## Discussion leading to Newton's second law

Teaching Guidance for 14-16

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*.