Environmental Engineering Reference
In-Depth Information
3
Energy
Newton's laws of motion lay down the foundations for a complete understanding
of dynamical systems. Starting from Newton's laws we showed, in Section 2.3.4,
that momentum is conserved for isolated systems and that it turns out to be very
useful when tackling problems. We also remarked that momentum conservation
really ought to be thought of as possessing a fundamental significance in its
own right. In particular, it is not right to think of momentum conservation as
being only a consequence of Newton's Second Law, rather we should think that
Newton's laws had better be consistent with the law of momentum conservation.
Why do we say that? Why is momentum conservation so fundamental that even
Newton's laws are destined to respect it? The answer is easy to state but less
easy to prove: momentum is conserved for the same reason that an experiment
performed in Manchester should deliver the same result as the same experiment
performed in New York. Of course that is true provided the experiment does not
depend upon local differences, such as the difference in temperature etc. The key
point is that moving experiments around should not, in itself, change the outcome.
It is a pity that the proof is a little too sophisticated for us to include it here and
that we are reduced to stating the result without any proof. Now it is clear why
Newton's laws are duty bound to satisfy momentum conservation. The idea that
it does not matter where an experiment is performed, all other things equal, is
an example of a symmetry of Nature and the link between symmetries of Nature
and conservation laws is not unique to momentum. It turns out that for every
symmetry in Nature there is a corresponding conserved quantity. Perhaps chief
amongst the other conserved quantities is the one associated with the fact that it
does not matter
when
we perform an experiment: an experiment performed today
should give the same result as the same experiment performed tomorrow (all other
things being equal). That quantity is called “energy”
1
.
1
The conservation of angular momentum is a result of the fact that experiments can be turned around
(i.e. rotated) without affecting their result.
