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Comments on If you're stopped and about to be hit from behind, should you brake or release the brake?

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If you're stopped and about to be hit from behind, should you brake or release the brake?

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The title is a framing for a theoretical question; I'm not asking for practical advice. A friend was recently in this situation and my attempts to apply what I remember of a couple semesters of college physics were inconclusive.

Suppose you are in a stopped car. You notice another car behind you moving too quickly to stop before hitting you. Your goal is to minimize your injury. Strictly from a physics perspective of these two cars, are you better off braking hard or releasing the brake so you'll be pushed? My gut feeling (assuming no one's in front of you) is that you should do the latter, but my friend and I got into a conversation about elastic and inelastic collisions and the effects of friction and of the masses of the two vehicles (if not similar), and now neither one of us knows how to answer the question with physics rather than with gut feels.

A comment pointed out that the speed of the moving car is important. Assume the stopped car is in city traffic (say, stopped at a traffic signal) and the car bearing down on it is going about 25mph.

In this collision, some force will be absorbed by the car being hit, some will be absorbed by the car doing the hitting, some will go into forward momentum (the front car being pushed), and some will be lost to friction. Some of the force that goes into the car being hit will be transmitted to the occupants and some to the car itself (crumple zones etc). How should I think about these forces and their distribution in the two scenarios (braking and not braking)? And how do the relative masses of the vehicles affect the outcome? A car hitting a car seems different from a motorcycle hitting a semi (or vice versa), but when does a less-extreme difference still matter?

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1 comment thread

What's the closing speed? (3 comments)
What's the closing speed?
Canina‭ wrote over 1 year ago · edited over 1 year ago

I think a fair portion of the answer to this question depends heavily on the closing speed of the two cars. For simplicity, spherical cow style, assume equal crumple zones fore and back that are equal on both identical cars. It then stands to reason that approximately half of the energy of the impact will initially be absorbed by each car. Kinetic energy grows with the square of the velocity, which in this case is going to be the relative speed at impact. (If the car behind you is braking or if the front and rear of each car don't have equal crumple zones, it gets more complex very quickly.) The kinetic energy of a collision of any kind at even, say, 20 km/h is hugely different from that at, say, 5 km/h. Assuming that the car being hit rolls freely (no braking, is in neutral or equivalent), then the brunt of the kinetic energy of the impact seems likely to be either taken up by the crumple zones or result in a forward acceleration, which absent braking must go into friction.

Canina‭ wrote over 1 year ago · edited over 1 year ago

If the front car is braking, that mostly changes how quickly the forward motion is converted into friction, because the brakes are designed to induce friction and the weight of the car in front would then be resting on mostly static wheels. (ABS may or may not make a difference here.)

There is also the issue of the jerk (by which I mean not the driver behind you, but the rate of change of acceleration). The initial impact is going to propel the front car forward, pushing the seats toward the occupants' backs. Being stopped from the front, as happens to the rearward car, is going to propel the occupants forward; they are going to hit the seatbelts (hopefully before moving too far) and then be thrown back toward the backs of their seats (all relative to some point in each respective car). This seems unlikely to have much of an effect on the total forces involved, but if the forces are great enough, it can very well make a very real medical difference for the occupants.

Monica Cellio‭ wrote over 1 year ago

Oh, good point -- I should have addressed speed. I'm assuming there's a spectrum where at one end it doesn't matter (too slow to be hurt) and at the other end it also doesn't matter (you're dead either way). I don't know what the "could make a difference" range is, but to keep this question from being too broad, I'll edit for the city-driving case that prompted the question.