Newton's Third Law and Car Crashes

[Balsam]

Homework Statement

In terms of Newton's Third Law, why is it better for 2 cars of the same mass, both going 50km/h to crash into each other than for 1 car going 100km/h to crash into a wall?

Homework Equations

Newton's Third Law
F=ma

The Attempt at a Solution

I have no idea. I'm really confused

 

[giokrutoi]

what do you mean in better

 

[RUber]

If there are two cars, each one will be subjected to the other's opposing force. If there is one car, and you assume the wall is strong enough to fully stop the car, it will be subjected to the larger resisting force of the wall.

Let's say that $F_1$ is generated by car 1 and $F_2$ is generated by car 2, then $F_1= -F_2$ for a perfect head-on crash ending in full stop.
Let's say that $F_3$ is generated by the fast (100km/hr) car 3 and $F_4$ is generated by the wall, then $F_3= -F_4$ for a car-on-wall crash ending in full stop.

 

[Balsam]

what do you mean in better

Less damaging

 

[Balsam]

If there are two cars, each one will be subjected to the other's opposing force. If there is one car, and you assume the wall is strong enough to fully stop the car, it will be subjected to the larger resisting force of the wall.

Let's say that $F_1$ is generated by car 1 and $F_2$ is generated by car 2, then $F_1= -F_2$ for a perfect head-on crash ending in full stop.
Let's say that $F_3$ is generated by the fast (100km/hr) car 3 and $F_4$ is generated by the wall, then $F_3= -F_4$ for a car-on-wall crash ending in full stop.

Of the 2 cars, each exerts a lesser force since their collision velocity is less. Whereas if the car crashed into the wall, the wall would exert a stronger reaction force on the car because of the increased velocity at the point of impact? Is this true?

 

[RUber]

That's about right. I would assume that in all cases, it takes the same time for the cars to come to a stop. Thus, acceleration would be proportional to velocity.
More velocity brought down to zero velocity over the same time results in more force.
There are finer points when you deal with impulses and collisions, but as it refers to F=ma, this is the most fundamental explanation.
More velocity, same mass, same time => more force.

 

[Balsam]

That's about right. I would assume that in all cases, it takes the same time for the cars to come to a stop. Thus, acceleration would be proportional to velocity.
More velocity brought down to zero velocity over the same time results in more force.
There are finer points when you deal with impulses and collisions, but as it refers to F=ma, this is the most fundamental explanation.
More velocity, same mass, same time => more force.

What if the masses were different for the 2 cars? I'm not sure how mass affects this situation

 

[RUber]

Then you would not expect both cars to come to a full stop.