Please answer the question below. An uncontrolled automobile traveling at 100 km
ID: 1340007 • Letter: P
Question
Please answer the question below.
An uncontrolled automobile traveling at 100 km/h strikes squarely a highway crash cushion of the type as shown in which the automobile is brought to rest by successively crushing barrels. The magnitude F of the force required to crush the barrels is shown as a function of distance x the automobile has moved into the cushion. Knowing that the mass of automobile is 1000 kg and neglecting the effect of friction, determine the distance the automobile will move into the cushion before it comes to rest, the maximum deceleration of the automobile.Explanation / Answer
a) Car wil come to rest when work done by force F equal to its initial KE.
v = 100 x 1000m / 3600sec = 27.78 m/s
Work done = Area under the curve F vs x
1000 x 27.78^2 /2 = (80 x 10^3 x 1.5) + (120x 10^3 x 2.5) + (160 x 10^3 x d)
d = 2.20 m
total distance traveled = 4 + 2.20 = 6.20 m
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max. deceleartion will be when F(x) is max.
that F = 160 x 10^3 N
a = F/m = 160 m/s^2