Fundamentals of Biomechanics

inverse dynamics. Other scientists build
complex computer models of biomechanical
systems and use direct dynamics, essentially
calculating the motion from the
“what-if” kinetics and body configurations
they input.
Newton's Third Law
Newton's third law of motion is called the
Law of Reaction, because it is most often
translated as: for every action there is an
equal and opposite reaction. For every force
exerted, there is an equal and opposite force
being exerted. If a patient exerts a sideways
force of +150 N on an elastic cord, there has
to be –150-N reaction force of the cord on
the patient's hand (Figure 6.4). The key insight
that people often miss is that a force is
really a mutual interaction between two
bodies. It may seem strange that if you
push horizontally against a wall, the wall is
simultaneously pushing back toward you,
but it is. This is not to say that a force on a
free-body diagram should be represented
by two vectors, but a person must understand
that the effect of a force is not just on
CHAPTER 6: LINEAR KINETICS 137
Figure 6.3. Friction forces acting on ice skaters during push-off and gliding. Newton' Second Law of Motion applied
in the horizontal direction (see text) will determine the horizontal acceleration of the skater.
one object. A free body diagram is one object
or mechanical system and the forces
acting on it, so the double vectors in
Figures 6.4 and 6.5 can sometimes be confusing
because they are illustrating both
objects and are not true free body diagrams.
If someone ever did not seem to kiss
you back, you can always take some comfort
in the fact that at least in mechanical
terms they did.
An important implication of the law of
reaction is how reaction forces can change
the direction of motion opposite to our applied
force when we exert our force on objects
with higher force or inertia (Figure
6.5a). During push-off in running the athlete
exerts downward and backward push
with the foot, which creates a ground reaction
force to propel the body upward and
forward. The extreme mass of the earth easily
overcomes our inertia, and the ground
reaction force accelerates our body in the
opposite direction of force applied to the
ground. Another example would be eccentric
muscle actions where we use our muscles
as brakes, pushing in the opposite direction
to another force. The force exerted