6-1
LAB 6:
Conservation of Linear Momentum
Intuitively, which of the following has more “motion,” a mosquito or a semi
-truck travelling at the same
velocity?
Which is more difficult to slow down?
Which would win in a collision and which is more
destructive?
In asking which object contains more “motion,” we seem to know the answer even though
both are travelling with the same velocity, and this means the velocity alone appears not to be enough
to answer the question.
Whatever this quality of “motion” is, it
appears also to depend upon the
object’s
mass.
You may be tempted to say that the kinetic energy of the objects can
serve as a “gauge” of the object’s
contained “motion,” but
consider an exploding ball.
Before the explosion, there is no motion.
After the
explosion, fragments may fly off in many directions
.
A system’s center of mass can only be moved when
acted upon by an
outside
force, and because
the explosion is considered an “internal” force,
the
fragments’
combined center of mass is unmoved.
Using kinetic energy (a scalar quantity) is
inappropriate for describing the “motion” an object possesses because there’s no way to add up
contributions from the fragments in a way that gives us zero for the combined center of mass.
We need
something else that is a vector.
The quality
of “motion”
we have described is called momentum, specifically
linear momentum
.
It is
given the symbol
⃗
, it is a vector quantity, and it is a conserved quantity in physics.
If we allow
to
represent an object’s mass and
⃗
to represent its velocity, then the object’s momentum is
⃗
⃗
Eqn. 6-1:
Linear Momentum
The momentum vector
’s
direction is the same as the velocity vector
’s
.
T
he momentum’s magnitude is
the product of (mass · velocity), which gives us the unit of momentum, kg · m/s.
Unlike Newtons (kg ·
m/s
2
) for force or Joules (N · m or kg · m
2
/s
2
) for energy, the unit for momentum has no special name.
In the case of the mosquito and semi-truck mentioned above, if we were to slow them both to a halt in
the same amount of time, the semi-truck would require much greater force due to its greater
momentum.
Similarly, it would have a more dominant effect than the mosquito in a head-on collision.
The faster-moving or more-massive object is not always the dominant one!
A speeding low-mass car
that didn’t see the red light will do much more damage than a high
-mass semi-truck slowly inching
forward at an intersection.
A light high-velocity spitwad will do much less damage than the heavy
slowly-lumbering bully who shot it.
One must always consider the product of mass and velocity over
either one of them alone.

6-2
The momentum of an object
can only be changed by an external force.
This is in fact Newton’s famous
Second Law of Motion; more specifically,
the net rate of change of momentum is proportional to the
net force applied.