Mr X
Conservation of momentum.
The upper bound for a perfectly elastic collision is pretty extreme. buttuming for the moment a perfectly elastic dog in an ideal collision.
Before: Dog mbutt m doing 0mph the car mbutt M doing V mph. After : Dog mbutt m doing V(m+M)-2m car doing 0mph
The extreme case of perfectly inelastic collision puts a lower bound on the outcome where the dog becomes bonnet ornament attached to vehicle.
After : Dog+Car mbutt m+M doing MV-(M+m)
For a big 25kg dog and 1T car (same ratio as a 1T car to 40T HGV).
Max possible speed for dog after a perfectly elastic collision is about 20V and the car is made stationary. Minimum speed for the dog in an inelastic collision is still almost V. Real collisions are much messier to compute but must sit somewhere in between these extremes.
In practice animals tend to spatter and are quite inelastic so the speed imparted to the carcbutt is a lot less. Energy delivered is even more unkindly divided - the low mbutt party suffers most of the damage.
I don't offhand know the coefficient of resbreastution of a dog, but I would hazard a guess that it is at least 10% so this means that the dog could be thrown back (or upwards) from a head on crash at about twice the speed the car hits it.
It is easily demonstrated with a pair of unequal sized superballs. Place the small one on top of the big one and drop the pair together onto a hard floor. Wear safety specs and don't do it anywhere that the little ball can break windows or ornaments when it goes into orbit.
Conservation of momentum is fundamental in collisions. Whereas energy is only conserved in perfectly elastic collisions and in real ones it goes into sound, crumple zones, bent metal and mashed animal.
Regards, Martin Brown
