and then branching out (by rearranging or substituting values) in order to solve a problem.
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| ===A Mathematical Model===
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| The Momentum Principle is defined as <math>{\frac{d\vec{p}}{dt}}_{system}= \vec{F}_{net}</math> (or <math>∆\vec{p} = \vec{F}_{net} * {∆t}</math>).
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| '''p''' is the momentum of the system. In the equation, momentum is expressed as the "change in momentum" (<math>∆\vec{p} = \vec{p}_{final} - \vec{p}_{initial}</math>), which includes both the magnitude and direction of the momentum.
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| '''F''' is the net force from the surroundings. Force (measured in Newtons, or N) includes the interactions between system and the surroundings, like the gravitational force exerted by the Earth on us or the force that a compressed spring exerts on a mass. In the Momentum Principle, the force includes both the magnitude and direction. Also, it is important to note that the Momentum Principle calls for the ''net'' force, which is the sum of all the different forces from the surroundings, like adding both the force of gravity and the force of the spring together to calculate the net force. Because of this, it is even more crucial to pay attention to the direction of the forces as a positive or negative sign error could cause an error in the calculated net force.
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| '''t''' is the time. Specifically, the Momentum Principle calls for the "change in time" (<math>∆\vec{t} = \vec{t}_{final} - \vec{t}_{initial}</math>), or in other words, the duration of the interaction is needed.
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| ===A Computational Model===
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| 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]
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| ==Examples==
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| Be sure to show all steps in your solution and include diagrams whenever possible
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| ===Simple===
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| Two external forces <40,-70,0>N and <20,10,0>N, act on a system. What is the net force acting on the system?
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| '''Answer: <60,-60,0>N'''
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| <math>\vec{F}_{net} = \vec{F}_{1} + \vec{F}_{2}</math>
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| <math>\vec{F}_{net}</math> = <40,-70,0)N + <20,10,0>N = <60,-60,0>N
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| ===Middling===
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| A hockey puck is sliding along the ice with nearly constant momentum <10,0,5>kg*m/s when it is suddenly struck by a hockey stick with a force <0,0,2000>N that lasts for only 3 milliseconds (3e-3s). What is the new (vector) momentum of the puck?
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| '''Answer: <10,0,11>kg*m/s'''
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| '''Explanation:'''
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| <math>∆\vec{p} = \vec{F}_{net} * {∆t}</math>
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| <math>\vec{p}_{final} - \vec{p}_{initial}</math> = \vec{F}_{net} * {∆t}</math>
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| <math>\vec{p}_{final}</math> - <10,0,5>kg*m/s = <0,0,2000>N * (3e-3)s
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| <math>\vec{p}_{final}</math> = <10,0,11>kg*m/s
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| ===Difficult===
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| ==Connectedness==
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| #How is this topic connected to something that you are interested in?
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| #How is it connected to your major?
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| #Is there an interesting industrial application?
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| ==History==
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| Although the Momentum Principle is credited as Newton’s second law of motion, it is difficult to just credit Isaac Newton (1643AD – 1727AD) for the development of the principle. As the Momentum Principle is the quantitative and more in-depth representation of Newton’s first law of motion (“An object tends to be at rest or moves in a straight line and a constant speed except to the extent that it interact with other objects”), the development of the first law also serves an important role in the history of the Momentum Principle. Aristotle (384BC – 322BC) initially proposed that objects had the natural tendency to be at rest and that a push (or a force) was absolutely needed to keep the object moving. His proposal was challenged by Galileo (1564AD – 1642AD), who introduced the idea that objects had the natural tendency to travel in a straight line at constant speed unless something (or a force) was interacting with something. Likewise, Descartes (1596AD – 1650AD) also contributed as he proposed three laws of nature in his “Principle of Philosophy,” which actually outlined the later published Newton’s first law of motion. After studying Descartes, Newton adopted Descartes’ principles as his first law of motion, and alongside the famous story of Newton sitting under an apple, Newton was able to create the Momentum Principle, or his second law of motion.
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| == See also ==
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| As the Momentum Principle is the first of three fundamental principles of mechanics, the next possible topics to examine would be the other fundamental principles, the [http://www.physicsbook.gatech.edu/The_Energy_Principle Energy Principle] and the [http://www.physicsbook.gatech.edu/The_Angular_Momentum_Principle Angular Momentum Principle]. Also, although the momentum principle is an extremely important concept that usually signals the start of a momentum related problem, the principle branches out into other momentum topics like [http://www.physicsbook.gatech.edu/Impulse_Momentum Impulse] and [http://www.physicsbook.gatech.edu/Iterative_Prediction Iterative Prediction], which are used to solve other types of problems.
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| ===Further reading===
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| Books, Articles or other print media on this topic
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| ===External links===
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| [1] https://www.khanacademy.org/science/physics/linear-momentum/momentum-tutorial/v/introduction-to-momentum | |
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| [2] https://www.youtube.com/watch?v=ZvPrn3aBQG8 | |
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| ==References==
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| [1] http://science.howstuffworks.com/innovation/scientific-experiments/newton-law-of-motion2.htm
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| [2] Matters & Interactions: Modern Mechanics 4th Ed. Vol. 1 (Chabay & Sherwood)
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| [3] Dr. Flavio Fenton's Lecture Notes on the Momentum Principle (8/26/15)
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| [[Category:Momentum]] | |