I understand that in an inelastic collision, mechanical energy is lost to heat, sound, deformation, etc. However, if there is no friction between the two objects that collide or the two objects with the ground, then is mechanical energy still lost in a collision where the two objects stick together afterward?
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In some ways you have answered your own question by making the statement, mechanical energy is lost to heat, sound, deformation, etc.
When bodies collide compression (shock) waves are produces within the colliding bodies and these waves bounce backwards and forwards within the bodies with the net result that the amplitude of these waves decreasing as the internal energy of the bodies increases, the molecules have a larger kinetic energy, the temperature of the bodies increases.
Also the waves compression internal to the bodies excite air molecules outside the bodies and thus sound waves are produced.
During the collision the colliding bodies are permanently deformed, ie intermolecular bonds are permanently broken a process which requires energy which comes from the kinetic energy of the colliding bodies.
To illustrate the complex nature of a collision I could not find a super slow motion video of two bodies colliding and sticking together so have a look at what happens to a golf ball hitting a steel plate.
You will note that I have not used the word friction, relating to the forces generated when two objects in contact are moving relative to one another, in my answer and so the one word answer to your question is "no".
