Clas Blomberg - Physics of life-Elsevier Science (2007)

Chapter 4. Basics of classical (Newtonian) dynamics 23
This would mean an energy expression:
E
osc
mv2
Epot
( x)
2
Now, there is an important feature that we hitherto have ignored. All motion is being damped
due to what most often is referred to as “friction”. No oscillator will vibrate forever; the
string will stop at an equilibrium position. A pendulum will stop. Even if it has such a high
velocity that it can pass the highest point and rotate for some turns, it will first stop rotating,
then show successively decreasing oscillations until it stops. (This of course under the assumption
that there is no restoring force as there is in a clock-work.) Any vehicle moving along
a road must have a force to move. Without force it stops. The principle of constant momentum
does not seem to be fulfilled. What we say here applies to “macroscopic objects”, the
objects we have around us of sizes that are meaningful for us. Friction is a property of the
macroscopic world. Friction can be apprehended as a force, but it is not expressible as a
potential energy. In many cases, it can be considered as a force acting against the motion
and being proportional to the velocity.
Friction and damping will play an important role in what comes. What are there sources?
Simple friction is an interaction between a moving object and the ground along which
it moves. There are always small obstacles, which may be in a very small scale, but anyhow
provides forces that hinder the motion. We also have a damping, similar to proper friction
as the resistance of air or water to the motion. The air resistance may be the most
important damping source for a cyclist, damping in water is what stops a boat. I used the
word “resistance”, which is quite appropriate here. The air resistance a cyclist feels is
similar although of a quite different scale as what hinders an electric current in an electric
conductor.
Resistance, damping, friction, viscosity. All are examples of damping. And these also give
the result that the sum of kinetic and potential energies is not constant in time but decreases.
An object will stop at the potential energy minimum. Objects fall to the floor and stops there.
Vibrations are damped out. Principles about this are important for our presentation, and we
start with some aspects here to go deeper with these problems together with thermodynamics
and statistical mechanics later.
The sum of kinetic and potential energies as well as the momentum is not preserved. An
object falls to the ground and remains there. It has gained energy by the fall, but then, this
seems to be lost. It should be quite clear that this energy has been taken up by the ground (and
to some extent by the air). We can express this as saying that the ground has been heated and
the lost energy is taken up by increasing motion of the atoms (molecules) of the ground.
The momentum is likewise not lost but transferred to the ground molecules, by moving them
a little. There are many of them, and they are held together by strong forces which decelerate
the motion. (Some of the loss of energy can have been taken up by a deformation: the fallen
object gets broken.) The spreading of kinetic energy and momentum is what we refer to as
“dissipation”, a central concept in much of our account.