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 a force constant 589175 N/m with a maximimum distance of compression of 0.614 m. (According to the manufacturer, beyond this compression the spring loses most of its ability to absorb an impact elastically.) The largest vehicle the guardrails are expected to stop are trucks of mass 5250.000 kg. What is the maximum speed at which these guard rails alone 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.)

(b) Given your result, which section of road most often features such a speed?

(c) Guard rails are pointless if the acceleration they create seriously injures passengers. One important safety factor is the acceleration experienced by passengers during a collision. Calculate the magnitude of the maximum acceleration of the vehicle during the time in which it is in contact with the guard rail.

Explanation / Answer

when springs are connected in parallel,

k = k1 + k2 + .....

k = 2(589175) = 1178350 N/m

now applying energy conservation,

m v^2 /2 + 0 = 0 + k x^2 /2

5250 v^2 / 2 = (1178350)(0.614^2) / 2

v = 9.20 m/s

(c) Fmax = k x

= (1178350)(0.614)

= 723506.9 N

a_max = Fmax / m = 137.8 m/s^2

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