frameworks:newtonian_formalism
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frameworks:newtonian_formalism [2018/03/27 07:25] jakobadmin [Concrete] |
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| - | ====== Newtonian Formalism ====== | ||
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| - | <tabbox Intuitive> | ||
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| - | The Newtonian formalism is a framework that allows us to predict how a system will evolve. | ||
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| - | The basis of it is summarized by three laws, commonly called "Newton's laws of motion": | ||
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| - | * **First law:** No force is needed to keep an object moving. If an object is at rest, it will remain at rest unless a force acts on it. Similarly, if an object moves with some constant velocity, it will keep moving unless a force acts on it. | ||
| - | * **[[equations:newtons_second_law|Second law]]:** The way the movement of an object changes depends only on two things: its mass and the total force acting on it. | ||
| - | * **Third law:** Whenever an object exerts a force on another object, inevitably this second object will also exert a force of equal magnitude on the first object. | ||
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| - | <tabbox Concrete> | ||
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| - | **First law:** | ||
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| - | If the forces acting on an object are balanced, i.e. the total force is zero $F=0$, the velocity of the object will remain constant: $v=\text{const}$. | ||
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| - | <diagram> | ||
| - | ||||| AA|| |AA=Forces are balanced $ \vec F=0$ | ||
| - | ||||||!@4||||||| | ||
| - | |||||BB||||||BB=$ \vec a=0$ | ||
| - | ||||,@4| -|^|- |.@4 | | | | | ||
| - | ||| AA||BB |AA=Object at rest: $\vec v=0$|BB=Object in motion $ \vec v\neq 0$ | ||
| - | ||||!@4||||!@4||| | ||
| - | ||| AA||BB |AA=Object stays at rest: $\vec v=0$|BB=Object remains in motion $ \vec v \neq 0$; same $ \vec v$. | ||
| - | </diagram> | ||
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| - | **Second law:** | ||
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| - | $$ \vec F = m \vec a$$ | ||
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| - | <diagram> | ||
| - | ||||| AA|| |AA=Forces are unbalanced $ \vec F\neq 0$ | ||
| - | ||||||!@4||||||| | ||
| - | |||||BB||||||BB=$ \vec a \neq 0$ | ||
| - | ||||,@4| -|^|- |.@4 | | | | | ||
| - | ||| AA||BB |AA=acceleration $\vec a$ depends directly on the net-force $\vec F$ that acts on the object|BB=acceleration $\vec a$ depends inversly on the mass $m$ of the object | ||
| - | </diagram> | ||
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| - | <tabbox Abstract> | ||
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| - | <note tip> | ||
| - | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| - | </note> | ||
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| - | <tabbox Why is it interesting?> | ||
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| - | The Newtonian formalism is still one of the most popular ways to describe what happens in a physical system. In contrast to the [[:frameworks|alternatives]] it is much easier to understand what is going on, since only concepts that are directly familiar to high-school students are used. | ||
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| - | </tabbox> | ||
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frameworks/newtonian_formalism.1522128317.txt.gz · Last modified: 2018/03/27 05:25 (external edit)
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