Discussion leading to Newton's second law
Students will have discovered that:
- a constant force accelerates a given mass with constant acceleration;
- doubling the force doubles the acceleration, i.e. the acceleration is directly proportional to the force for a given mass. F is proportional to a;
- the force, F, needed for a given acceleration is inversely proportional to the mass, m
- for a given force, F, the acceleration, a, is inversely proportional to the mass,m.
(many students find inverse proportion a problem).
Considering these points together leads to F is proportional to ma or F = a constant x ma.
Mass is measured in kg and acceleration in m/s/s but what of force? If the constant is equated to unity, then we are defining a unit of force. In the SI system the force is measured in newtons (symbol N), leading to F = ma.