Imagine a car involved in a head-on crash. The driver, whose mass is m, is to be
ID: 1967555 • Letter: I
Question
Imagine a car involved in a head-on crash. The driver, whose mass is m, is to be brought uniformly to rest within the passenger compartment by compressing an inflated air bag through the distance sc. Write an expression for average force exerted on the air bag in terms of m, vi, and si. Compute the average force for a 95 km/hr collision, where the drivers mass is 65 kg, and the allowed stopping distance of the air bag is 35 cm. Assume the car deforms only negligibly.
I dont get the question as it is not given with a figure. :/
Explanation / Answer
Consider the conservation of energy principle Initially for a no-crash condition, K.E of man = (1/2)m(v^2) where v is velocity of car (as velocity of car and man is same) m is mass of the man Since there is no compression to be exerted on the air bag, the compression energy is zero. Finally, after the crash velocity of man is brought to zero. and since allowed compression is 's' (Consider it for avg. force) Total Energy = (1/2)*k*(s^2) Where k is compression constant of the bag (Assuming it behaves like a spring) Then (1/2)m(v^2)=(1/2)k(s^2) Hence k=m*(v^2)/(s^2) Thus the Restoring Force of the air bag is k*s Hence Force exerted BY the airbag is m*(v^2)/s Since net force=0, Force exerted on Bag = Restoring Force Hence Avg. Force exerted on bag = m*(v^2)/s PROB: v=95km/hr=95*1000/(60*60) metres/second =26.4 m/s s= 35 cm = 0.35 m m=65 kg Avg. F = 129435.43 Newtons = 129.4 KiloNewtons