# Extending run-time of Newton cradle?

## Main Question or Discussion Point

I got an idea the other day in class about Newton's cradles.
I was wondering if you put one in a vacuum and started it, would it run for longer, as opposed to being in normal conditions because of sound's inability to travel through vacuums etc? Would anyone be able to clarify because I was thinking of basing an EEI on this?
Cheers.

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AlephZero
Homework Helper
There are at least two ways that the system loses its kinetic energy.

One is air resistance, friction between the wires and the supports, etc.

The other is that when the stress level changes in the materal, some of the energy is converted into heat.

You could separate those two effects by swinging the cradle like a pendulum, with no impacts, and doing the usual Newtons Cradle demonstrations. You might be able to get a theoretical result for the damping caused by the aerodynamic force acting on a pendulum made with single sphere. (Hint: don't try to solve the equations of motion for this. Assume you have the same simple harmonic motion as for a pendulum without damping, and find the amount of work done by the drag force in one cycle of oscillation).

If you did both of those in air and in a vacuum, you might be able to deduce how much of the damping comes form the material and how much from the air. You could also try using different materials for the balls of the cradle. Most structural metals have similar (and low) levels of hysteretic damping, but rubber or plastic, probably behave differently.

It might be interesting to compare spheres and cubes, with the whole face coming into contact compared with a "single point". For the cubes, the stress in the materal would be lower becaise of the bigger contact area, and that might result in lower hysteretic damping. But there might be more aerodynamic damping because you have to "pump" all the air out of the gap between the cubes and "suck" it back in again, losing energy because of the viscosity of the air.

Hope that gives you some ideas to think about!

rcgldr
Homework Helper
There's also the issue of the duration of collisions versus the time it takes for the force of the collisions to propagate through the balls (speed of sound for the material in the balls). The result is that the outcome isn't quite the "perfect" outcome you'd like to have with a Newtons cradle. I'm not sure if this is why the "inner" pack tends to start swinging over time, or why the outer ball(s) bounces back a bit instead just stopping when they collide with the "inner" pack. This web site has a lot of info: