- #1
Soren4
- 128
- 2
I do not get why systems such as the rocket in space are defined as "variable mass" since the mass of the system is not varying.
The equation used for such systems $$\sum F^{(E)}=\frac{d\vec{P}}{dt} \tag{1}$$ (sum of external forces on the system equals the change in momentum) holds true only if the total mass of the system does not change during the time interval [itex]dt[/itex] considered. Is this correct? I'm not sure of what I'm saying, only supposing it, because in the proof for [itex](1)[/itex] on textbook the center of mass is used and the mass of the system is taken as constant in the derivatives.
In rocket motion for istance we consider a time interval [itex]dt[/itex] in which the mass of the rocket(with the gas inside of it) decreases of a quantity d[itex]m[/itex], but that mass of gas [itex]dm[/itex] is still in the system (rocket+ mass [itex]dm[/itex] of gas), even if it is not in the rocket anymore. In fact, writing the momentum of the system we do include the mass [itex]dm[/itex].
$$P(t)=mv$$
$$P(t+dt)=(m-dm)(v+dv)+dm(v-u)$$
(Where [itex]u[/itex] is the relative velocity of the gas)
Does the total mass of the system really increase or decrease and [itex](1)[/itex] holds true also if the total mass of the system is varying?
The equation used for such systems $$\sum F^{(E)}=\frac{d\vec{P}}{dt} \tag{1}$$ (sum of external forces on the system equals the change in momentum) holds true only if the total mass of the system does not change during the time interval [itex]dt[/itex] considered. Is this correct? I'm not sure of what I'm saying, only supposing it, because in the proof for [itex](1)[/itex] on textbook the center of mass is used and the mass of the system is taken as constant in the derivatives.
In rocket motion for istance we consider a time interval [itex]dt[/itex] in which the mass of the rocket(with the gas inside of it) decreases of a quantity d[itex]m[/itex], but that mass of gas [itex]dm[/itex] is still in the system (rocket+ mass [itex]dm[/itex] of gas), even if it is not in the rocket anymore. In fact, writing the momentum of the system we do include the mass [itex]dm[/itex].
$$P(t)=mv$$
$$P(t+dt)=(m-dm)(v+dv)+dm(v-u)$$
(Where [itex]u[/itex] is the relative velocity of the gas)
Does the total mass of the system really increase or decrease and [itex](1)[/itex] holds true also if the total mass of the system is varying?