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dimensional coordinate system with its x axis parallel the direction of
motion. Forces that point along the positive x axis are positive, and forces in
the opposite direction are negative. Forces that are not directly along the x
axis cannot be immediately incorporated into this scheme, but that’s OK,
because we’re avoiding those cases for now.
Discussion questions
In chapter 0, I defined 1 N as the force that would accelerate a 1-kg mass from
rest to 1 m/s in 1 s. Anticipating the following section, you might guess that 2
N could be defined as the force that would accelerate the same mass to twice
the speed, or twice the mass to the same speed. Is there an easier way to
define 2 N based on the definition of 1 N.
4.2Newton’s First Law
We are now prepared to make a more powerful restatement of the
principle of inertia.
Newton's First Law
If the total force on an object is zero, its center of mass
continues in the same state of motion.
In other words, an object initially at rest is predicted to remain at rest if the
total force on it is zero, and an object in motion remains in motion with the
same velocity in the same direction. The converse of Newton’s first law is
also true: if we observe an object moving with constant velocity along a
straight line, then the total force on it must be zero.
In a future physics course or in another textbook, you may encounter
the term net force, which is simply a synonym for total force.
What happens if the total force on an object is not zero. It accelerates.
Numerical prediction of the resulting acceleration is the topic of Newton’s
second law, which we’ll discuss in the following section.
This is the first of Newton’s three laws of motion. It is not important to
memorize which of Newton’s three laws are numbers one, two, and three. If
a future physics teacher asks you something like, “Which of Newton’s laws
are you thinking of,” a perfectly acceptable answer is “The one about
constant velocity when there’s zero total force.” The concepts are more
important than any specific formulation of them. Newton wrote in Latin,
and I am not aware of any modern textbook that uses a verbatim translation
of his statement of the laws of motion. Clear writing was not in vogue in
Newton’s day, and he formulated his three laws in terms of a concept now
called momentum, only later relating it to the concept of force. Nearly all
modern texts, including this one, start with force and do momentum later.
Example: an elevator
Question: An elevator has a weight of 5000 N. Compare the
forces that the cable must exert to raise it at constant velocity,
lower it at constant velocity, and just keep it hanging.
Answer: In all three cases the cable must pull up with a force of
exactly 5000 N. Most people think you’d need at least a little
more than 5000 N to make it go up, and a little less than 5000 N
to let it down, but that’s incorrect. Extra force from the cable is
Chapter 4Force and Motion