5-1 NEWTON’S FIRST AND SECOND LAWS 95pole causes the car to stop. Science, engineering, legal, and medical journals are
filled with articles about forces on objects, including people.
A Heads Up.Many students find this chapter to be more challenging than the
preceding ones. One reason is that we need to use vectors in setting up equations—
we cannot just sum some scalars. So, we need the vector rules from Chapter 3.
Another reason is that we shall see a lot of different arrangements: objects will
move along floors, ceilings, walls, and ramps. They will move upward on ropes
looped around pulleys or by sitting in ascending or descending elevators.
Sometimes, objects will even be tied together.
However, in spite of the variety of arrangements, we need only a single key
idea (Newton’s second law) to solve most of the homework problems. The pur-
pose of this chapter is for us to explore how we can apply that single key idea to
any given arrangement. The application will take experience—we need to solve
lots of problems, not just read words. So, let’s go through some of the words and
then get to the sample problems.
Newtonian Mechanics
The relation between a force and the acceleration it causes was first understood
by Isaac Newton (1642 –1727) and is the subject of this chapter. The study of that
relation, as Newton presented it, is called Newtonian mechanics.We shall focus
on its three primary laws of motion.
Newtonianmechanics does not apply to all situations. If the speeds of the in-
teracting bodies are very large —an appreciable fraction of the speed of light — we
must replace Newtonian mechanics with Einstein’s special theory of relativity,
which holds at any speed, including those near the speed of light. If the interacting
bodies are on the scale of atomic structure (for example, they might be electrons
in an atom), we must replace Newtonian mechanics with quantum mechanics.
Physicists now view Newtonian mechanics as a special case of these two more
comprehensive theories. Still, it is a very important special case because it applies
to the motion of objects ranging in size from the very small (almost on the scale of
atomic structure) to astronomical (galaxies and clusters of galaxies).
Newton’s First Law
Before Newton formulated his mechanics, it was thought that some influence,
a “force,” was needed to keep a body moving at constant velocity. Similarly, a
body was thought to be in its “natural state” when it was at rest. For a body to
move with constant velocity, it seemingly had to be propelled in some way, by
a push or a pull. Otherwise, it would “naturally” stop moving.
These ideas were reasonable. If you send a puck sliding across a wooden
floor, it does indeed slow and then stop. If you want to make it move across the
floor with constant velocity, you have to continuously pull or push it.
Send a puck sliding over the ice of a skating rink, however, and it goes a lot
farther. You can imagine longer and more slippery surfaces, over which the puck
would slide farther and farther. In the limit you can think of a long, extremely
slippery surface (said to be a frictionless surface), over which the puck would
hardly slow. (We can in fact come close to this situation by sending a puck sliding
over a horizontal air table, across which it moves on a film of air.)
From these observations, we can conclude that a body will keep moving with
constant velocity if no force acts on it. That leads us to the first of Newton’s three
laws of motion:
Newton’s First Law:If no force acts on a body, the body’s velocity cannot
change; that is, the body cannot accelerate.