Newton’s Cradle…

The inestimable Mrs Ives ‘tagged’ me on Facebook yesterday when she posted a funny cartoon that referred to a Newton’s Cradle. These are toys to have on your desk that rather neatly show the principles of conservation of momentum and conservation of energy. Momentum is mass × velocity (mv) whereas you calculate kinetic energy with the formula ½mass × velocity² (½mv²). If you need to know more about what kinetic energy is you should read this post first.

When we think about how the Newton’s Cradle works, it is best first to ignore the effects of air resistance and friction – imagine that the cradle is in a vacuum. As the first metal ball drops it transfers its momentum and kinetic energy to the arrangement of four balls. Because there is nothing blocking the fifth ball from moving, it swings out to the same height from which the first ball was released. This is what we mean when we say that the momentum is conserved – the fifth ball ends up with all the momentum that was initially given to the first ball.

Of course, we have been ignoring the energy lost through friction and the heat & sound released as the balls strike one another. This lost energy is the reason that the balls eventually come to rest. The kinetic energy gradually diminishes as energy is lost to the environment in the form of heat & sound. Cradle is really well constructed, with excellent hinges for the wires that keep friction to a minimum then the cradle can keep clacking away for quite a while before all the energy is lost. And this brings me to the cartoon that Mrs Ives posted on Facebook.

I loved this cartoon but can’t help thinking about why it wouldn’t work. The swings are wired in such a way that they move front to back easily but not side to side. The chains attached to the seats do not stretch so the seat has to follow the arc described by the chain to the child’s left. This will tend to lift the child before it is able to strike the next one along. You might be able to get child one to hit child two but there would never be enough momentum to make that child hit child three – it would be lost to the swing’s chains. In the real thing, each ball strikes the next at the very bottom of its swinging arc (6 o’clock). That would not be the case here.

Questions…

1. What is meant by a force?
2. What is the force that opposes motion?
3. What force keeps a helium-filled balloon afloat?
4. If a car is travelling at a constant speed, what can we say about the forces acting upon it?
5. What is Newton’s Third Law of Motion?