Car versus lorry

Problem

A car and a lorry collide head-on. On which vehicle does the larger force act during the collision? In which vehicle do the occupants experience the larger acceleration? Are these the same thing?

Solution

Force. During the collision the car and the lorry exchange forces that, by Newton’s third law, are equal in magnitude and opposite in direction: $\vv{F}_{\text{camion}\to\text{auto}} = -\,\vv{F}_{\text{auto}\to\text{camion}}$ So the force acting on the car has the same magnitude as the one acting on the lorry. There is no vehicle “that pushes harder”.

Acceleration. Acceleration depends on mass (Newton’s second law): $a = \frac{F}{m}$ For the same force $F$, the vehicle with the smaller mass (the car) experiences the greater acceleration. Its occupants are decelerated more abruptly, which is why they are at greater risk.

These are not the same thing: the force is equal on the two vehicles (third law), the acceleration is not (it depends on $1/m$).

Final result: $\ev{F_\text{auto} = F_\text{camion};\quad a_\text{auto} = \tfrac{F}{m_\text{auto}} > a_\text{camion} = \tfrac{F}{m_\text{camion}}}$

Links

Topics: Quantità di moto e urti Concepts: Terza legge di Newton · Impulso Skills: Impostazione simbolica