Pairs of point masses interact

An austere, but productive, view of the world

The world of Newton is extremely simple, and therefore extremely powerful. We can be certain of what to expect, because there are so few interacting entities. The world of Newton consists only of point masses and of forces acting on those point masses.

Given the force and mass, you can calculate the acceleration. From the acceleration you can calculate the accumulation in velocity – that is, how much the velocity changes. From the velocity you can calculate the accumulations in displacement – that is, how much the displacement changes (so giving changes in position).

When a pair of masses interact, you have choices to make in modelling the interaction.

• You can choose to calculate accelerations from forces (perhaps using Newton's third law as a short cut).
• You can choose to look at the momentum before and after the collision (perhaps using the conservation of momentum as a short-cut, or as a basis for deciding what the possible outcomes are – and so what is impossible).

This pair of alternatives has been the focus of this topic.

• You could also choose to look at how the energy is shifted from store to store, looking before and after the collision (perhaps using the conservation of energy as a short-cut, or as a basis for deciding what the possible outcomes are – and so what is impossible).

In later studies, students may combine these different approaches. For now, it is enough to know that there are different ways of modelling the same situation and that you should choose one that allows you to make predictions simply.