Ratio of Kinetic Energy lost in a collision.

[Yuqing]

For collisions wouldn't the distance traveled during the collision be the same? The energy lost is from heat, sound, deformation, etc. but wouldn't the work done on each car be the same since during the duration of contact they have to move the same distance (as soon as they move different distances they are no longer in contact) and apply the opposite but equal force?

So is there a set ratio of kinetic energy lost for each object? If not, can anyone give me an example where the force is applied over different distances for a collision because I can't think of any examples.

 

[kuruman]

You are mostly correct. The magnitude of the work done on car A by car B is the same as the magnitude of the work done on B by A. Their signs are opposite because the directions of the forces that do the work are equal in magnitude and opposite in direction. That's s clear loss of energy by one object and gain by the other. However, the ratio is not set but depends on the object. For example, consider two colliding shells partilly filled with water. The ratio of kinetic energy lost will vary depending on if the water is frozen in both balls, or in only one ball or in none. When some of the kinetic energy is converted into internal energy, the ratio depends on the specifics.