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 a distance sc. Write an expression for the average force exerted on the bag in terms of m, vi, and sc. Compute the average force for a 100 km/h collision, where the driver’s mass is 60 kg and the allowed stopping distance in the bag is 30 cm.

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 a distance sc. Write an expression for the average force exerted on the bag in terms of m, vi, and sc.  Compute  the  average  force  for  a  100  km/h  collision,  where  the  driver’s  mass  is  60  kg  and  the   allowed stopping distance in the bag is 30 cm.

i don't even understand this question....theres a lot going on in the question.....help needed..

Elena · Answer

100km/hr = 27.78 m/s.
Through the Work-Kinetic Energy Theorem, the amount of work done by the air bag on the driver must equal the change in the driver's kinetic energy (the final kinetic energy is 0, the initial KE = m• v²/2)
ΔKE = W,
ΔKE = 0 - m• v²/2 = m• v²/2.
W =F(ave) •s(c).
m• v²/2 = F(ave) •s(c).
F(ave) = m• v²/2• s(c) =
= 60•(27.78)²/2•0.3 = 7.7•10^4 N.