Until 2023 there was a widespread belief, that kinetic energy and
momentum were fundamentally different, kinetic energy proportional to
v^2 and momentum to v.
Experiments can be done dropping putty onto an airtrack vehicle. There
will be some energy loss from the collision, but with good experiments
and comparative measurement of kinetic energy by lifting weights by the vehicles, it can be shown that E=0.5mv^2 is not correct.
This is an equivalent to the rocket sled experiment where velocity is increased in stages by firing rockets, but using the addition of mass to decrease velocity.
A multilayer track where the weight is transferred down from one vehicle
to another in several stages can be used for checking how much energy is
lost in one drop.
This post isn't the experiment, but in general terms how schools can
move away from the ticker tape trolley.
This is at a basic level.
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