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11.1 Impulsive Forces 339

? In a two-car collision, how are the initial velocities related to the final direction
of motion? (Example 7, page 351)

he collision between two bodies—an automobile and a solid wall, a ship and an ice-
Tberg, a molecule of oxygen and a molecule of nitrogen—involves a violent change of
the motion, a change brought about by very strong forces that begin to act suddenly
when the bodies come into contact, last a short time, and then cease just as suddenly
when the bodies separate.The forces that act during a collision are usually rather com-
plicated,so their complete theoretical description is impossible (e.g.,in an automobile col-
lision) or at least very difficult (e.g.,in a collision between subatomic particles).However,
even without exact knowledge of the details of the forces, we can make some predictions
about the collision by taking advantage of the general laws of conservation of momen-
tum and energy we studied in the preceding chapters. In the following sections we will
see what constraints these laws impose on the motion of the colliding bodies.
The study of collisions is an important tool in engineering and physics. In auto-
mobile collision and safety studies, engineers routinely subject vehicles to crash tests.
Collisions are also essential for the experimental investigation of atoms, nuclei, and
elementary particles. All subatomic bodies are too small to be made visible with any
kind of microscope. Just as you might use a stick to feel your way around a dark cave,
a physicist who cannot see the interior of an atom uses probes to “feel” for subatomic
structures. The probe used by physicists in the exploration of subatomic structures is
simply a stream of fast-moving particles—electrons, protons, alpha particles (helium
nuclei), or others. These projectiles are aimed at a target containing a sample of the
atoms, nuclei, or elementary particles under investigation. From the manner in which
the projectiles collide and react with the target, physicists can deduce some of the prop-
erties of the subatomic structures in the target. Similarly, materials scientists, chemists,
and engineers deduce the structure and composition of solids and liquids by bom-
barding such materials with particles and examining the results of such collisions.

11.1 IMPULSIVE FORCES Online
13
Concept
The force that two colliding bodies exert on one another acts for only a short time, Tutorial
giving a brief but strong push. Such a force that acts for only a short time is called an
impulsive force. During the collision,the impulsive force is much stronger than any other
forces that may be present; consequently the impulsive force produces a large change in
the motion while the other forces produce only small and insignificant changes. For
instance, during the automobile collision shown in Fig. 11.1, the only important force
on the automobile is the push of the wall on its front end; the effects produced by grav-
ity and by the friction force of the road during the collision are insignificant.
Suppose the collision lasts some short time t, say, from t 0 to t t, and that
during this time an impulsive force F acts on one of the colliding bodies.This force is
zero before t 0 and it is zero after t t, but it is large between these times. For
example, Fig. 11.2 shows a plot of the force experienced by an automobile in a collision
with a solid wall lasting 0.120 s.The force is zero before t 0 and after t 0.120 s, and
varies in a complicated way between these times.
The impulse delivered by such a force to the body is defined as the integral of the force
over time:

¢t impulse
I F dt (11.1)
0