The question is whether a head-on collision between two identical car traveling at a speed S is the same as one of the same cars driving into an immovable wall at S or at 2S. The answer is that it is at the same speed S as each of the 2 cars. This can be seen from the fact that in both the head-on and immovable wall case each car stops completely at the point of impact. The change in momentum for the individual cars is the same independent of what it collides with. The change in momentum is equal to the time integral of the forces acting on the car and the effects are the same. In effect each car is effectively an immovable wall to the other car.
Energy is measured in joules, not in “Newtons of energy” or newtons. Work requires that force be applied over a distance; hence, one joule = one newton-meter (one joule of energy is equivalent to one newton of force acting over a distance of one meter).
Ask Bill in Maine (last weeks show) to donate his three identical cars for this physics lesson.
“What’s your vector, Victor?” (http://www.killerclips.com/util/view-greeting.php?mqg=24700)
You were not clear. AS you state, even you had to go back and listen several times.
Energy is the integral of the force or momentum equation. Hence they are related. The fate of one quantity matches the other. No way about that. The problem with vectors is getting the problem in the proper context. And getting the right question.
Interesting, you can criticize but not offer enlightenment. Good application of the social principal, screw the world, I will climb to the top of the heap of dead carcasses.
Clarification, it is your organs that do the getting hurt.
Car is moving and stops, then you are moving and stop, then you organs are moving and stop (against your body cavity.
Whether the stone hits the pitcher or the pitcher hits the stone, it’s gonna be bad for the pitcher.
The real question is if you crash into the other car v. the wall can you still donate the car to Car Talk for an environmental credit?
Well that depends if it is leaking or not.
What are the criteria to trade a car in?
You put forth too many questions. Read Tyler’s post for clarification on your confusion. And look up what the integral gives you too.
A small correction to my post on 06/02/2008 at 7:26 p.m.
I said I was working with a simploified version of the problem and included “conservation of energy.” I was imprecise: energy is always conservevd. What I meant to say was I considered only conservative forces. That is, all collisions are totally elastic – no energy dissipation.
It looks like Speed Bump updated his old response with your fix within a day of your catching it. Good for both of you.
Where are you with this now? The two cases (car@60-vs-car@60 & wall-vs-car@60) are the same, yes?
Your A has withstood the test of time.
Thank you Professor Paul, this should have ended the controversy.
if the two cars are
completely identical, they would compact in
the same way. say you put a high speed
camera, that watches the crash from the side,
the two cars would bend and break in the same
exact way, in the end it would look like
there was a wall between them. There for the
crash would be the same as hitting a brick
wall going 60MPH not 120MPH. Now your answer
was correct if the cars are not completely
identical in every way.
Only one question is discussed and that is the question from the show and the correct answer to that question is in the second sentence. The rest is an explanation. As stated above the integral is the change in momentum.
Intuitions differ. Mine “feels” like a car going from 60mph to 0mph upon a head-on collision with an identical car is like a car going from 60mph to 0mph upon a collision with an immovable wall. It seems some intuitions “feel” like going from 60mph to 0mph because of a collision with a car would be like going from 120mph to 0mph because of a collision with a wall. The physics behind the crash indicates the caller was right, it would [i]feel the same[/i] whether car or wall. The dad’s intuition (and Ray’s & Tom’s, along with many contributors’ here) differs. I offer the following intuitively only view:
If you were going to have a head-on collision, you would rather have it be with a smaller, slower vehicle than with a larger, faster one; yes? The heavier the vehicle you collide with is, the slower it need be moving in order to bring you to a complete stop (think M1A2 Abrams main battle tank!). In fact, if it is large enough, it need not be moving at all (think wall!). On the other hand, if the vehicle is lighter than yours, it can still bring yours to a stop if it is moving quickly enough. The number crunchers here, and there are MANY of them, can provide the math behind creating equal momentums for cars of unequal masses; and, they can find the correct ratios between velocities and masses to balance the kinetic energy equations. My hope is to help those whose intuition led them astray. Ray & Tom, feel the force(s) ~ ~ ~ 
Guy’s, I think we settled this about 100 posts ago. Do we need to call in a middle school science teacher?