As a civil engineer for your City, you have been assigned to evaluate the purcha

Question

As a civil engineer for your City, you have been assigned to evaluate the purchase of spring-loaded guard rails to prevent cars from leaving the road. In response to a request for proposals*, one company states their guard rails are perfect for the job, Each section of their guard rails consists of two springs, each having n force constant 589175 N/m with a maximum distance of compression of 0 724 m. (According to the manufacturer, beyond this compression the spring loses most of its ability to absorb an impact elasticity.) The largest vehicle the guardrails are expected to stop are trucks of mass 4850,000 kg. What is the maximum speed at which these guard rails atone can be expected to bring such vehicles to a halt within the stated maximum compression distance'' (Assume the vehicles can strike the guard rail head on and that the springs are perfectly elastic.) Given your result, which section of road most often features such a speed?

Explanation / Answer

spring constant of each k = 589175 N / m spring constnat of the system K = k + k = 2k = 1178350 N / m maximum compression   x = 0.724 m mass of the vehicle m = 4850 kg from law of conservation of energy , maximum kinetic energy of the vehicle = maximum potential energy of the spring system ( 1/ 2) mv^ 2 = ( 1/ 2) K x^ 2 from this maximum speed v = x [ K / m]                                            = 11.28 m / s

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