54
3 Mechanical Aspects of Biosystems
Frictional Forces
Frictional forces are a type of shearing force of one layer of material against another,
and are accounted for by how molecules interact. They can exist in the boundary
between any pair of solids and liquids, and between gases and either solids or
liquids.
Two solid layers of material can act on each other tangentially largely because
their surfaces are never perfectly smooth, given that material surfaces are made
from discrete molecules. On an atomic scale (or larger scale, if there are larger
microscopic bumps), the molecules across the boundary can interleave and push
sideways against each other. Since the interleaving becomes more intimate as the
pressure acting to push the layers together increases, the frictional force available
increases with this pressure.
With macroscopic materials under typical pressures, the frictional force will be
proportional to the normal (perpendicular) force squeezing the layers together. This
relationship is found to hold for most smooth surfaces, but is not a universal law;
rather such relationships are called ‘phenomenological laws’.
Because friction between two tangentially sliding solid surfaces can break
molecules away from either surface, debris can be left between the surfaces, often
rolling and acting like ball bearings. This reduces the frictional force needed to
slide, for the given normal force. The induced vibration of surface molecules during
slipping and the breaking of microbumps will generate heat, making friction a
dissipative process. Rubbing our hands together can warm the skin.
If the frictional force is large during a macroscopic motion of one surface against
another over a short enough time (so that the heat generated has insufficient time to
spread much), then the solid material at the contact point can undergo thermal phase
changes. Sparks made by striking flint is a good example.
Frictional forces caused by the motion of fluids acting on bodies are called
viscous forces. We will deal with these in the section on fluid dynamics (4.3).
3.5 Response of Materials to Stress
The response of materials to unopposed force is to start moving. The initial motion
will be linear acceleration of the center of mass of the material if the net forces on an
element are unbalanced, and rotational acceleration about the center of mass if the
net torques are unbalanced. Additional types of motion may occur if the materials
are not acting rigidly. However, if mechanical equilibrium is re-established, the
accelerations must vanish.
A lemma from Einstein’s Special Theory of Relativity says there are no rigid
bodies, i.e. bodies with a fixed separation between any pair of material points. 29
29 See footnote (24) in Sect. 3.3.4.
3 Mechanical Aspects of Biosystems
Frictional Forces
Frictional forces are a type of shearing force of one layer of material against another,
and are accounted for by how molecules interact. They can exist in the boundary
between any pair of solids and liquids, and between gases and either solids or
liquids.
Two solid layers of material can act on each other tangentially largely because
their surfaces are never perfectly smooth, given that material surfaces are made
from discrete molecules. On an atomic scale (or larger scale, if there are larger
microscopic bumps), the molecules across the boundary can interleave and push
sideways against each other. Since the interleaving becomes more intimate as the
pressure acting to push the layers together increases, the frictional force available
increases with this pressure.
With macroscopic materials under typical pressures, the frictional force will be
proportional to the normal (perpendicular) force squeezing the layers together. This
relationship is found to hold for most smooth surfaces, but is not a universal law;
rather such relationships are called ‘phenomenological laws’.
Because friction between two tangentially sliding solid surfaces can break
molecules away from either surface, debris can be left between the surfaces, often
rolling and acting like ball bearings. This reduces the frictional force needed to
slide, for the given normal force. The induced vibration of surface molecules during
slipping and the breaking of microbumps will generate heat, making friction a
dissipative process. Rubbing our hands together can warm the skin.
If the frictional force is large during a macroscopic motion of one surface against
another over a short enough time (so that the heat generated has insufficient time to
spread much), then the solid material at the contact point can undergo thermal phase
changes. Sparks made by striking flint is a good example.
Frictional forces caused by the motion of fluids acting on bodies are called
viscous forces. We will deal with these in the section on fluid dynamics (4.3).
3.5 Response of Materials to Stress
The response of materials to unopposed force is to start moving. The initial motion
will be linear acceleration of the center of mass of the material if the net forces on an
element are unbalanced, and rotational acceleration about the center of mass if the
net torques are unbalanced. Additional types of motion may occur if the materials
are not acting rigidly. However, if mechanical equilibrium is re-established, the
accelerations must vanish.
A lemma from Einstein’s Special Theory of Relativity says there are no rigid
bodies, i.e. bodies with a fixed separation between any pair of material points. 29
29 See footnote (24) in Sect. 3.3.4.