Re: Momentum

[Doug Craigen <dcc@ESCAPE.CA>]

> The original question was whether a head-on collision between two cars,
> each going 35 mph, was equivalent to a car hitting a tree at 70 mph.
>  The answer is no.  The collision between two cars each going 35 mph is
> more equivalent to a car hitting a tree at 35 mph.

A curious thing to me is how hard we jump on something that *almost*
correct.  According to the parenting advice we follow, if one of my kids
had suggested this I would have started by praising them for knowing
about relativity of motion and would have then sought to show them where
the error lay in their application.

In this case, we start by saying that if we are in a reference frame
(the center of mass frame to be precise) where we see 2 cars collide,
each with a speed of 35 mph, then surely the result must be the same as
that seen by each driver who sees a collision of themself being parked
and getting hit by a car going 70 mph.  The error lies in equating a
parked car with a tree.  Quite aside from small details of crumple zones
etc, the fact is that the center of mass frame when one of the objects
is fixed (infinite mass) is the frame where that object is at rest.
Since the center of mass frame is different than for the case of 2 cars
colliding head on, it is a different problem.

Beyond this there are various levels of demonstrating the differences if
one wishes.  From a momentum/impulse point of view we have twice as
large a jolt coming to rest from 70 as compared to coming to rest from
35.  From an average force point of view it gets messy since we need to
know the duration of the collisions.  From an energy point of view there
is twice as much total kinetic energy in the collision at 70 with the
tree (70^2 compared with 35^2 + 35^2).

()-()-()-()-()-()-()-()-()-()-()-()-()-()-()-()

Doug Craigen
          Latest Project - the Physics E-source
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