Forces and equilibrium - Orthopaedic Biomaterials in Research and Practice - page 12

known are those exerted by the foot weight (49 N) and the gravitational
force of the foot and the leg. The latter two are directed vertically down-
ward and are shown acting on the center of mass of each segment. The
center of mass is a point that appears to be exactly in the center of a
homogeneous object.
The properties of the center of mass are such that, if the entire mass
of the object were transferred to that single point, it would behave the
same as the object with a distribute d mass.
The two unknown forces are − R , the joint reaction force produced
by the desired tension on the femur, and R , the transverse forc e applied
by the joint capsule, which is assumed to be orthogonal to − R . Since
the limb is known to be at rest, both equilibrium conditions apply (Sum
F x = 0, Sum F y = 0), and given two conditions, one may solve for both R
and R . In this case, and often in others, it may be convenient to transfer
all forces into mutual orthogonal directions using trigonometric func-
tions presented earlier in this chapter.
Thus, the combination of the use of a free body diagram and the
application of the equilibrium conditions permits solutions of quite
complex force and moment problems. Such solutions are essential to an
understanding of the behavior of materials under load, since the forces
within the material are dependent on the forces acting on the outside of
the material.

Dy namics

It is necessary to understand statics to perceive the relationship between
internal and external forces in the steady state. However, within the
human body, there is a relatively constant state of motion, resulting from
respiration, blood circulation, locomotion, and so on. The relationship
of forces to changes in velocity is the subject of dynamics. The field of
biomechanics addresses this field primarily at the level of organs, limb
segments, and the whole body. Biomechanics and biomaterials merge
together when consideration is given to dynamic effects at the tissue
or material level. Specific velocity-related issues will be discussed in
later chapters, as in consideration of the strain rate dependence of the
mechanical properties of articular cartilage (see Chapter 5). For our pur-
poses, it is not necessary to deal completely with dynamics but merely to
extract some simple principles.

Force and
acceleration

Acceleration is the relationship between force, in the sense of a net resul-
tant force on an object, and a change in velocity of that object. This
is embodied in Newton's second law and is, in fact, the origin of the
specific derivation of force units from the sets of basic units given in
Table 1.1.
Suppose that w e return to Figure 1.1 and increase the magnitude of
the applied force A until the cube begins to move. We have a common-
sense idea that we may do this by pushing with increasing effort along