Many cars have \"5 mi/h (8 km/h ) bumpers\" that are designed to compress and re

Question

Many cars have "5 mi/h (8 km/h ) bumpers" that are designed to compress and rebound elastically without any physical damage at speeds below 8 km/h .

If the material of the bumpers permanently deforms after a compression of 1.5 cm , but remains like an elastic spring up to that point, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1400 kg and is tested by ramming into a solid wall?

Please don't respond unless you know what you're doing. I've already posted this twice and have gotten incorrect answers both times.

Explanation / Answer

apply the law of conservation of eenrgy as

KE = EPE of the spring

so

0.5 mv^2 = 0.5 kx^2

so

Spring constant K = mv^2/x^2

K = 1400 * (8*5/18)*(8*5/18)/(0.015* 0.015)

K = 3.07 *10^7 N/m or 30727.033 kN/m---------<<<<<<<<<<Answer

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