Biomedical Engineering Reference
In-Depth Information
Momentum and
impulse
In the same way that forces produce acceleration in the movement of
objects with mass, changes in velocity of objects produce reaction forces.
Calculation of such forces requires introduction of the second concept,
conservation of momentum.
A moving object with a mass
m
and a velocity
v
is said to have
a momentum equal to
m
×
v
(written as
m
∙
v
). This quantity,
m
∙
v
, is
also sometimes called the inertia of an object, since it is a reflection
of Newton's first law; that is, it remains constant in the absence of an
applied force. If no external forces act on a group of objects, then the
sum of the momentum of all objects in the group remains a constant,
even if the velocities and thus the momentum of the individual objects
change. Therefore, we say that momentum is
conserved
in such a group;
this principle permits us to calculate the forces that moving objects exert
on each other when they collide.
Suppose an osteotome is placed on a piece of bone and struck with
a surgical mallet (Figure 1.10). Is it possible to calculate the force that
the osteotome exerts on the bone from observing the mallet? (This is a
somewhat artificial example since a mallet head swings in an arc rather
than moving in a straight line. The actual case may be analyzed with
more difficulty, but the conclusions are qualitatively the same as for this
simplified case.)
Let us suppose that the mallet (
m
= 0.5 kg) moves with a speed of
0.1 m/s and comes to rest after striking the osteotome. Thus, before
striking, the mallet has a momentum of 0.05 kg ∙ m/s or 0.05 N ∙ s, and
after striking, it has a momentum of zero. The osteotome must have
acquired a momentum of 0.05 N ∙ s. If it were free to move, it would
move in the same direction as the mallet, with a greater velocity, since
it has a lower mass. However, it is positioned against the bone so that
it cannot move to any great degree and must transfer its momentum,
m
= 0.5 kg
V
= 0.1 m/s
FIGUre 1.10
momentum and impulse (Problem 1.5).
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