2. An inflatable bag is located in the dashboard of a car. In acollision, the ba
ID: 1681116 • Letter: 2
Question
2. An inflatable bag is located in the dashboard of a car. In acollision, the bag expands suddenly and cushions the impact of thepassenger. The forward motion of the passenger must be stopped inabout 30 cm of motion if contact with the hard surfaces of the caris to be avoided.a) For a 70-kg person with a 30-cm allowed stopping distance, showthat the magnitude of the average force is given by the followingexpression: F = 117 Vo^2, newtons.
Notice that the necessary stopping force increases as the square ofthe velocity of the automobile (and the passenger).
b) Assume that Vo = 70 km/h and find F.
c) If the force that you evaluated in part b) is uniformlydistributed over a 1000-cm^2 area of the passenger's body, find theapplied force per square meter. The estimated strength of bodytissue is 500,000 Pa. NOTE: One Pa (Pascal) is a force of 1 Ndivided by one area of 1 square meter.
d) Kindly, repeat the calculation of part c) with v = 100 km/h. Itis safe to say that the force per unit area just calculated wouldprobably injure the passenger?
Explanation / Answer
a) use equations Vf2=Vo2-2a(Df-Do) and F=ma => a=F/m Vf2=Vo2-2(F/m)(Df-Do) where Vf=0 and Do=0 solve for F to get F=(1/2)(m/Df)Vo2=116.66Vo2 b) convert 70 km/hr into m/s = 19.4 19.42*117=44135 N c) 1000 cm2=0.1m2 Pressure = P= F/area = 44135/0.1 =441350 Pa d) 100 km/hr =28 m/s F=91000 N P=91000/0.1 =910000 Pa yes, the pressure will rupture body tissue
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