Newton's Cradles vs Ball Bouncing off Wall

[Tik]

Hello everyone!

I was just reading about the working of Newton's Cradles and ended up having some confusion.

When a ball is taken to a certain height and dropped, it comes down and hits the next ball. Now the explanation as to why the first ball stops and doesn't bounce back is attributed to the law of conservation of momentum. Since momentum has direction, if the ball were to bounce back, the momentum would no longer be conserved as the direction would be reversed. Hence the momentum is transferred to the next ball.

Considering another situation, a ball bounces back when it hits a wall. The explanation given in this case is that the momentum of the ball changes from +mv to -mv and a momentum of 2mv is transferred to the wall, hence conserving momentum. Why can't this idea be applied to the case of Newton's Cradles as well?

 

[A.T.]

Now the explanation as to why the first ball stops and doesn't bounce back is attributed to the law of conservation of momentum...

...and conservation of energy.

Why can't this idea be applied to the case of Newton's Cradles as well?

Because it would violate conservation of energy.

 

[Tik]

Thanks for the reply.

But just like a ball bouncing off the wall, why can't the first ball in the cradle retain some energy and bounce back, passing on the remaining energy to the next ball, hence conserving energy?

 

[A.T.]

But just like a ball bouncing off the wall, why can't the first ball in the cradle retain some energy and bounce back, passing on the remaining energy to the next ball, hence conserving energy?

Conserving momentum and kinetic energy at the same time gives you a unique solution, which depends on the mass ratio of the objects. Hence there different outcomes.

 

[Tik]

Alright, I get it now. Thanks a lot!

 

[rcgldr]

But just like a ball bouncing off the wall, why can't the first ball in the cradle retain some energy and bounce back, passing on the remaining energy to the next ball, hence conserving energy?

There are multiple solutions that conserve both momentum and energy. You need to consider the direction of forces and how the forces propagate through the balls. Real world experiments show that the ball does bounce back a very small amount (not sure if this happens with an idealized cradle). There's also the issue that the pack of balls is shifting back and forth, when results in some component of opposing force from the strings the balls are attached to. Here's a website with a good explanation:

http://www.lhup.edu/~dsimanek/scenario/cradle.htm

 

[A.T.]

There are multiple solutions that conserve both momentum and energy.

For the outcome of the full cradle with > 2 balls, yes. But for the collision of two balls (which seemed to the OPs focus) there is only one.