We know that Newton's second law tells us $F=ma+v\frac{dm}{dt}$ so, if a body has a constant velocity but a changing mass, then the equation tells us that the net force acting on the body is $F=v\frac{dm}{dt}$. But then, according to Newton's first law, the net force on the body is 0, since it is unaccelerated. So aren't they both contradicting each other?
Asked
Active
Viewed 69 times
2 Answers
0
Whatever mass is being lost needs to be considered in the system.
If the mass that's being lost is moving at the same speed, then the remaining mass must exert a force on it to accelerate it to that speed. The net force on the remaining mass will be zero if you do the calculations.
Señor O
- 7,882
0
In classical mechanics, the total mass of a closed system is conserved (constant). So necessarily $\frac{dm}{dt} = 0$, and the laws hold. In the case of a rocket, however, we might ignore the mass that is ejected. Then, the rocket would appear to an observer to be losing mass, but the system is no longer closed. In short, either the mass being lost must be accounted for (net force is zero), or there must be a corresponding change in the velocity of the body of interest (conservation of momentum). Note that without further assumptions these are your only two options because Newton's laws are axioms of the theory.
