I received a Newton's Cradle as a present and have been playing with it.
How come when I drop 2 balls onto 3 the centre ball remains motionless but when I drop 3 balls onto 2 the centre ball oscillates?
I thought that 3 on 2 and 2 on 3 would be effectively the same.
It's simple conservation of momentum
Two balls have enough momentum to move balls, and only this much (the third ball in the centre remains motionless)
Three balls have more than enough momentum to move the remaining two balls so the third ball in the middle has enough momentum to oscillate
When you lift up 2 balls, you build up two balls worth of energy. Then you let go and when they hit the three balls, the two balls worth of energy goes into the three balls. Now the energy wants to go as far as it can, so it goes all the way to the end of the three balls. So the first ball takes one balls worth of energy and shoots out; the second ball takes the other balls worth of energy and shoots out. They do this at the same time, so the two balls shoot out together since they take all the energy; but there's no energy left for the third (center) ball, so it stays still.
Followup question: is the momentum transmitted instantly?
if I had a newton cradle a mile long would there be an appreciable delay between the inital ball's contact and the resultant movement on the opposite end?
It travels at the speed of sound in the material, which for steel is about 1400 m/s if I remember correctly, you'd certainly notice the delay in a mile long cradle, though it'd only be about a second
If you'd like an example that takes longer, think of a pressure wave from an explosion travelling (at 340m/s:the speed of sound) through the air