How can kinetic energy decrease in an inelastic collision, but momentum stay the same?

Question

I have been doing research and the explanations don’t make sense. Kinetic energy is based off of velocity, and so is momentum. If the kinetic energy decreases, the momentum would also have to decrease, because the objects in the collision have less energy and therefore move at slower rate, and therefore have less momentum. It seems like momentum and energy are one, but but in reality it isn’t? And here’s my thought experiment:

Two objects collide and lock together. They maintain their original momentum, but are now locked together as one. According to what I am currently learning, they have lost kinetic energy, but they have maintained their total momentum. Now, the locked objects hit an equal copy of themselves in front of them, except the copies are unlocked. Due to conservation of momentum, the locked object stops, and the copies are now at the same point the two objects were at the start of the experiment, before they collided. How can energy be lost, and then gained? Where did they go? If someone could simply explain what I’m missing, that would be very helpful as I have a test in 12 hours. Thanks!!

In: Physics

Answer 1

Hi,

Energy is never lost, period.

Kinetic energy might be lost to heat in a collision, but the total energy before the collision (all kinetic) will be the same as the energy after the collision (kinetic plus heat in this example.)

Momentum is always conserved in a collision, regardless of whether the total kinetic energy changes.

From a math perspective, the kinetic energy is proportional to mass * velocity * velocity, and the momentum is mass * velocity, so it is completely plausible that one can be constant while the other changes.

I found this answer to be fairly clear:
https://physics.stackexchange.com/a/132763

But you really should give one example, with details, of a collision that is confusing you. Your multiple collision example is tough to follow and is surely not helping your understanding. Break it down to small bits, understand the small bits, and then the total situation will be clear.