Car bumpers are designed to limit the extent of damage to the car in the ease of

Question

Car bumpers are designed to limit the extent of damage to the car in the ease of low-velocity collisions. Consider a 3, 400 lb passenger car impacting a concrete barrier while traveling at a speed of 3.5 mph. Model the car as a particle, and consider two types of bumper: (1) a simple linear spring with constant k and (2) a linear spring of constant k in parallel with a shock absorbing unit generating a nearly constant force of696 lb over 0.27 ft. If the bumper is of type 1, find the value of k necessary to stop the car in a distance of 0.27 ft. k = times 10^4 lb/ft

Explanation / Answer

For the type 1 bumper, by the law of conservation of energy, we have

Decrease in kinetic energy of the car = Potential energy stored in the bumper as a spring of stiffness K which is constant.

===> (1/2) * m * v2 = (1/2) * K * x2

Note that 1 mph = 22/15 ft/sec and thus Initial speed of the car is v = 3.5 mph = 5.133 ft/sec.

===> (3400/32.2)slugs * (5.133 ft/sec)2 = K * (0.27 ft)2

===> K = 3.817 * 104 lb/ft

Thus the stiffness of the bumper of type 1 is K = 3.817 * 104 lb/ft

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