2011-02-26, 06:30 PM
Maybe I should have provided an example.
A car of mass 1 kg, initially moving at 2 m/s, collides into another car of mass 1 kg, initially at rest. After the collision, they stick together, so since momentum is conserved, both cars have to move together at a velocity of 1 m/s. Now let's examine their energies. Before the collision: 1/2 (1 kg) (2 m/s)^2 = 2 J. After the collision: 1/2 (2 kg) (1 m/s)^2 = 1 J. Half the energy just "disappeared"... assumed to disappear into heat, sound, whatever other by-product.
If we do this the other way, and assume that all the energy is conserved, then the final velocities of the cars have to be sqrt(2) m/s, but it's just not... or at least, it's not in most sources. Momentum somehow takes always priority in these calculations.
What is the mathematical basis for this assumption?
A car of mass 1 kg, initially moving at 2 m/s, collides into another car of mass 1 kg, initially at rest. After the collision, they stick together, so since momentum is conserved, both cars have to move together at a velocity of 1 m/s. Now let's examine their energies. Before the collision: 1/2 (1 kg) (2 m/s)^2 = 2 J. After the collision: 1/2 (2 kg) (1 m/s)^2 = 1 J. Half the energy just "disappeared"... assumed to disappear into heat, sound, whatever other by-product.
If we do this the other way, and assume that all the energy is conserved, then the final velocities of the cars have to be sqrt(2) m/s, but it's just not... or at least, it's not in most sources. Momentum somehow takes always priority in these calculations.
What is the mathematical basis for this assumption?