Help with Kinematic Problem?

Question

Suppose you are driving a car. Would you rather collide into another car (with same mass) with the same speed coming straight at you or collide into a solid wall at twice the speed? Make appropriate assumptions on the coefficient of restitution or duration of collision

Answer 1

Assume inelastic collisions:

Case 1:

initial vel = v

final vel = 0

for both cars

So your car absorbs 1/2 mv^2 of KE from the other car

Case 2:

initial mom = 2mv

your final vel = 0

Initial KE = 2mv^2

This KE is absorbed by the car and the wall. If the wall is indestructible, then all of it will be absorbed by the car making Case 2 worse than Case 1.

However if the wall is made in such a way that it absorbs a lot of the KE, then I'd rather hit the wall. It really depends on what the wall is made of.

Answer 2

In your example, I would definitely choose the head-on collision at speed = 1 X, and NOT colliding with the solid wall at 2 X.  

This is a classic problem that fools even the most skilled and educated people - I had engineers at each other's throats over this one.

As it turns out, colliding with a solid, immovable object versus a head-on collision with a another car (of the same mass) is precisely equal (assuming the same speeds in both cases).

You can envision it like this:

1) In the collision with a solid object, the front of your car will stop at the surface of the wall.

2) In the collision with another car of matched mass and velocity, the front of your car will stop at the interface betwen your car and the one you are collding with.

In both cases, exactly the same crush and deceleration will occur to your car.    IOW, in both cases, the point of impact does not move in space.