You are asked to design spring bumpers for the walls of aparking garage. A freel

Question

You are asked to design spring bumpers for the walls of aparking garage. A freely rolling 1200kg car moving at 0.750m/s isto compress the spring no more than 7.00cm before stopping. What should be the force constant of the spring? What is the maximum amount of energy that gets stored init? If the springs that are actually delivered have the properforce constant but can become compressed by only 5.00cm, what isthe maximum speed of the given car for which they will provideadequate protection? You are asked to design spring bumpers for the walls of aparking garage. A freely rolling 1200kg car moving at 0.750m/s isto compress the spring no more than 7.00cm before stopping. What should be the force constant of the spring? What is the maximum amount of energy that gets stored init? If the springs that are actually delivered have the properforce constant but can become compressed by only 5.00cm, what isthe maximum speed of the given car for which they will provideadequate protection?

Explanation / Answer

the spring is compressed by x= 7 cm=0.07 m k=force constant of the spring kinetic energy of the car is converted in elastic potentialenergy (1/2)*1200*0.752=(1/2)*k*0.072k=1.38*105N/m maximum amount of energystored=(1/2)*1.38*105*0.072=337.5 J let the car's maximum speed=v when the spring can be onlycompressed by 5cm=0.05 m (1/2)*1200*v2=(1/2)*1.38*105*0.052 v=0.536 m/s

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