Environmental Engineering Reference
In-Depth Information
our force experiment and for our definition of force? An observer moving relative
to us will claim that the mass in Figure 2.1 is in motion whilst we assert that it
is stationary. We need, as a matter of some urgency, to encorporate the frame of
reference into our definition of force. To help us choose a good frame of reference
we shall consider a situation in which no forces are present.
For a force on a particle to exist there must be something else somewhere in the
Universe that is responsible, i.e. a spring or something that can counter a spring.
A particle, completely alone in the Universe would experience no forces. This
hypothetical object, of point size and subject to no forces, is referred to as an
isolated particle. What sort of motion do we expect for such an isolated particle?
Similar problems troubled ancient thinkers who concluded that force was necessary
to maintain the motion of a body
1
. This is a conclusion very close to our everyday
experience. If you push a topic along a table it may move, but when you decide to
stop pushing, the topic stops moving: the force is needed to maintain the motion.
If however, one looks at a rolling ball, then the behaviour is noticeably different.
A hard sphere set in motion on a flat, hard, horizontal surface travels a long
way before stopping. So the rule that force is needed to maintain motion appears
suspect. It was Galileo, studying the motion of rolling spheres on inclined planes
who proposed that a moving body continues moving, i.e. we might say that the
body has “inertia”. This means that the behaviour of the rolling ball is closer to
that of the isolated particle than is that of the topic on the table. Galileo's genius
was to realise that the motion of everyday objects is complicated by friction and
that to see the raw, unhindered, motion of an isolated particle we need to devise
careful experiments that are insensitive to friction.
Newton's First Law, as written in
Principia
is is restatement of Galileo's Princi-
ple of Inertia: “every body preserves its state of rest, or of uniform motion in a right
line, unless compelled to change that state by forces acting upon it.” In other words,
the isolated particle will have a constant velocity vector, and this velocity may be
zero. Forces are responsible for changes in the velocity of a body. On the surface
this sounds very clear; a watertight rule for the motion of bodies in the absence of
forces. There is however, an important weakness in the First Law as stated above.
Specifically, there is no statement as to what frame of reference should be used,
and this is crucial for the complete description of the state of motion of the parti-
cle. Consider the situation illustrated by the cartoon in Figure 2.2. Two observers,
called A and B are measuring the motion of an isolated particle. B observes that
the particle is stationary and, according to the First Law, the particle will remain
A
B
Figure 2.2
Two observers and the motion of an isolated particle.
1
A common view among the Ancient Greek philosophers was that the ability to cause motion was a
sign of life. The apparent motion of the heavenly bodies was taken as a sign of their divine nature.
