In a crash test, a truck with mass 160o kg traveling at 19 m/s smashes head-on i
ID: 1661126 • Letter: I
Question
In a crash test, a truck with mass 160o kg traveling at 19 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.71 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 collsion 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 wall on the truck during the colision? m/s (a) 2t is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the why a colision is so damaging wall to the gravitational force mg on the truck. This large ratio shows mg (e) What approximations were necessary in making this analysis? (Select all that apply) 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 The deceleration of the truck is approximately equal to gExplanation / Answer
Vf = final speed = 0
Vi = initial speed = 19 m/s
d = stopping distance = 0.71 m
a = deceleration
using the equation
Vf2 = Vi2 + 2 a d
02 = 192 + 2 a (0.71)
a = - 254.23 m/s2
using the equation
Vf = Vi + a t
0 = 19 + (-254.23) t
t = 0.075 sec
average speed = distance / time = 0.71/ 0.075 = 9.5 m/s
b) t = 0.075 sec
c) F t = m (Vf - Vi)
F (0.075) = 1600 (0 - 19)
F = -405333.33 N
d) Fg = mg = 1600 x 9.8 = 15680 N
ratio = F/Fg = 405333.33/ 15680 = 25.85
Please rate my answer, good luck...