cannot be solved by itself. In such a case, one must apply the principle of conservation of
mechanical energy. It does apply here. The expression "completely elastic" tells you that
conservation of mechanical energy does apply.
In applying conservation of momentum one first sketches a before and an after picture in which
one defines symbols by labeling objects and arrows (indicating velocity), and defines which
direction is chosen as the positive direction. The first line in the solution is always a statement
that the total momentum in the before picture is the same as the total momentum in the after
picture. This is typically written by means an equation of the form:
∑ p = p′
→
∑ → (4-2)
The Σ in this expression is the upper case Greek letter “sigma” and is to be read “the sum of.”
Hence the equation reads: “The sum of the momenta to the right in the before picture is equal to
the sum of the momenta to the right in the after picture.” In doing the sum, a leftward
momentum counts as a negative rightward momentum. The arrow subscript is being used to
define the positive direction.
Examples
Now let's get down to some examples. We'll use the examples to clarify what is meant by
collisions and anti-collisions; to introduce one more concept, namely, relative velocity
(sometimes referred to as muzzle velocity); and of course, to show the reader how to apply
conservation of momentum.
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