9781118230725.pdf

Conservation of Linear Momentum

Suppose that the net external force (and thus the net impulse ) acting on a

system of particles is zero (the system is isolated) and that no particles leave or

enter the system (the system is closed). Putting in Eq. 9-27 then yields

, which means that

(closed, isolated system). (9-42)

In words,

P

:

constant

dP

:

/dt 0

F

:

net^0

J

:

F

:

net

230 CHAPTER 9 CENTER OF MASS AND LINEAR MOMENTUM

9-5CONSERVATION OF LINEAR MOMENTUM

After reading this module, you should be able to...

9.26For an isolated system of particles, apply the conservation
of linear momenta to relate the initial momenta of the particles
to their momenta at a later instant.

9.27Identify that the conservation of linear momentum can be

done along an individual axis by using components along

that axis, providedthat there is no net external force com-

ponent along that axis.

●If a system is closed and isolated so that no net external

force acts on it, then the linear momentum must be constant

even if there are internal changes:

P (closed, isolated system).

:

constant

P

: ●This conservation of linear momentum can also be written

in terms of the system’s initial momentum and its momentum

at some later instant:

P (closed, isolated system),

:

iP

:

f

Learning Objectives

Key Ideas

If no net external force acts on a system of particles, the total linear momentum

of the system cannot change.

P

:

This result is called the law of conservation of linear momentumand is an extremely

powerful tool in solving problems. In the homework we usually write the law as

(closed, isolated system). (9-43)

In words, this equation says that, for a closed, isolated system,

.

Caution:Momentum should not be confused with energy. In the sample problems

of this module, momentum is conserved but energy is definitely not.

Equations 9-42 and 9-43 are vector equations and, as such, each is equivalent

to three equations corresponding to the conservation of linear momentum in

three mutually perpendicular directions as in, say, an xyzcoordinate system.

Depending on the forces acting on a system, linear momentum might be

conserved in one or two directions but not in all directions. However,



total linear momentum

at some initial time ti



total linear momentum

at some later time tf 

P

:

iP

:

f

If the component of the net externalforce on a closed system is zero along an axis, then

the component of the linear momentum of the system along that axis cannot change.

In a homework problem, how can you know if linear momentum can be con-

served along, say, an xaxis? Check the force components along that axis. If the net of

any such components is zero, then the conservation applies. As an example, suppose

that you toss a grapefruit across a room. During its flight, the only external force act-

ing on the grapefruit (which we take as the system) is the gravitational force ,

which is directed vertically downward. Thus, the vertical component of the linear

F

:

g