In this coordinate system, we have the following picture:. Consider the perfectly elastic collision between two massive point objects moving with individual velocities:. Some of the kinetic energy is converted into sound, heat, and deformation of the objects.
The relationship between kinetic energy and velocity is exponential, which means that as you increase your speed, kinetic energy increases dramatically.
Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic. We can find the motion of the center of mass by utilizing the definition that the net momentum is equal to the total mass times the velocity of the center of mass:.
There are two general types of collisions in physics: Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force.
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. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles out of contact with each other.
In this limit, the change in velocity for ball 1 is 2 times time difference between their original velocities, i. A car's bumper works by using this principle to prevent damage.
Making their bumpers this way benefits the car companies: However, car bumpers are often made to collapse if the speed is high enough, and not use the benefits of an elastic collision. The problem is much more easily solved in the center of mass coordinate system because the total momentum in that coordinate system is zero. Ball 2 on the other hand, has a change of velocity that tends towards zero, that is, it is unaffected by the much smaller ball bouncing off of it. 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.
For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic.
This implies that there is no dissipative force acting during the collision and that all of the kinetic energy of the objects before the collision is still in the form of kinetic energy afterward.
Almost no energy is lost to sound, heat, or deformation. Two rubber balls are a good example. Momentum is conserved, because the total momentum of both objects before and after the collision is the same.
Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic. If two balls are sent in, two come out, and so forth.