Considering the swinging ball apparatus:
If 2 balls are pulled out and released, they strike the other balls and 2 balls pop out the other side:
Looking at this situation in accordance with the Law of Conservation of Momentum (m v):

Momentum is conserved since momentum before = mv + mv = 2 mv equals momentum after = mv + mv = 2 mv
But momentum would also be conserved if 1 ball popped out at twice the velocity, i.e.,
Momentum before = mv + mv = 2 mv
Momentum after = m (2 v) = 2 m v

But now look at this situation in accordance with the Law of Conservation of Energy (KE = ½ m v2):

If only 1 ball pops out with twice the velocity
Energy before = ½ m v2 + ½ m v2 = m v2
Energy after = ½ (m) (2 v)2= ½ (m) (4 v2) = 2 m v2
These energies are not equal and, therefore, the law of conservation of energy is not obeyed!
But, since 2 balls actually popped out
Energy before = ½ m v2 + ½ m v2 = m v2
Energy after = ½ m v2 + ½ m v2 = m v2
These energies are equal and, therefore, both laws of conservation are obeyed.

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