If two autos of the same size and mass  collide head on, does it
matter, in terms of damage to the vehicles or injury to occupants,
whether the speeds were 90 and 30 MPH, or 60 and 60 MPH?  I understand
that motion is relative, and that in outer space (for instance the
collision of asteroids) it shouldn't matter.  But perhaps in the case
of autos there are practical considerations, such as rubber tires
on asphalt, or ...????

pdq2


pdq2

        It does matter, in the space or on the road. Speed is relative, true,
but that does not mean it is irrelevant. In common language people would say
"it's all relative" and mean sometime 'not important, not real'. In physics
 it means that speed of one body is measured by monitoring change of distance
to another body (rather then to 'absolute' space.) 

 The peak force obtained during the impact is (in rough approximation)

   2 * mass * velocity / contact-time

  Contact time is shorter for hard, inelastic bodies. It may be as short as
10 ms for metal, 100 ms for hard rubber, wood, etc.

  So, the peak force (which breaks things) is 

 proportional to relative speed  of the colliding objects.

Here is an illustration of impact in space:
http://deepimpact.jpl.nasa.gov/science/cratering.html

In automobile collision, speed is the second most important factor
determining extent of the injury

1) Type of vehicle striking and struck - Mass ratio.
2) speed of travel - This is of absolute importance at high speeds. At
low speeds, the correlation between crash velocity and injury
occurrence is less predictable
http://www.theberries.ns.ca/Archives/Whiplash.html

 So safety rule is : slow down

Hedgie

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Request for Answer Clarification by pdq2-ga on 30 Aug 2005 23:38 PDT

I think Hedgie is wrong in his answer, for example, in his comment
about what happens in outer space..  Racecar seems more on the mark,
but wouldn't the car traveling 90 MPH have a tendency to keep plowing
forward and push the slower moving car backward?  Would this then make
a difference to damage or injury?

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Clarification of Answer by hedgie-ga on 31 Aug 2005 07:43 PDT

I have indeed misinterpreted  your question.
 I was explaining that the magnitude of relative speed is important.

 For the two cases of  collision of two objects at

 1) 60 and -60 
and
 2) 90 and -30
 
 the objects have the same relative speed (v1-v2) but two cases will
have slightly different outcomes.

Racecar is right saying that 
" the initial impact will still have exactly the same effect on each car. "

I would add 'almost' since the center of mass of the system is
moving in the second case, so there are some extra forces during the
collision. Effect is small since contact-time is short.

The center-of-mass system is described here:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Momentum/CenterOfMassMomentum.htm
This reference  also explains the difference between 'elastic' and
'inelastic' collisions - which describes the amount of energy
'dissipated in the collision.'

As further explained here, the wrecks in case 2) will move after the collision
http://hyperphysics.phy-astr.gsu.edu/hbase/col1d.html
and may incur additional damage.

The animation shown here describes a slightly different situation
(different masses) where  total momentum is non-zero, as in our  case
2)
 http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/momentum/cthoi.html

The cars may bounce apart and when both wrecks are moving in the
direction of the original total momentum, car which has lost momentum,
may even catch up, leading to multiple impacts.

 I cannot say much about 'tumbling' after the collision, as that 
depend on details of cars, road, and  parameters of impact and the
road..
http://www.lboro.ac.uk/research/esri/vsrc/pdf files/RF IRCOBI 2001.pdf

  So, the answer to the question correctly interpreted is:
 
  The difference between case 1 and 2, the total momentum,
  will have a small effect in principle, but a negligible effect for practical
  purposes, as long as we consider the primary collision only
  rather than the fates of the cars after the first impact.

  This small effect makes the high-energy case, case 2) a tiny bit
more dangerous. The effect can be quantified if we would know contact
time and
friction data for the road and tires.

P.S.  In  case 2, the high enefgy case, the "system" of the two cars
considered as a whole has more energy. The extra energy is dissipated
after the first impact.

Hedgie

In outer space, of course you are right that it does not matter. 
There, in fact, there is no way to say whether one car is going 30 and
the other 90, whether both are going 60, or whether one is going 120
and the other is standing still.  There is no absolute rest frame.  I
know that hedgie knows this; I think as English is not his first
language, he may have misunderstood the question.  On land, as you
say, there are practical considerations.  The initial impact will
still have exactly the same effect on each car (and I think for head
on collisions, the initial impact is where almost all the damage
occurs), but after the collision, one of the cars or the other will
probably bounce and tumble around more than the other, possibly doing
some additional damage.  It is not obvious whether the 90 mph car or
the 30 mph car will tumble more--it depends on how much energy is
dissipated in the collision, among other things.

PDQ2,
 I think this passage from the  "theberries" website supports your clarification:

"Type of vehicle striking and struck - Mass ratio.  The weight or mass
of the striking and struck vehicle have significant influence on
injury occurrence. E.g. A large car of 4000 lb and a small car of 2000
lb hit head-on at 30 mph. Mass ration is 2:1. At collision, larger car
will slow to 10 mph and the smaller car will be instantly propelled
backwards at 10 mph. Larger car has a 20 mph total velocity change
while smaller car has 40 mph velocity change. Smaller cars have more
severe crash injuries."

If the cars have the same mass, the one with the higher speed will
have greater intertia and plow ahead, pushing the slower car back. 
Maybe the damage to the vehicles remains unchanged, but for the
passengers this will be significant.

I wonder if this is supported by airbag statistics  - probably at
lower speeds - i.e., that those in the faster car were not not set
off, but those in the slower car were.

Myoarin

For "what it's worth" as they say .. 2 vehicles at the same constant speed
approaching one another .. double the speed to calculate the force.
The momentum of both vehicles in collision will of course create more
impact
compared to one vehicle being stationary, whilst the other is travelling at
twice the speed.

Hmm .. perhaps.

While this is tangential to the original question about damage to the
cars: if one is travelling slower than the other it will be pushed
back in the direction it was coming from. In real life this car is
more likely to be involved in secondary crashes from following cars