91Ó°ÊÓ

An internal force is aforce exerted by one part of a system on another.

An external force is a force exerted on any part ofa system by something outside the system.

If thenet external force on a system is zero, the totalmomentum of the system$\stackrel{\mathbf{→}}{\mathbf{P}}$ (the vector sum of themomenta of the individual particles that make upthe system) is constant or conserved. Each componentof total momentum is separately conserved.

$\stackrel{\mathbf{→}}{\mathbf{P}}\mathbf{=}\stackrel{\mathbf{→}}{{\mathbf{P}}_{\mathbf{A}}}\mathbf{+}\stackrel{\mathbf{→}}{{\mathbf{P}}_{\mathbf{B}}}$

If$\underset{\mathbf{}}{\mathbf{∑}\stackrel{\mathbf{→}}{\mathbf{F}}\mathbf{=}\mathbf{0}}$

Then

$\stackrel{\mathbf{→}}{\mathbf{P}}$= constant.

Referring to Example 8.4 (Section 8.2),

Since no external force is acting on the system, according to the conservation of the moment the total momentum is conserved.

Since the system was initially at rest, therefore total momentum must be zero.

We know that

$P_{total}=M{\stackrel{→}{v}}_{cm}$

Since mass cannot be zero, therefore ${\stackrel{→}{v}}_{cm}$must be zero.

Hence the velocity of the center of mass of the system after the rifle is fired must be zero.