5. You are designing guardrails for the highways in your These guardrails are de

Question

5. You are designing guardrails for the highways in your These guardrails are designed with four springs which will hopefully bring a runaway automobile to rest as they are compressed. The road in question is regularly travelled by large trucks with a mass as large as travelling with speeds as high as 20.0 m/s. If the springs are only able to compress as much as 0.500 meters a) What must the spring constant of the springs be? b) What is the maximum acceleration that will be experienced by cars which strike the guard rail?

Explanation / Answer

Four springs are connected in parallel,

Keff = K1 +K2 + K3 + K4

K.E. = spring energy

1/2 * m * V^2 = 1/2 * Keff * x^2

5000 * 20^2 = Keff * 0.5^2 =

Keff = 8 * 10^6 N /m

Force constant of each spring = Keff /4 = 2 * 10^6 N/m

(b) F = - kx = m a

a = k x /m = ( 2*10^6 * 0.5 ) / 5000 = 200 m/s^2

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