Forces - Biomechanics of the Human Body - page 16

Table 1.1 Coefficients of static and kinetic friction
Materials μ μ s k

Steel on steel 0.74 0.57

Rubber on concrete 1.00 0.80

Glass on glass 0.94 0.40

Ice on ice 0.10 0.03

Wood on wood 0.25-0.50 0.20

Bone on bone with synovial fluid in human beings 0.01 0.003

body to move. Therefore, when an applied force overcomes f s , the body begins to
move. Experimentally, it is found that

f s ¼ μ s N ; (1.3)

where μ s is the coefficient of static friction and N is the normal force ( 1.3 ), whose
intensity is equal to that of the weight of the body.
When the body is in motion, a smaller applied force is enough to maintain a
constant velocity. This force is called force of kinetic friction f k and can be obtained
from ( 1.4 ):

f k ¼ μ k N ; (1.4)

where μ k is the coefficient of kinetic friction.

The values of μ k depend on the nature of the surfaces in contact but are

almost independent of the surface areas in contact. They are dimensionless, that is,
net numbers without units.
Table 1.1 lists the values of coefficients of static and kinetic friction between
different materials. It is possible to observe from the table that the synovial fluid
causes the coefficient of friction in bone joints to have a much smaller value than
the coefficients of friction between other materials. This fluid acts as a lubricant in
order to facilitate the movement after the frictional force is overcome. The
lubricants used, for example, in the motors of cars have exactly the same role,
that is, to facilitate the motion, besides reducing the erosion of materials. In the
human body, there are many fluids that have this function. Saliva acts as a lubricant
making the deglutition (swallowing) of food possible. Its lack would make it
painful for the swallowing of toasts and granola, for example.
However, the existence of friction is essential in many situations. When we walk
or run, as the heel of the foot touches the ground, the foot pushes it in a forward
direction and the ground, in its turn, exerts a frictional force in the backward
direction, preventing the person from slipping. When the toe leaves the ground,
the frictional force prevents the toe from slipping backward. Therefore, we would
not be able to walk or run on a surface without friction. Who has not fallen down
while walking or running on wet and slippery or icy ground or on soapy or well-
waxed floors? Going for a walk on smooth ground, it is important to wear tennis
shoes with rough soles to increase the friction. The rubber tires of vehicles rotate
without effect and slip when there is oil or ice on the ground, the cause of many
accidents due to the lack of friction.

μ s and