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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