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11.1 Impulsive Forces 343

PHYSICS IN PRACTICE AUTOMOBILE COLLISIONS

We can fully appreciate the effects of the second- However, the impact can still be fatal—you wouldn’t expect to
Concepts
in ary impact on the human body if we compare the survive a jump from an 11-floor building onto an air mattress.
Context
impact speeds of a human body on the dashboard For maximum protection,a seat belt should always be worn
or the windshield with the speed attained by a even in vehicles equipped with air bags. In lateral collisions, in
body in free fall from some height.The impact of the head on repeated collisions (such as in car pileups), and in rollovers, an
the windshield at 15 m s is equivalent to falling four floors air bag is of little help, and a seat belt is essential. The effec-
down from an apartment building and landing headfirst on a tiveness of seat belts is well demonstrated by the experiences of
hard surface.Our intuition tells us that this is likely to be fatal. race car drivers. Race car drivers wear lap belts and crossed
Since our intuition about the dangers of heights is much better shoulder belts. Even in spectacular crashes at very high speeds
than our intuition about the dangers of speeds, it is often (see the figure), the drivers rarely suffer severe injuries.
instructive to compare impact speeds with equivalent heights
of fall. The table lists impact speeds and equivalent heights,
expressed as the number of floors the body has to fall down to
acquire the same speed.
The number of fatalities in automobile collisions has been
reduced by the use of air bags.The air bag helps by cushioning
the impact over a longer time,reducing the time-average force.
To be effective,the air bag must inflate quickly,before the pas-
senger reaches it,typically in about 10 milliseconds.Because of
this, a passenger, especially a child, too near an air bag prior to
inflation can be injured or killed by the impulse from the infla-
tion. But for a properly seated adult passenger, the inflated air
bag cushions the passenger, reducing the severity of injuries.

COMPARISON OF IMPACT SPEEDS AND
HEIGHTS OF FALL

EQUIVALENT HEIGHT
SPEED SPEED (NUMBER OF FLOORS) a

15 km h 9 mi h 1 3
30 19 1
45 28 3
60 37 5
75 47 8
90 56 11
105 65 15 In a race at the California Speedway in October 2000, a car flips
over and breaks in half after a crash, but the driver, Luis Diaz, walks
a
Each floor is 2.9 m. away from the wreck.

SOLUTION: The only horizontal force on the ball is the normal force exerted
by the wall; this force reverses the motion of the ball (see Fig. 11.3). Since the wall
is very massive, the reaction force of the ball on the wall will not give the wall any
appreciable velocity. Hence the kinetic energy of the system, both before and
after the collision, is merely the kinetic energy of the ball. Conservation of this