One question in collision?

Question

You are the design engineer in charge of the cash worthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30mph). A new model of mass 1500 kg takes 0.15s from the time of impact until it is brought to rest.

(a) Calculate the average force exerted on the car by the barrier.

(b) Calculate the average deceleration of the car.

Answer 1

KE = (1/2)mv0^2 = (1/2)(1500)(5x10^4)^2

If x is the distance it takes to stop then:

Work in stopping = W = F*x

If we assume constant deceleration for the car then:

x = v0*t - (1/2)a*t^2 and v0 = a*t

x = v0*t - (1/2)(v0/t)t^2 = v0*t - (1/2)v0*t = (1/2)v0*t

W = F*x = F*{(1/2)v0t] = KE = (1/2)mv0^2

F = m*v0/t

a. Need initial speed in m/s

50 km/h = (50)(1000)/3600 = 13.889 m/s

F = m*v0/t = (1500)(13.889)/0.15

F = 138,889 N

b. v0 = a*t

13.889 = a(0.15)

a = 32.59 m/s^2