I’m reading a book that mentions an incident involving a teenage girl deliberately crashing head-on into oncoming traffic in order to commit suicide. The author (not a physicist) writes the following:
Her focus on her goal of suicide may have had paradoxical effects; the more she accelerated toward the oncoming car as it braked, the more momentum transferred to the other car, making it more likely that she would kill or injure those in the other car but not herself.
(For the record, this girl survived but the driver of the other car did not)
Despite having an engineering degree and having taken the full sequence of calculus-based physics, I’m not as certain of where I come out on this as I’d like to be. My initial thought was that the primary consideration in a two-car accident was the speed of the vehicles relative to one another. If car A is going 50 mph and car B is going 50 mph in the opposite direction, each car’s speed relative to the other is 100 mph. If car A is going 75 mph and car B is going 25 mph, their relative speeds don’t change.
I looked at the passage again and the author specifically talked about momentum transfer, so I thought about conservation of momentum. I assumed a close system and worked out a few different scenarios, and each case resulted in both cars experiencing the same change in momentum as a result of the collision (provided I kept the relative speed the same in each case).
My takeaway, then, is that the victim in the passage above did not suffer a worse collision outcome as a result of braking. I’m inclined to believe it’d increased the likelihood of surviving for both drivers. I googled around a bit and did not see anything to the contrary. Did I misunderstand the author or is he mistaken in his assertion?
Assuming the masses of both vehicles are the same, the primary consideration is the speed of each vehicle measured relative to the combined center of mass of both vehicles.
If A and B are approaching each other at 50 MPH absolute, the combined CoM is stationary, and each car experiences a crash equivalent to hitting an immovable wall.
If A is going 75 MPH absolute and B 25 MPH absolute, the combined center of mass is moving toward B at 25 MPH absolute. This means A’s speed relative to that moving CoM is 50 MPH, and B’s speed relative to that moving CoM is also 50 MPH. The violence of the crash is the the same for each vehicle as in the previous scenario.
If one of the vehicles is braking at 1g during the collision, they add that decel to whatever decel is being provided by the interaction with the other vehicle, so the braking vehicle would experience a larger total decel (i.e. a more violent crash). I’m having trouble thinking this through, but I suspect this also means that the unbraked vehicle has its crash decel reduced by 1g compared to what it would experience if nobody were braking.
Imagine two cars in deep space with no reference points. They collide at 100mph. There is absolutely no way the cars can tell (absent reference to another point) which contributed what to the collision. And even if from the perspective of an external observer it appeared one car was stationary and the other moving at 100mph, or vice versa, that observation is irrelevant to the experience of the cars themselves.
The introduction of a planet and a road does not change this scenario, as far as the cars are concerned.
Actually now that I think about it there is an even easier thought experiment.
Imagine suicide girl decides she’s going to kill herself by driving head on into another car at 3mph. The other car is doing 100mph. According to this author, the other car is making their situation worse by braking.
Take that to it’s logical conclusion - if the other car manages to brake to 1mph before the collision, the collision would occur at 4mph. But according to this author, it would have been better for the occupants of the other car not to brake, such that the collision happened at 103mph!
We are not told at what point the other driver begins to brake, but the scenario is that the combined speed at the point of collision is 100mph. This implies that the other car was travelling faster when they saw SG and were braking hard at impact. Thus adding their deceleration to the effect of the collision.
How do you see that as relevant? At the point of collision they are doing a certain speed. The speed they were going immediately before that - due to either acceleration or deceleration - is irrelevant.
The only way anything other than relative velocity at the moment of collision could have any effect at all is through the brakes of the car(s), but the forces exerted by the brakes would be negligible compared to the forces from the collision itself. Her accelerating certainly made it more likely that the occupants of the other car would die, but certainly did not improve her own odds of survival.
I think the braking car helped their chances by braking, not worsened them.
The energy is the important consideration here, and it’s proportional to the square of the relative velocity between the cars.
Momentum had to be conserved, yes, but the consequence of that is how fast each car is skidding away from the impact. Unless the braking car got propelled backwards over a cliff, or some such, with that consequence being important, I think the momentum per se wasn’t relevant to survival.
Conservation of momentum implies that if car A is going faster than Car B, the end result of an inelastic collision would be both cars moving in the direction of car A, meaning that the impulse applied to car B would be more than the impulse applied to car A.
So having car B brake would certainly improve the odds of A surviving, both because the force of impact is lower and because momentum transfer would keep A going while B would change directions and the impulse on B would be greater.
Just to put some concrete numbers to this:
100 mph is about 45 m/s. If the total crumple distance on the cars is 4 meters, we get a deceleration of 253 m/s^2, or 26 gees. That’s in comparison to the ~1 gee from the braking.
4 meters of crumple distance is probably generous, too. Not to mention non-linear. Peak deceleration is likely 50-100 gees.
I had worked out a few scenarios with the two cars going different velocities (but the same relative speed to one another) and the change in momentum for each car after the crash was the same in all scenarios. Furthermore, both cars experienced identical changes in momentum (I assumed the cars were identical).
I did think Machine Elf made a good point about the implication of the victim’s car braking during the collision, but from what Chronos and Dr. Strangelove say, it looks like whatever deceleration is added as a result is negligible when compared to the deceleration resulting from the impact itself.
Why? I’m talking about impulse, not energy or momentum. Impulse is force over time. An airbag going off in one of the cars changes the impulse felt by the occupant without changing the nature of the collision. I’m just saying that while momentum is conserved, felt impulse may be different.
Also, if two cars are going 50 mph each and collide, they both come to rest and momentum is conserved. But kinetic energy is not - kinetic energy goes to zero, and it is converted to heat, deformation of materials, noise, damage to the bodies, etc.
Now imagine one car going 75, and the other going 25. Momentum before the collision is the same as in the 50/50 case. However, after the collision the two vehicles will continue to move in the direction of the faster one, retaining some kinetic energy which doesn’t then get dissipated as damage.
The faster car will continue in the same direction after the collision, so speed of deceleration (impulse) is different than in the slower car, which will go from moving forwards to backwards. The deceleration impulse will be less in the faster car than in the slower one, right?
Wondering if acceleration, causes the front of the car to rise, thereby if a accelerating car hits another car, the accelerating car will have more of a chance of “going over” the other car thereby causing more injuries to the car beneath ?
There’s more kinetic energy left over (in the road’s reference frame) because (in that reference frame) there was more kinetic energy to begin with. The same amount is dissipated as damage.
Impulse is the integral of change in momentum over time.
If you hit a brick wall and it takes you .5 seconds to stop, the impulse is much higher than if it takes you 1 second to stop. The change in momentum is the same.
Lets go simple. A car traveling at 50mph striking another car of equal mass and design would be the same as one car hitting a solid brick wall. When both cars hit they should stop at the point of impact with a little bounce back.
Now one car going 75 mph head on to another going 25 mph. The 75 mph car is going stop over a longer time and is going to push the slower car backwards. The 25 mph car is going to stop in an instant and start to roll back wards. Ther will be a greater change of velocity. more deacceleration.
A test. take two balls the same mass each tied to a string. One stationary the 2nd ball pulled back and let swing into the 1st ball what happens. Now make one of the balls 1/2 the mass and repeat.
Kinetic energy.
If two identical objects collide head on at different velocities, one has more kinetic energy.
A structure has mass. Speed adds kinetic energy to that mass.
So the object going at lower speed has less kinetic energy at every point of its mass. At any point of contact, the equal mass with lower kinetic energy, will deform more in response to the same mass with more kinetic energy. I think…
The two objects are not equal in all aspects of energy.