acceleration - "Weight" of moving object in a car collision

From time to time I see safety warning about keeping loose items in your car. The last warning used a 2kg object, and claimed that if a collision occurred at $50{km\over h}$ it would have a weight equal to 80kg. At $90{km\over h}$ it would have a weight of 256kg.

How are these "new weights" calculated?

Answer

From $dp/dt\simeq \Delta p/\Delta t=F$. A 2 kg object at 50 km/hr has an initial momentum of

$$p=mv = 2\,{\rm kg}\cdot13.9\,{\rm m/s}=27.8\,{\rm kg\,m/s}$$ If we naively assume that the crash is over the course of a 0.05 seconds, then the force is $F=556\,{\rm N}\to m_{eff}\simeq58\,{\rm kg}$ (final momentum being 0 because the velocity is zero). Letting $\Delta t=0.03\,{\rm s}$ gives $m_{eff}=94.6\,{\rm kg}$.