105
frictional force must be canceling it out.
Contrary to Aristotle, more force is not needed in order to
maintain a higher speed. Zero total force is always needed to
maintain constant velocity. Consider the following made-up
numbers:
boat moving at a
low, constant
velocity
boat moving at
a high, constant
velocity
forward force of the
wind on the sail......10,000 N20,000 N
backward force of
the water on the
hull........................-10,000 N-20,000 N
total force on the
boat......................0 N0 N
The faster boat still has zero total force on it. The forward force
on it is greater, and the backward force smaller (more negative),
but that’s irrelevant because Newton’s first law has to do with the
total force, not the individual forces.
This example is quite analogous to the one about terminal
velocity of falling objects, since there is a frictional force that
increases with speed. After casting off from the dock and raising
the sail, the boat will accelerate briefly, and then reach its
terminal velocity, at which the water’s frictional force has become
as great as the wind’s force on the sail.
Discussion questions
A. Newton said that objects continue moving if no forces are acting on them,
but his predecessor Aristotle said that a force was necessary to keep an object
moving. Why does Aristotle’s theory seem more plausible, even though we
now believe it to be wrong. What insight was Aristotle missing about the
reason why things seem to slow down naturally.
B. In the first figure, what would have to be true about the saxophone’s initial
motion if the forces shown were to result in continued one-dimensional
motion.
C. The second figure requires an ever further generalization of the preceding
discussion. After studying the forces, what does your physical intuition tell you
will happen. Can you state in words how to generalize the conditions for one-
dimensional motion to include situations like this one.
8 N
2 N
3 N
3 N
4 N
4 N
Discussion question B.Discussion question C.
Section 4.2Newton’s First Law