j
Pinitial
j
Pfinal
MOMENTUM PRINCIPLES
Force and Motion
CP-03
Page 8
Rev. 0
Figure 1 Momentum
The development of the law of conservation of momentum does not consider whether the
collision is elastic or inelastic. In an elastic collision, both momentum and kinetic energy (i.e.,
energy due to an objects velocity) are conserved. A common example of an elastic collision is
the head-on collision of two billiard balls of equal mass. In an inelastic collision, momentum is
conserved, but system kinetic energy is not conserved. An example of an inelastic collission is
the head-on collision of two automobiles where part of the initial kinetic energy is lost as the
metal crumples during the impact. The concept of kinetic energy will be discussed further in
Module 5 of this course.
The law of conservation of momentum can be mathematically expressed in several different
ways. In general, it can be stated that the sum of a system's initial momentum is equal to the sum
of a system's final momentum.
(3-7)
In the case where a collision of two objects occurs, the conservation of momentum can be stated
as follows.
P
+ P
= P
+ P
(3-8)
1 initial
2 initial
1 final
2 final
or
(m v )
+ (m v )
= (m v )
+ (m v )
(3-9)
1 1 initial
2 2 initial
1 1 final
2 2 final
In the case where two bodies collide and have identical final velocities, equation 3-10 applies.
m v + m v = (m + m )v
(3-10)
1
1
2
2
1
2
f
For example, consider two railroad cars rolling on a level, frictionless track (see Figure 1). The
cars collide, become coupled, and roll together at a final velocity (v ). The momentum before
f
and after the collision is expressed with Equation 3-10.
