Question

What do we do with F=ma when the mass, m, is actually a moving fluid (i.e. air)? Hint: This is used to derive the fundamental equation for Thrust.

Answer 1

from Newton's second law

F=ma

F=dP/dt

F=Pf-Pi/dt

considering both the parts of masses $\bigtriangleup$ M ans M- $\bigtriangleup$ M as forming one and the same system we can write

F=Pf-Pi/dt={(M+ $\bigtriangleup$ M)(V+ $\bigtriangleup$ V)+ $\bigtriangleup$ Mu}-[Mu]/dt

where pf and pi are the final and initial momentum of the system respectively

F=M $\bigtriangleup$ v/ $\bigtriangleup$ t-V $\bigtriangleup$ M/ $\bigtriangleup$ t- $\bigtriangleup$ V * $\bigtriangleup$ M/ $\bigtriangleup$ t+u * $\bigtriangleup$ M/ $\bigtriangleup$ t

here we observed

$\bigtriangleup$ V* $\bigtriangleup$ M/ $\bigtriangleup$ t is not possible

$\bigtriangleup$ M/ $\bigtriangleup$ t=-dM/dt

M* $\bigtriangleup$ V/ $\bigtriangleup$ t=0

the force F=Mdv/dt+v dM/dt-udM/dt

=0+vdM/dt-u dM.dt

the thrust force =dM/dt(V-u)