When 2 particles collide in 1 dimension inelastically or when a
particle attached via an inextensible string to a smooth pulley is
dropped from rest and the string jerks taut, then kinetic energy is
lost from the system.
Is it possible to say what the energy becomes?
Alistair,
Within the laws of Newtonian physics - energy is always conserved.
Often when energy is said to be "lost" from the system, what is
meant is it is transfered to heat energy. An example of this is a
squash ball - after it has collided with the walls a number of
times it starts to warm up.
Hope this helps - you've started exploring laws of thermodynamics
about which there's lots of classical mathematical theories.
There can also be the transfer of energy into sound!