- #1
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Many persons think that classical systems with varying mass obey the fundamental law:
[tex]\vec{F}=\frac{d\vec{P}}{dt}[/tex]
This is simply wrong!
Every classical system in which the mass is variable, is a GEOMETRIC system, meaning that it does not consist of the same material particles over time.
The opposite is called a MATERIAL system, in which the system does consist of the same material particles over time.
In the classical approximation, a material system DO obey F=dP/dt; however, at the same time, a classical, material system is characterized by CONSTANT MASS (this is in actuality wrong; due to relativistic mass increase).
So, what law does a geometric system obey?
The forces acting upon a set of material particles enclosed by a geometric control volume obeys:
[tex]\vec{F}=\frac{d\vec{P}}{dt}+\dot{\vec{M}}[/tex]
where [tex]\frac{d\vec{P}}{dt}[/tex] is the change of momentum enclosed by the control volume, and [tex]\dot{\vec{M}}[/tex] is the momentum flux out of the geometric control surface.
The interpretation of the momentum flux is quite simple:
Material particles may choose to leave (or enter) our chosen control volume, carrying their own momentum with them.
This is a mechanism for momentum change within the control volume which is not necessarily the result of some force acting upon the enclosed material!
Without including the momentum flux you will end up with wrong answers, except in a few lucky special cases.
[tex]\vec{F}=\frac{d\vec{P}}{dt}[/tex]
This is simply wrong!
Every classical system in which the mass is variable, is a GEOMETRIC system, meaning that it does not consist of the same material particles over time.
The opposite is called a MATERIAL system, in which the system does consist of the same material particles over time.
In the classical approximation, a material system DO obey F=dP/dt; however, at the same time, a classical, material system is characterized by CONSTANT MASS (this is in actuality wrong; due to relativistic mass increase).
So, what law does a geometric system obey?
The forces acting upon a set of material particles enclosed by a geometric control volume obeys:
[tex]\vec{F}=\frac{d\vec{P}}{dt}+\dot{\vec{M}}[/tex]
where [tex]\frac{d\vec{P}}{dt}[/tex] is the change of momentum enclosed by the control volume, and [tex]\dot{\vec{M}}[/tex] is the momentum flux out of the geometric control surface.
The interpretation of the momentum flux is quite simple:
Material particles may choose to leave (or enter) our chosen control volume, carrying their own momentum with them.
This is a mechanism for momentum change within the control volume which is not necessarily the result of some force acting upon the enclosed material!
Without including the momentum flux you will end up with wrong answers, except in a few lucky special cases.