Jump to... Question 8 of 14 Sapling Learning Mapm As a civil engineer for your c

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Jump to... Question 8 of 14 Sapling Learning Mapm 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 a force constant 589175 N/m with a maximimum distanc manufacturer, beyond this compression the spring loses most of its ability to absorb an impact job. Each section of their guard rails consists of two springs, each having e of compression of 0.724 m. (According to the The largest vehicle the guardrails are expected to stop are trucks of mass 4350.000 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.) Number m/s Given your result, which section of road most often features such a speed? impact O School zone O Large avenue Highway (Scroll down for more questions.) Guard rails are pointless if the acceleration they creatè 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. Exit PreviousCheck Answer Next Hint

Explanation / Answer

1)

I'll have to assume that the springs are mounted in parallel.
Effective spring stiffness k = 2*589175 N/m = 1178350 N/m

spring energy = kinetic energy
½kx² = ½mv² ½ cancels
1178350 N/m * (0.724 m)² = 4350kg * v²
v = 11.92 m/s  

v1 = initial velocity = 11.92 m/s
v2 = final velocity = 0 m/s
v = (v2 - v1) = change in velocity = -11.92 m/s
t = elapsed time of the collision = to be determined

Impulse Equation
Ft = mv
t = mv / F
t = 0.12156 s

Newton's Second Law
F = ma = m(v/t)

a = v/t
a = - 11.92m/s / 0.12156 s
a = -98.1 m/s²

a = 10g < 20g

So, guard’s rail is safe

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