60 The Poetry of Physics and The Physics of Poetry
masses the lighter body will sustain a greater acceleration than the
heavier body or putting it in terms of everyday experience it is easier to
push a small rock than a big rock. In our previous example the force the
falling rock exerts on the Earth and the force the Earth exerts on the
falling rock are the same but since the mass of the Earth is so much
greater than that of the rock the acceleration it experiences in
unobservable. However, we can observe the effects on the Earth of
another body, which is gravitationally attracted to it. This is the Moon,
which is captured in an orbit about the Earth by the Earth’s gravitational
pull and which in turn pulls back on the Earth creating the high and low
tides, which occur twice a day as the Earth rotates about its axis. The
tides are a result of the Moon’s gravitational pull on the waters of the
oceans.
We have completed our discussion of the relationship of force and
motion within the Newtonian framework. Newton formulated these ideas
in terms of his famous three laws of motion, which we shall reproduce in
their original form for historic interest. They also serve as a summary of
our discussion.
Law I: Every body continues in its state of rest, or of uniform motion
in a right [straight] line, unless it is compelled to change that state by a
force impressed upon it.
Law II: The change in motion [rate of change of momentum] is
proportional to the motive force impressed; and is made in the direction
of the right [straight] line, which that force is impressed.
Law III: To every action there is always opposed and equal reaction;
or the mutual actions of two bodies are always equal and directed to
contrary parts.
The first law we recognize as the oft-cited principle of inertia. The
first part of the second law literally states that the force equals the rate of
change of the momentum. The momentum is the product of the mass
times the velocity and, since the mass does not change, the change of
the momentum is the mass times change of the velocity or the mass
times the acceleration. Hence the first part of the second law is a
statement that the force is the product of the mass times the acceleration
which is often formulated mathematically as F = ma. The second part of
Law II states that the change in motion occurs only in the direction of the
force and embodies the principle of superposition. In other words if a car
traveling at 30 m/s is driven off the side of a cliff it will continue to
travel at 30 m/s, i.e. in the horizontal direction. Its velocity in the vertical