Quote from: Delburt Phend on December 15, 2021, 09:45:30 AM
Floor quote: "The kinetic energy the object has (due to its motion), is the same amount of energy as
was needed to cause its acceleration it to that specific velocity."

How is this statement consistent with ballistic pendulums?

It is consistent, that is how. 

Unless we are examining in terms of other than ordinary physics / mechanics.

A 5 kg mass moving 8 m/sec can collide with a 20 kg mass at rest. The input kinetic energy is 160 J and the output KE is 32 J.

To make 5 kg move 8 m/sec it takes an application of 9.81 N of force applied for 4.077 second.
 
To make 25 kg move 1.6 m/sec it takes an application of 9.81 N of force applied for 4.077 second.

The conserved quantity is Force * time:   Ft; but Ft is not a form of energy. 

It would be interesting to see an elastic collision take 4 seconds....


However, in the real world the 20kg mass has a moment of inertia
defined by the mass*radius^2
And the momentum of the smaller mass is transferred in a fraction of a second

Want to see this? Shoot a pool cue at a bowling ball

quote
"It would be interesting to see an elastic collision take 4 seconds...."
end of the quote

! was thinking of an experiment along these lines, (in another topic).

explanation ...

1. Place a section of copper tube or a thick roll of aluminum foil upon a digital weight scales,
with the long axis vertical. Note its weight.

2. Drop a powerful neodymium magnet into the tube and note the weight as
the magnet falls through the tube.

3. Note the weight of both the tube and the magnet when the magnet is at rest
at the bottom of its descent / resting on the scale.


It is probably a good idea to isolate the magnet from contact with or very near
proximity to the weight scales (as it might damage the scales).

I am pretty certain that less weight will register during the magnets descent than
when the magnet is at rest at the bottom of the tube.

             What are your opinions ?

4. Next place the magnet upon a vertical, wooden, dowel rod, upon the scales.

5. Drop the the tube around / over the magnet.

6. Use a tubular copper wire coil, first shorted then not shorted.

             P.S.
Hope this hasn't drifted too far off topic.
   best wishes
            floor