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 4.23710 Times 10^5 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 elastically.) The largest vehicle the guardrails are expected to stop are trucks of mass 5450.000 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.) Given your result, which section of road most often features such a speed? School zone Large avenue Highway 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. If the highway department considers 20 g's the maximum safe acceleration, is this guard rail safe in regards to acceleration? Yes No In the plot of acceleration as a function of distance, which of the four curves most closely represents the acceleration exhibited by the car while colliding with the guard rail (assuming ideal springs)?

Explanation / Answer

k = 4.2371 *10^5 N/m

two springs so effective K = 2 * 4.2371 * 10^5 = 8.4742 * 10^5 N/m

x = 0.724 m

m = 5450 kg

let the max speed = v

the total kinetic energy is to be absorbed by springs..

1/2* k*x^2 = 1/2*m*v^2

8.4742 * 10^5 * 0.724^2 = 5450 * V^2

V = 9.028 m/s

mostly in school zones

V^2 - u^2 = 2*a*S ==> 81.505 = 2* a* 0.724 ==> a = 56.288 m/s^2

"yes"

max accelaration felt is 115.3735 m/s^2... so it is safe...

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