This may be a silly question, but I’ve been thinking about it for a long time, and hopefully someone here can give me the answer…
If you drive a car with a constant speed of, say 60 mph, and you hit a brickwall, will the impact be weaker than if you accellerate very quickly and hit the wall at the exact moment when you reach 60 mph?
(Please forgive my English, as Norwegian is my native language…)
Since what your talking about is conservation of momentum, and momentum is mass times velocity. My guess would me that it would make no difference. When you enter velocity into the equation, you would use the velocity at that instant. I think you would have to assume, though, that at the exact instant it happened your speed was infact constant. But it has been several years since I’ve cracked open a physics book, and IIRC whenever we did conservation of momentum problems you always used a constant velocity, even when IRL the velocity would not have been contant (ie jumping from one moving object to another and assuming that the jump was at a constant speed). I don’t think we ever dealt with accelarating objects with these equations. I suppose there could be a reason.
BTW this was a calculus based class, so if accelelaration was a major issue (more then negligable) I don’t think it would have been that hard to work into the equation.
I think Joey P is essentially correct. Given that the rate of acceleration for a car is very small in relation to the timespan of a collision between said car and a solid wall, I should think a first-order approximation using the instantaneous velocity would be more than adequate.
Think of it this way. In order for the car to decellerate, there has to be a force acting on it from the front (from the wall, of course). In the first case (constant speed) this is the only force involved, but in the second case (accelerating) you’ve also got a force in the opposite direction pushing the car forward. More force from the wall is going to be required to stop the car in the second case, since it has to balance out the force from the momentum of the car plus the force from the engine’s acceleration.
If I understand what your saying, then I thought of that. So I assumed at the instant the wall was hit the accelaration stopped. Otherwise, it would be another force to take into consideration like friction (which is commonly ignored unless that’s what your specifacally working with). Of course empirical and experimental results are going to differ. (any volunteers)
I really appreciate your replies, allthough I must admit I have allready thought of the possibility that I have to consider the speed being constant at the exact moment of the impact, even though the car is accellerating.
It sounds reasonable…
Maybe the correct question is: Is accelleration a force? The answer is no…
-Isn’t it?
If we are willing to make several reasonable approximations:
force = mass*acceleration, in this case mass is constant so the accelertion on the car would be a direct measure of the force acting on it.
Repeating the same thing that’s been said before in a different wording, because I want to contribute and it might have been unclear (1 chance in a 1,000).
It depends on the wall, but the best answer “they’re the same.” F=MA, and the car going 60->0 is the effective (net) acceleration, which is 60 divided by how much time it takes the car to stop. The difference is negligible.
For tiny differences, though… if the wall is small enough for the car to move a bit (but not indefinitely), then the accellerating car experiences a slower acceleration, because it’s pushing forward and thus takes more time to slow down.
If the car continues to accelerate after the front hits (Front crumples and engine continues to provide power), it will be experience negligibly more force afterwards, because it would have decellerated less when the driver runs out of room to crumple.
Ignoring these two damn-near-impossible cases, though, it’s the same.
This may be a small point, but in the real world, I would prefer being the car that was doing a stable 60 as opposed to hard acceleration.
When the car hits the wall and the car frame frame begins to slow down, the springs (or whatever provides the cushion) in the seat of the accelerating car will continue to to accelerate the driver towards the now slowing steering wheel.
Even better would be if the car was decelerating hard and hit at 60. The seatbelt would already be tight and hold you where it should.
And I who thought that this was just a simple yes or no question…
