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7.1 Work 205

onservation laws play an important role in physics. Such laws assert that some
C quantity is conserved, which means that the quantity remains constant even when
particles or bodies suffer drastic changes involving motions, collisions, and reactions.
One familiar example of a conservation law is the conservation of mass. Expressed in
its simplest form, this law asserts that the mass of a given particle remains constant,
regardless of how the particle moves and interacts with other particles or other bodies.
In the preceding two chapters we took this conservation law for granted, and we treated
the particle mass appearing in Newton’s Second Law (ma F) as a constant, time-
independent quantity. More generally, the sum of all the masses of the particles or
bodies in a system remains constant, even when the bodies suffer transformations and
reactions. In everyday life and in commercial and industrial operations, we always rely
implicitly on the conservation of mass. For instance, in the chemical plants that reprocess
the uranium fuel for nuclear reactors, the batches of uranium compounds are carefully
weighed at several checkpoints during the reprocessing operation to ensure that none
of the uranium is diverted for nefarious purposes.This procedure would make no sense
if mass were not conserved, if the net mass of a batch could increase or decrease
spontaneously.
This chapter and the next deal with the conservation of energy.This conservation
law is one of the most fundamental laws of nature. Although we will derive this law from
Newton’s laws, it is actually much more general than Newton’s laws, and it remains
valid even when we step outside of the realm of Newtonian physics and enter the realm
of relativistic physics or atomic physics, where Newton’s laws fail. No violation of the
law of conservation of energy has ever been discovered.
In mechanics, we can use the conservation law for energy to deduce some features of the
motion of a particle or of a system of particles when it is undesirable or too difficult to cal-
culate the full details of the motion from Newton’s Second Law. This is especially
helpful in those cases where the forces are not known exactly; we will see some exam-
ples of this kind in Chapter 11.
But before we can deal with energy and its conservation, we must introduce the con-
cept of work. Energy and work are closely related. We will see that the work done by
the net force on a body is equal to the change of the kinetic energy (the energy of
motion) of the body.

7.1 WORK Online
9
Concept
To introduce the definition of work done by a force, we begin with the simple case of Tutorial
motion along a straight line, with the force along the line of motion, and then we will
generalize to the case of motion along some arbitrary curved path, with the force in some
arbitrary direction at each point. Consider a particle moving along such a straight line,
say, the x axis, and suppose that a constant force F , directed along the same straight
x
line, acts on the particle.Then the work done by the force F on the particle as it moves
x
some given distance is defined as the product of the force and the displacement x:

W F x (7.1) work done by one constant force
x
This rigorous definition of work is consistent with our intuitive notion of what
constitutes “work.” For example, the particle might be a stalled automobile that you are
pushing along a road (see Fig. 7.1). Then the work that you perform is proportional
to the magnitude of the force you have to exert, and it is also proportional to the
distance you move the automobile.