50-100 dumb ways to die

Classical Mechanics Level 2

Which of these scenarios will exert more force on your vehicle?

Scenario A : Crashing head-on at 50 mph with another identical car traveling at 50 mph.

Scenario B : Crashing into an unbreakable wall at 50 mph.

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Scenario B They are both the same! Scenario A

Alex Li by Alex Li , 22, USA

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2 solutions

Alex Li
Jul 30, 2015

Contrary to popular belief, Scenario A is not equivalent to a collision at 100 100 mph; it normally would be equivalent to a collision at 50 50 mph. In fact, Scenario B is more damaging, because Scenario A will allow the car to penetrate into the other vehicle, which will slightly reduce the deceleration, while the wall is impenetrable.

For more information: See this .

(Next time you read an article stating that head-on collision is double the usual force, spit on that nonsense and remember Newton's Laws!)

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This is debatable. First, I agree with Steven that it should be stated that we are dealing with identical vehicles to make the question tractable. Second, there is twice the energy involved in scenario A than in scenario B prior to the crash, but after the crash in scenario A that energy is evenly dissipated between the two (identical) cars, resulting in the same amount of damage to my car in both scenarios.

If we were to imagine a vertical plane dividing the two identical cars at the point of impact, then the compression of each car on either side of this dividing plane would be equal, and thus, (in my mind, anyway), we could essentially imagine the dividing plane as equivalent to the unbreakable wall. The "penetration" of the two cars into each other seems rather arbitrary, so I'm not sure if it a valid argument for choosing scenario B. I'd be interested to hear what others have to say.

Brian Charlesworth - 5 years, 10 months ago

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I've added clarification that the two cars are identical.

Alex Li - 5 years, 10 months ago

It seems to me that it partially depends on the relative masses of the vehicles. For substantially identical vehicles, you are likely correct, assuming the wall is completely unbreakable as stated.

Steven Perkins - 5 years, 10 months ago

If the cars are perfectly identical, and lined up in the collision, every piece of car from the right side should collide with the corresponding piece of car from the left side exactly at the dividing line, just like hitting a wall.

Josh Silverman Staff - 5 years, 10 months ago
Curtis Clement
Aug 3, 2015

It is important to note that we are talking about force rather than momentum or kinetic energy. We could F= ma (Newton's 2nd Law) to prove that the forces exerted on the car is equal in both scenarios. Now the assumption that the car's are identical and moving at the same speed (in opposite direction) means that the (negative) acceleration is the same in both circumstances. The mass of the car is unchanged, so the F= ma force is also unchanged.

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