This month's Challenge Question: Specs & Techs from IHS Engineering360:
This month
we had the largest automotive recall in U.S. history: 33.8 million vehicles
made by 11 different automakers were recalled due to malfunctioning frontal
airbags. These airbags were made by the parts supplier Takata. So, let's think
about airbags for this month's challenge question.
We know
that airbags are very soft inflatable devices; during a crash the airbag is the
best accessory to save a life. The question this month is: Why? Why do airbags
save lives? It is not enough to say that lives are saved during a crash because
the airbags are soft devices. I am looking here at the physics that supports
this notion.
And the answer is:
Let's
assume, for instance, that a car is moving at 60 mph and crashes into a tree. A
passenger in the front seat, before the crash, is moving at 60 mph. At the time
of the crash their body will stop (normally by hitting the dash of the car, if
there is no airbag). So the passenger momentum will change from mv to 0, where
v = 60 mph.
Now, in
order to change momentum, according to Newton, a force needs to act for a given
amount of time. This concept is a consequence of Newton's second law, which is
stated as follows
F = ma
where a is the
acceleration of an object of mass m and F is the force
generated by this acceleration. We know that acceleration is a change in
velocity/time, so we can write the above expression as follows
and
finally,
The
expression on the left is called the impulse. So the impulse is equal to the
change in momentum. t is the time
we must apply the force F in order to
produce a change in momentum.
The
equation can be written as,
In the
case of the crash in a car without airbags, at the moment of the crash the
passenger will start moving at 60 mph toward the dash. At the very moment that
the passenger hits the dash, a force F will be
applied by the dash to the passenger (Newton's first law) and in practically
zero time (because the dash does not subside) the speed of the passenger goes
to zero. Looking at the last equation, we see that the force the dash is
applying to the passenger is almost infinity. This, of course, will kill the
passenger.
If airbags
are available, the passenger will hit the airbag instead of the dash. As soon
as the passenger hits the airbag, a force F will be
applied to the passenger by the bag, but because the airbag is flexible this
force will be applied during a finite time (not zero). This is the time
measured from the moment the passenger touches the bag until the speed of the
passenger is zero. Because the time is not zero, we see from the above equation
that the force is not infinity.
Therefore
airbags save lives because they allow the force used to stop the speed of the
passenger to act for a certain period of time.
