the cars are effectively hovercrafts: their weight is supported by the excess pressure in a thin layer between them and the track. The first examples are (almost perfectly) elastic collisions. During the collision, kinetic energy is briefly transferred into potential energy in a spring at the end of the car on the left, then back to kinetic energy again. This process is almost completely reversible, so the collision is almost completely elastic. The red line shows the horizontal position of the centre of mass . Because the two cars have equal mass, the centre of mass is halfway between their centres. In the example above, the centre of mass continues moving, at constant velocity, throughout the collision. The kinetic associated with the relative motion of the cars (the kinetic energy measured with respect to the centre of mass) is briefly turned into potential energy in the spring at the moment of maximum compression, and then converted back to kinetic energy. Conservation of momentum requires: initial = p final (1). We apply this in one dimension (x or horizontal). The mass of each car is m, the velocity in the the x direction is v for the car on the left and zero for the other. Let their final velocities be v 1 and v 2 respectively, so the above equation is: mv + 0  =  mv 1 + mv 2 so v  =  v 1 + v 2 (2). Because the collision is elastic , we can apply conservation of