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Auto manufactures study the collision of...

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 .

Text Solution

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At maximum compression, KE of car gets converted completely into PE of the spring.
`KE "of car" K=1/2mv^(2)" ""("v=36xx5/18=20m//s")"`
`=1/2xx1500xx10xx10`
`7.5xx10^(4)J`
At maximumcompression `x_(m)` PE,V of the spring =KE,K of car
`V=1/2kx_(m)^(2)`
`=7.5xx10^(4)J`
`x_(m)=sqrt((2xx75xx10^(4))/(7.5xx10^(3)))=4.47m`
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