This is a question on a worksheet that I'm giving to a student:
A man of weight $W$ steps into the lift. The lift then moves downwards with a constant speed. If $R$ represents the force acting on the man by the lift floor, which of the following statements is/are correct?
(3) $R$ and $W$ are an action-reaction pair according to Newton's third law
Why isn't this statement (3) correct?
Best Answer
Action/reaction pairs are describing momentum flow. Momentum is a vector, so it is more difficult to explain intuitively, so you should start with money, which is a scalar. Let me call a "payment" money that enters your posession. A payment can be negative, in which case you lose money, like when you buy a hat.
Newton's third law of finance says: for any payment, there is a negative equal payment associated to it on somone else (if you aren't a central bank!). So if you have a payment of -100 dollars, someone else got 100 dollars. This should be completely intuitive, because, outside of banking, on the personal level, money is a conserved quantity.
Newton's law is the same: the conserved quantity is momentum, and the momentum is flowing between objects. The flow is called the force, and the force is the "payment", it tells you how many units of momentum are incoming per unit time. The third law says that every payment is associated with a reverse payment going the other way (just like money, except the quantity is a vector).
So when the Earth pulls on you, it is paying you downward momentum, which means that you are paying the Earth upward momentum. That's the action reaction pair. If you are on a scale, the scale pays you up momentum (it pushes you up), and you pay the scale down-momentum (you push the scale down). The end result is that the force from the Earth and the scale cancel out, and the gravitational force on the Earth from you plus the downward force you exert on the Earth through the scale cancel out, and nothing ends up moving.
This is like a closed circuit of momentum, and elucidating the way in which momentum is flowing, even though the objects don't move, is the subject of statics. Newton's laws add to this the interpretation of momentum as a dynamical quantity, mass times velocity, so when an object accumulates momentum, you know how fast it is going.
This point of view is very useful, but it is not often explicitly taught.