3.4 Forces on Materials
47
bodies, and almost all the small ones of their particles by some other attractive and repelling
powers which intercede the particles.
—Isaac Newton
3.4.1 Systems in Mechanical Equilibrium
Systems in which no macroscopic accelerations occur are said to be in mechanical
equilibrium, and their study is the subject of statics. Applications to cells, bodies,
and biomaterials abound.
Having a ‘rigid’ system be static requires that the net force and torque on the
system vanish. If the system is non-rigid, additional conditions must be applied.
Mechanical equilibrium can be stable, neutral, or unstable. These are distinguished
by slightly changing the body from its static position and then releasing. If the body
forces act to restore the original position, the equilibrium was stable. If the forces
still vanish, the equilibrium was neutral. If the body accelerates further away from
its original position, the equilibrium was unstable. Standing a pen on its tip is an
example of unstable equilibrium.
A fish with a fixed amount of air in a passive air sack will be in unstable
equilibrium, because raising the fish slightly causes the air sack to expand under
a reduced pressure, which increases the buoyant force on the fish. A live fish
compensates. There is more on this buoyancy topic in Sect. 4.2.3.
3.4.2 Surface Tension
Identical molecules on the surface of a liquid interact with each other (‘cohere’)
differently than when the same molecules are within the volume of the liquid.
Without similar molecules attracting on one side of an interface, those on the surface
tend to pack closer together than within the liquid, and tend to hold together.
Polar molecules, such as water, will attract each other by electric dipole-dipole
interactions, some atoms will have weak mutual electron orbital attraction, and even
neutral identical molecules will attract by van der Waals forces. The van der Waals
forces are effective in liquids when the molecules are separated by distances on the
order of a nanometer or less.
If we imagine ‘cutting’ the surface of a liquid, the force needed to keep the two
edges closed would depend linearly on the length of the cut. The force per unit
length to hold a surface cut together defines the ‘surface tension’ σ (Table 3.2).
When the surface is stretched or expanded a relatively small amount, the surface
molecules can cause an elastic restoring force, acting like a sheet of rubber.
Surface tension tends to decrease with increasing temperature. For water, the
decrease is nearly linear from 20 ◦ C to the boiling point.
47
bodies, and almost all the small ones of their particles by some other attractive and repelling
powers which intercede the particles.
—Isaac Newton
3.4.1 Systems in Mechanical Equilibrium
Systems in which no macroscopic accelerations occur are said to be in mechanical
equilibrium, and their study is the subject of statics. Applications to cells, bodies,
and biomaterials abound.
Having a ‘rigid’ system be static requires that the net force and torque on the
system vanish. If the system is non-rigid, additional conditions must be applied.
Mechanical equilibrium can be stable, neutral, or unstable. These are distinguished
by slightly changing the body from its static position and then releasing. If the body
forces act to restore the original position, the equilibrium was stable. If the forces
still vanish, the equilibrium was neutral. If the body accelerates further away from
its original position, the equilibrium was unstable. Standing a pen on its tip is an
example of unstable equilibrium.
A fish with a fixed amount of air in a passive air sack will be in unstable
equilibrium, because raising the fish slightly causes the air sack to expand under
a reduced pressure, which increases the buoyant force on the fish. A live fish
compensates. There is more on this buoyancy topic in Sect. 4.2.3.
3.4.2 Surface Tension
Identical molecules on the surface of a liquid interact with each other (‘cohere’)
differently than when the same molecules are within the volume of the liquid.
Without similar molecules attracting on one side of an interface, those on the surface
tend to pack closer together than within the liquid, and tend to hold together.
Polar molecules, such as water, will attract each other by electric dipole-dipole
interactions, some atoms will have weak mutual electron orbital attraction, and even
neutral identical molecules will attract by van der Waals forces. The van der Waals
forces are effective in liquids when the molecules are separated by distances on the
order of a nanometer or less.
If we imagine ‘cutting’ the surface of a liquid, the force needed to keep the two
edges closed would depend linearly on the length of the cut. The force per unit
length to hold a surface cut together defines the ‘surface tension’ σ (Table 3.2).
When the surface is stretched or expanded a relatively small amount, the surface
molecules can cause an elastic restoring force, acting like a sheet of rubber.
Surface tension tends to decrease with increasing temperature. For water, the
decrease is nearly linear from 20 ◦ C to the boiling point.