Auto manufactures study the collision of cars with mounted spring of different spring constant. Consider a car of mass 1500 kg moving with a speed of `36 kmh^(-1)` on a smooth road and colliding with a horizontally mounted spring of spring constant `7.5xx10^(3) Nm^(-1)`. Find the maximum compression of the spring .

Explanation

At maximum compression, KE of car gets converted completely into PE of the spring.
`KE " of " car =K=(1)/(2)mv^(2)=(1)/(2)xx1500xx10xx10`
`(v=36xx(5)/(18)=10 ms^(-1))`
`=7.5xx10^(4) J`
At maximum compression `x_(m)`, PE,U of the spring =KE, K of car
`U=(1)/(2)kx_(m)^(2)=7.5xx10^(4) Jimpliesx_(m)=sqrt((2xx7.5xx10^(4))/(7.5xx10^(3)))=4.47 m`