In a crash test, a truck with mass 2400 kg traveling at 19 m/s smashes head-on i

Question

In a crash test, a truck with mass 2400 kg traveling at 19 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck s 0,63 m shorter than before (a) What is the average speed of the truck during the collision (that is, during the interval between first contact with the wall and coming to a stop)? (b) About how long does the collision last? (That is, how long is the interval between first contact with the wall and coming to a stop?) (c) What is the magnitude of the average force exerted by the wail on the truck during the collision? m/s (d) It is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the wall to the gravitational force mg on the truck. This large ratio shows why a collision is so damaging mg (e) What approximations were necessary in making this analysis? (Select all that apply) Neglect the horizontal component of the force or the road on the truck tires Assume a nearly constant force exerted by the wall, so the speed changes at a nearly constant rate. The deceleration of the truck is approximately equal to g

Explanation / Answer

given that

initial speed is Vo = 19 m/s

final speed is V = 0 m/s

distance travelled is s = 0.63 m

using kinematic equations

V^2 - Vo^2 = 2*a*S

0^2 - 19^2 = 2*a*0.63

a = -286.5 m/s^2

and also using

S = (Vo*t)+(0.5*a*t^2)

0.63 = (19*t)-(0.5*286.5*t^2)

t = 0.0667 sec

so a) Vavg = total distance travelled / total time taken

Vavg = 0.63/0.0667 = 9.45 m/sec

b) time taken is deltat = 0.0667 sec

c) Fwall,avg = m*a = 2400*286.5 = 687600 N

d) Fwall,avg / (m*g) = 687600/(2400*9.81) = 29.2

e) approximations are

Neglect the horizontal component of the force of the road on the truck tires

Assume a nearly constant force exerted by the wall,so the speed changes at a nearly constant rate

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