Question

Newton's cradle consists of an aligned row of identical elastic balls suspended by strings so they barely touch one another. when two balls are raised from one end and released, they strike the row and two balls pop out from the other end. if instead, one ball popped out with twice the speed of the two, this would violate

Answer 1

Initial momentum = 2 * m v

so if 1 ball popped out with 2 v momentum would be conserved

but the initial kinetic energy of the two balls is

1/2 m v^2 + 1/2 m v^2 = m v^2

But the kinetic energy of one ball with twice the speed would be

KE = 1/2 m (2 v)^2 = 2 m v^2 thus violating conservation of energy