- #1
mcastillo356
Gold Member
- 560
- 267
Hello, my name is Marcos, I have a bachelor in advertising and public relations, and my hobby is maths and physics
The equation of variable-mass motion is written as ##\mathbf{F}_{ext}+\mathbf{v}_{rel}\dfrac{dm}{dt}=m\dfrac{d\mathbf{v}}{dt}##
There are different derivations for the equation:
Mass accretion:
Mass ablation/ejection:
The initial momentum of the system is ##\mathbf{p}_1=m\mathbf{v}##. Since the mainbody will be losing mass, ##dm## will be negative. At a time ##t+dt## the momentum is ##\mathbf{p}_2=(m+dm)(\mathbf{v}+d\mathbf{v})+\mathbf{u}(-dm)##. Why in the same equation ##dm## is first positive and at the end negative?.
Full text at https://en.wikipedia.org/wiki/Variable-mass_system
Thanks!
The equation of variable-mass motion is written as ##\mathbf{F}_{ext}+\mathbf{v}_{rel}\dfrac{dm}{dt}=m\dfrac{d\mathbf{v}}{dt}##
There are different derivations for the equation:
Mass accretion:
Mass ablation/ejection:
The initial momentum of the system is ##\mathbf{p}_1=m\mathbf{v}##. Since the mainbody will be losing mass, ##dm## will be negative. At a time ##t+dt## the momentum is ##\mathbf{p}_2=(m+dm)(\mathbf{v}+d\mathbf{v})+\mathbf{u}(-dm)##. Why in the same equation ##dm## is first positive and at the end negative?.
Full text at https://en.wikipedia.org/wiki/Variable-mass_system
Thanks!