Figure 21 illustrates how we might use Hooke's law to quantify the force we exert
on a body of mass when we pull on the handle of
a spring attached to it. The magnitude of the force is proportional to the extension
of the spring: twice the extension means twice the force. As shown, the direction of the force
is towards the spring, parallel to its axis (assuming that the extension is positive).
The magnitude of the force can be quantified in terms of the critical extension required to
impart a unit acceleration
(*i.e.*,
) to a body of unit mass (*i.e.*, ).
According to Eq. (94), the force corresponding
to this extension is 1 *newton*. Here, a newton (symbol N) is
equivalent to a kilogram-meter per second-squared, and is the mks unit of force. Thus,
if the critical extension corresponds to a force of then half the critical
extension corresponds to a force of , and so on. In this manner, we
can quantify both the direction and magnitude of the force we exert, by means of a spring,
on a given body.

Suppose that we apply two forces, and (say), acting in different directions,
to a body of mass by means of two springs. As illustrated in Fig. 22, the body accelerates
as if it were subject to a single force which is the *vector sum* of the individual
forces and . It follows that the force appearing in
Newton's second law of motion, Eq. (94), is the *resultant* of all the external forces to which
the body whose motion is under investigation is subject.

Suppose that the resultant of all the forces acting on a given body is *zero*. In other words,
suppose that the forces acting on the body exactly balance one another. According to Newton's second law of motion,
Eq. (94), the body does not accelerate: *i.e.*, it either remains at rest or
moves with uniform velocity in a straight line. It follows that Newton's first law
of motion applies not only to bodies which have no forces acting upon them but also to
bodies acted upon by exactly balanced forces.