Types of Collisions
A collision is an event where momentum or kinetic energy is transferred from one object to another. Momentum (p) is the product of mass and velocity (p = mv). A large truck massing 10,000 kg and moving at 2 meters/sec has the same momentum as a 1,000 kg compact car moving at 20 meters/sec; they both have p = 20,000 kg m/sec. The other quantity that can be transferred in a collision is kinetic energy. Kinetic energy is the energy of motion; it is defined as K = (1/2) m v^2. The relationship between kinetic energy and mass is linear, which means that a vehicle massing twice as much has twice as much kinetic energy. The relationship between kinetic energy and velocity is exponential, which means that as you increase your speed, kinetic energy increases dramatically.
There are two general types of collisions in physics: elastic and inelastic. An inelastic collisions occurs when two objects collide and do not bounce away from each other.
Momentum is conserved, because the total momentum of both objects before and after the collision is the same. However, kinetic energy is not conserved. Some of the kinetic energy is converted into sound, heat, and deformation of the objects. A high speed car collision is an inelastic collision. In the above example, if you calculated the momentum of the cars before the collision and added it together, it would be equal to the momentum after the collision when the two cars are stuck together. However, if you calculated the kinetic energy before and after the collision, you would find some of it had been converted to other forms of energy.
An elastic collision occurs when the two objects "bounce" apart when they collide. Two rubber balls are a good example.
In an elastic collision, both momentum and kinetic energy are conserved. Almost no energy is lost to sound, heat, or deformation. The first rubber ball deforms, but then quickly bounces back to its former shape, and transfers almost all the kinetic energy to the second ball.
A car's bumper works by using this principle to prevent damage. In a low speed collision, the kinetic energy is small enough that the bumper can deform and then bounce back, transferring all the energy directly back into motion. Almost no energy is converted into heat, noise, or damage to the body of the car, as it would in an inelastic collision.
However, car bumpers are often made to collapse if the speed is high enough, and not use the benefits of an elastic collision. The rational is that if you are going to collide with something at a high speed, it is better to allow the kinetic energy to crumple the bumper in an inelastic collision than let the bumper shake you around as your car bounces in an elastic collision. Making their bumpers this way benefits the car companies: they get to sell you a new bumper, and you can't sue them for whiplash.