64 The Poetry of Physics and The Physics of Poetry
retards it descent to Earth, which is a negligible effect with stones. If the
same experiment were repeated in a vacuum then indeed the feather and
the stone would fall at exactly the same rate in the vacuum. The
explanation for why all masses fall at the same rate when air resistance
may be ignored is due to the fact that the force acting on the falling body
is proportional to its mass and that this force produces an acceleration
inversely proportional to the falling body’s mass (F = ma). As a result
the effects of the mass cancel and the acceleration of the particle is
independent of its mass. Putting it less technically, the greater the
particle’s mass, the greater the gravitational force it experiences. The
greater its mass, however, the more difficult it is to change its velocity.
These two effects of the mass just cancel so that all bodies accelerate
in the Earth’s gravitational field at the same rate as is verified by
experiment.
If we reflect carefully on the role the mass of a particle plays in
Newtonian physics we quickly realize that the mass serves two functions.
On the one hand it determines the strength of a body’s gravitational
interaction (the greater the mass of a body the stronger is its gravitational
interaction). On the other hand the mass also determines the body’s
resistance to acceleration or a change of its velocity. The acceleration a
body experiences as a result of a force is inversely proportional to its
mass since the force is equal to the product of the mass times the
acceleration (F = ma or a = F/m). Hence the greater the mass of a body,
the smaller the acceleration it experiences as a result of a given force.
The mass also determines the momentum or amount of motion since the
momentum is the product of the mass times the velocity. The greater the
mass of a body the greater its momentum for a fixed velocity and hence
the more difficult it is to change that velocity.
The property of a body to attract other bodies gravitationally and
the property to resist acceleration are two separate properties of a body,
each ascribed to the body’s mass. However, these two properties are so
different that we should recognize that a body has really two masses; a
gravitational mass, which generates a gravitational force with other
masses and an inertial mass, which resists being accelerated when a force
is applied to it. These two masses, which are quite distinct, nevertheless
turn out to be equal. This seemingly bizarre coincidence accounts for the
fact that all masses fall at the same rate. The heavy bodies experience a
greater gravitational pull. However, they are less affected by the force
because of their greater inertial mass. Because of the equality of these