Castellan said:Try another example. Let's say two cars heading in opposite directions strike the same building, clearly an immovable object. For each of them, the building absorbs the energy of the collision and imparts no net force on the cars whatsoever. We can't deny that.
Uh, no.
If the car experiences a change in velocity, it experiences an acceleration. If it experiences an acceleration, it experiences a force. You cannot change the velocity of the car without applying a foce to it.
The "no net force" is a deliberately misleading statement. It is generally inappropriate to add forces that act on different objects and claim there is no net force. The fact that you are correct in particulars later doesn't make this correct.
There's a better way to approach this. Each car goes from moving at some speed to a stop. They must feel some acceleration, and therefore there are forces doing work upon them.
However, the only source of work in the system is the kinetic energy of the two cars. The work done on Car #1 plus the work done on Car #2 cannot exceed the total kinetic energy in the system. If the two cars are identical, then by symmetry they have the the same work done upon them. Each car, then experiences work equal to half the total kinetic energy in the system.