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 $m_{eff}=94.6\,{\rm kg}$.
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