simple accounting (bookkeeping) procedures. The case of momentum is complicated by the fact
that momentum has direction, but in this initial encounter with the conservation of momentum
you will deal with cases involving motion along a straight line. When all the motion is along one
and the same line, there are only two possible directions for the momentum and we can use
algebraic signs (plus and minus) to distinguish between the two. The principle of Conservation
of Momentum applies in general. At this stage in the course however, we will consider only the
special case in which there is no net transfer of momentum to (or from) the system from outside
the system.
Conservation of Momentum in One Dimension for the Special Case in
which there is No Transfer of Momentum to or from the System from
Outside the System
In any process involving a system of objects which all move along one and the same line, as long
as none of the objects are pushed or pulled along the line by anything outside the system of
objects (it’s okay if they push and pull on each other), the total momentum before, during, and
after the process remains the same.
The total momentum of a system of objects is just the algebraic sum of the momenta of the
individual objects. That adjective "algebraic" means you have to pay careful attention to the plus
and minus signs. If you define "to the right" as your positive direction and your system of
objects consists of two objects, one moving to the right with a momentum of 12 kg⋅m/s and the
other moving to the left with momentum 5 kg⋅m/s, then the total momentum is (+12 kg⋅m/s) +
(−5 kg⋅m/s) which is +7 kg⋅m/s. The plus sign in the final answer means that the total
momentum is directed to the right.
Upon reading this selection you'll be expected to be able to apply conservation of momentum to
two different kinds of processes. In each of these two classes of processes, the system of objects
will consist of only two objects. In one class, called collisions, the two objects bump into each
other. In the other class, anti-collisions the two objects start out together, and spring apart.
Some further breakdown of the collisions class is pertinent before we get into examples. The
two extreme types of collisions are the completely inelastic collision, and the completely elastic
collision.
Upon a completely inelastic collision, the two objects stick together and move off as one. This is
the easy case since there is only one final velocity (because they are stuck together, the two
objects obviously move off at one and the same velocity). Some mechanical energy is converted
to other forms in the case of a completely inelastic collision. It would be a big mistake to apply
the principle of conservation of mechanical energy to a completely inelastic collision.
Mechanical energy is not conserved. The words "completely inelastic" tell you that both objects
have the same velocity (as each other) after the collision.
In a completely elastic collision (often referred to simply as an elastic collision), the objects
bounce off each other in such a manner that no mechanical energy is converted into other forms
in the collision. Since the two objects move off independently after the collision there are two
final velocities. If the masses and the initial velocities are given, conservation of momentum
yields one equation with two unknowns—namely, the two final velocities. Such an equation
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